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diff --git a/17571-h/17571-h.htm b/17571-h/17571-h.htm new file mode 100644 index 0000000..cc5bd07 --- /dev/null +++ b/17571-h/17571-h.htm @@ -0,0 +1,8308 @@ +<!DOCTYPE html + PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> + <head> + <meta http-equiv="content-type" content="text/html; charset=utf-8" /> + <title> + The Project Gutenberg eBook of Piano Tuning, by J. Cree + Fischer. + </title> + <style type="text/css"> + + p { margin-top: .75em; text-align: justify; margin-bottom: .75em; } + h1,h2,h3,h4,h5,h6 { text-align: center; clear: both; } + hr { width: 25%; margin-top: 2em; margin-bottom: 1em; margin-left: auto; margin-right: auto; + clear: both; + } + ul { list-style: none; } + table {margin-left: auto; margin-right: auto; font-size: small;} + body{margin-left: 10%; margin-right: 10%; } + .linenum {position: absolute; top: auto; left: 4%;} /* poetry number */ + .blockquot{margin-left: 5%; margin-right: 10%;} + .pagenum {position: absolute; left: 92%; font-size: smaller; text-align: right;} /* page numbers */ + .bb {border-bottom: solid 2px;} + .bl {border-left: solid 2px;} + .bt {border-top: solid 2px;} + .br {border-right: solid 2px;} + .break {margin-top: 1em;} + .bbox {border: solid 2px;} + .ctr {text-align: center;} + .center {text-align: center;} + .center table { margin: 0 auto; text-align: left; } + .smcap {font-variant: small-caps;} + .sf {font-size: small;} + .center img { margin-left: auto; margin-right: auto; } + img { + border: none; + padding: 6px; + } + p.caption {text-align: center; + margin-top: 0; + font-weight: bold; + font-variant: small-caps;} + .figcenter {margin: auto; text-align: center;} + .poem {margin-left:10%; margin-right:10%; text-align: left;} + .poem br {display: none;} + .poem .stanza {margin: 1em 0em 1em 0em;} + .poem span.i0 {display: block; margin-left: 0em; padding-left: 3em; text-indent: -3em;} + .poem span.i2 {display: block; margin-left: 2em; padding-left: 3em; text-indent: -3em;} + .poem span.i4 {display: block; margin-left: 4em; padding-left: 3em; text-indent: -3em;} + .ralign { position: absolute; right: 10%; top: auto;} + .footnotes { border: dashed 1px gray; background-color: #EEE; color: black; padding: 0 1em 1em 1em; } + .footnotes h3 { text-align:center; margin-top: 0.5em; font-weight:normal; font-size:90%;} + .footnote { font-size: .9em;} + .footnote .label { float:left; text-align:left; width:2em; } + .fnanchor { font-size: .8em; text-decoration: none; vertical-align: super;} + ins.corr { + text-decoration:none; + border-bottom: thin dotted gray; + } + + </style> + </head> + <body> + + +<pre> + +The Project Gutenberg EBook of Piano Tuning, by J. Cree Fischer + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Piano Tuning + A Simple and Accurate Method for Amateurs + +Author: J. Cree Fischer + +Release Date: January 22, 2006 [EBook #17571] + +Language: English + +Character set encoding: UTF-8 + +*** START OF THIS PROJECT GUTENBERG EBOOK PIANO TUNING *** + + + + +Produced by Mark C. Orton, L.N. Yaddanapudi and the Online +Distributed Proofreading Team at http://www.pgdp.net + + + + + + +</pre> + + <div class="center"> + <img src="images/imagetitle.png" width="117" height="100" + alt="" title="" /> + </div> + <h2> + J. CREE FISCHER + </h2> + <h1> + <span class="bb bt">PIANO TUNING</span> + </h1> + <h3> + A SIMPLE AND ACCURATE METHOD FOR AMATEURS + </h3> + <h4> + DOVER PUBLICATIONS, INC. NEW YORK + </h4> + <p> + Copyright © 1907 by Theo. Presser. + </p> + <p> + All rights reserved under Pan American and International + Copyright Conventions. + </p> + <p> + Published in Canada by General Publishing Company, Ltd., 30 + Lesmill Road, Don Mills, Toronto, Ontario. + </p> + <p> + Published in the United Kingdom by Constable and Company, + Ltd., 10 Orange Street, London WC 2. + </p> + <p> + This Dover edition, first published in 1975, is a + republication of the work originally published in + Philadelphia in 1907. The following sections have been + omitted from the present edition because they were + out-of-date: Practical Application of Piano Tuning as a + Profession, Business Hints, Ideas in Advertising, and + Charges for Services. This edition is reprinted by special + arrangement with Theodore Presser Company, Presser Place, + Bryn Mawr, Pennsylvania, publisher of the original edition. + </p> + <p> + <i>International Standard Book Number: 0-486-23267-0</i> + </p> + <p> + <i>Library of Congress Catalog Card Number: 75-14759</i> + </p> + <p> + Manufactured in the United States of America + </p> + <p> + Dover Publications, Inc. + </p> + <p> + 180 Varick Street + </p> + <p> + New York, N.Y. 10014 + </p> + <hr style="width: 65%;" /> + <p><span class='pagenum'><a name="Page_i" id="Page_i"></a>[Pg + i]</span></p> + <h2> + <a name="PREFACE" id="PREFACE"></a>PREFACE. + </h2> + <hr /> + <p> + For some years past a lack of competent men in the + profession of Piano Tuning has been generally acknowledged. + This may be accounted for as follows: The immense + popularity of the piano and the assiduous efforts of + factories and salesmen have led to the result that nearly + every well-to-do household is furnished with an instrument. + To supply this demand the annual production and sale for + the year 1906 is estimated at three hundred thousand pianos + in the United States. These pianos must be tuned many times + in the factory before they are shipped to the salesroom; + there they must be kept in tune until sold. When, finally, + they take up their permanent abode in the homes of the + purchasers, they should be given the attention of the tuner + at least twice a year. This means work for the tuner. But + this is not all. Presuming that the average life of the + piano is about fifty years, it is evident that there exists + in this country an accumulation of instruments <span + class='pagenum'><a name="Page_ii" id="Page_ii"></a>[Pg + ii]</span> variously estimated at from four to five + millions. This means <i>more work for tuners</i>. + </p> + <p> + While production and accumulation have been increasing, + there has been little, if any, effort made to provide + tuners to look after the needs of this ever-increasing + number of instruments, no provision for the thorough + instruction of the learner of Piano Tuning, outside the + walls of the factories, and of the few musical colleges + where the art is taught. Doubtless there are many persons + who are by nature well adapted to this agreeable and + profitable occupationpersons who would make earnest effort + to acquire the necessary skill and its honest application + if they had a favorable opportunity. Musical colleges in + which tuning is taught are few and far between; piano + factories are built for the purpose of producing pianos and + not tuners, for mechanics and laborers and not for teachers + and pupils; furthermore, very little fine tuning is done in + the factory; rough tuning is the bulk of the work there, + and a long apprenticeship in the factory, with its meager + advantages, is rarely sufficient to meet the demands of the + would-be-thorough tuner. This may account, in part, for the + fact that <span class='pagenum'><a name="Page_iii" + id="Page_iii"></a>[Pg iii]</span> many who are incompetent + are following this profession, and that there is an + increasing demand for tuners of skill. + </p> + <p> + In view of these facts the author came to the opinion that + if a course of instruction were prepared which would + demonstrate clearly the many abstruse details of the art in + an interesting and comprehensible way, it would be + appreciated by those who are desirous to learn. Acting upon + this impulse, he began the preparation of such a course. + </p> + <p> + The present book is the outgrowth of a course of + instruction, used successfully with pupils from various + parts of the United States and Canada, conducted partly by + correspondence; partly at the school directed by the + author. Although it has been necessary to revise the course + somewhat for publication in the present form, no essential + matter has been omitted and much has been added. + </p> + <p> + In preparing this course of study the utmost effort has + been made to present the various topics in the clearest, + most comprehensive manner, literary excellence being a + secondary consideration. + </p> + <p> + While the book is designed for self-instruction, the + systematic arrangement of the text, and the <span + class='pagenum'><a name="Page_iv" id="Page_iv"></a>[Pg + iv]</span> review questions with each lesson, suggest its + use as a text-book for schools and colleges which give + personal training in the care of the piano. + </p> + <p> + To the talented individual of either sex who is ambitious + to acquire a dignified and profitable profession, to the + scientifically-inclined musician who is eager to learn the + fundamental principles underlying all musical harmony, and + finally to the non-professional who loves to read because + of a fondness for science, the book is submitted; if it + should prove a boon to the former, a benefit to the second, + or a pleasure to the latter, I shall feel rewarded for the + work of its preparation. + </p> + <div class="smcap ralign"> + The Author. + </div> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_v" id="Page_v"></a>[Pg + v]</span> + </p> + <h2> + <a name="CONTENTS" id="CONTENTS"></a>CONTENTS. + </h2> + <hr /> + <p> + <a href="#PREFACE"><b>PREFACE.</b></a><span + class="ralign"><a href="#Page_i">i</a></span> + </p> + <p> + <a href="#CONTENTS"><b>CONTENTS.</b></a><span + class="ralign"><a href="#Page_v">v</a></span> + </p> + <p> + <a href="#LESSON_I"><b>LESSON I.</b></a><span + class="ralign"><a href="#Page_007">7</a></span> + </p> + <p class="blockquot"> + Introduction. + </p> + <p> + <a href="#LESSON_II"><b>LESSON II.</b></a><span + class="ralign"><a href="#Page_011">11</a></span> + </p> + <p class="blockquot"> + General Construction of the Piano and Something of its + Evolution and History. + </p> + <p> + <a href="#LESSON_III"><b>LESSON III.</b></a><span + class="ralign"><a href="#Page_020">20</a></span> + </p> + <p class="blockquot"> + Technical Names and Uses of the Parts of the Upright + Action. + </p> + <p> + <a href="#LESSON_IV"><b>LESSON IV.</b></a><span + class="ralign"><a href="#Page_032">32</a></span> + </p> + <p class="blockquot"> + Action of the Square Piano. Action of the Grand Piano. + Instructions for Removing the Square and Grand Piano + Actions. + </p> + <p> + <a href="#LESSON_V"><b>LESSON V.</b></a><span + class="ralign"><a href="#Page_043">43</a></span> + </p> + <p class="blockquot"> + Regulating and Repairing. Faults in Pianos aside from the + Action and their Remedies. Regulating and Repairing the + Upright Action. + </p> + <p> + <a href="#LESSON_VI"><b>LESSON VI.</b></a><span + class="ralign"><a href="#Page_056">56</a></span> + </p> + <p class="blockquot"> + Regulating and Repairing the Square Action. Miscellaneous + Repairs. + </p> + <p> + <a href="#LESSON_VII"><b>LESSON VII.</b></a><span + class="ralign"><a href="#Page_066">66</a></span> + </p> + <p class="blockquot"> + The Study and Practice of Piano Tuning. + </p> + <p> + <a href="#LESSON_VIII"><b>LESSON VIII.</b></a><span + class="ralign"><a href="#Page_072">72</a></span> + </p> + <p class="blockquot"> + The Temperament. Beats, Waves, Pulsations. The New System + of Temperament. The Octave. The Fifth. Pitch. Diagram of + the Fischer System of Temperament. + </p> + <p> + <a href="#LESSON_IX"><b>LESSON IX.</b></a><span + class="ralign"><a href="#Page_085">85</a></span> + </p> + <p class="blockquot"> + Specific Instructions in Setting Temperament. The + Continuous Mute. + </p> + <p> + <a href="#LESSON_X"><b>LESSON X.</b></a><span + class="ralign"><a href="#Page_097">97</a></span> + </p> + <p class="blockquot"> + Theory of the Temperament. Equal Temperament. Unequal + Temperament. + </p> + <p> + <a href="#LESSON_XI"><b>LESSON XI.</b></a><span + class="ralign"><a href="#Page_109">109</a></span> + </p> + <p class="blockquot"> + Technique or Modus Operandi in Piano Tuning. Manipulation + of the Tuning Hammer. Setting the Mutes or Wedges in the + Upright Piano. Setting the Mutes or Wedges in the Square + Piano. + </p> + <p> + <a href="#LESSON_XII"><b>LESSON XII.</b></a><span + class="ralign"><a href="#Page_126">126</a></span><span + class='pagenum'><a name="Page_vi" id="Page_vi"></a>[Pg + vi]</span> + </p> + <p class="blockquot"> + Mathematics of the Tempered Scale. Rationale of the + Temperament. Proposition I. + </p> + <p> + <a href="#LESSON_XIII"><b>LESSON XIII.</b></a><span + class="ralign"><a href="#Page_139">139</a></span> + </p> + <p class="blockquot"> + Rationale of the Temperament, Concluded. Proposition II. + Proposition III. Numerical Comparison of the Diatonic with + the Tempered Scale. Various Mathematical Tables and + Examples. + </p> + <p> + <a href="#LESSON_XIV"><b>LESSON XIV.</b></a><span + class="ralign"><a href="#Page_150">150</a></span> + </p> + <p class="blockquot"> + Miscellaneous Topics Pertaining to the Practical Work of + Tuning. Cause of the Beats. Finishing up the Temperament. + Tuning the Treble. Tuning the Bass. False Waves. + </p> + <p> + <a href="#LESSON_XV"><b>LESSON XV.</b></a><span + class="ralign"><a href="#Page_163">163</a></span> + </p> + <p class="blockquot"> + Miscellaneous Items Pertaining to the Practical Work of + Tuning, Regulating, and Repairing. Comparison of the + Different Systems of Temperament. System A. System B. + System C. Final Inspection. Loose Pins. Split Bridges. + Stringing. Wire Splicing. + </p> + <p> + <a href="#LESSON_XVI"><b>LESSON XVI.</b></a><span + class="ralign"><a href="#Page_178">178</a></span> + </p> + <p class="blockquot"> + Tuning and Repairing the Reed Organ. Cleaning. Stops. + Examination. Sticking Keys. Leaks. Pedal Defects. + Sympathetic Vibrations. Tuning. + </p> + <p> + <a href="#LESSON_XVII"><b>LESSON XVII.</b></a><span + class="ralign"><a href="#Page_193">193</a></span> + </p> + <p class="blockquot"> + Concluding Professional Hints. Peculiar Expressions Used in + Designating Qualities of Tone. Questions often Asked the + Piano Tuner. Seasons for Tuning. + </p> + <p> + <a href="#INDEX"><b>INDEX.</b></a><span class="ralign"><a + href="#Page_199">199</a></span> + </p> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_007" + id="Page_007"></a>[Pg 007]</span> + </p> + <h2> + <a name="LESSON_I" id="LESSON_I"></a>LESSON I. + </h2> + <hr style="width: 25%;" /> + <h3> + INTRODUCTION. + </h3> + <p> + Undoubtedly every human being is fitted for some sphere of + usefulnesssome industry by which he can benefit mankind and + support himself in comfort. Just what we are fitted for + must, almost invariably, be decided by ourselves; and the + sooner the better, else we may plod among the thousands + whose lives are miserable failures for the reason that + "they have missed their calling." + </p> + <p> + In the consideration of Piano Tuning as a profession, one + should first determine if he possesses the necessary + qualifications, the most important of which are a musical + ear and some degree of mechanical ability. Having these, + all else may be acquired by study. It is not necessary to + possess a musical education or to be a musician; although a + knowledge of music will be found a great aid. Still, an + elementary <span class='pagenum'><a name="Page_008" + id="Page_008"></a>[Pg 008]</span>knowledge of the + principles of music is a necessity to the student of this + course, as it has been found impossible to avoid the use of + a few technical terms. In most cases, however, they are set + forth in such a way that they will be readily apprehended + by anyone who has even a slight knowledge of the + fundamental principles of music. + </p> + <p> + In teaching Piano Tuning, it is the custom of the "Central + School of Piano Tuning," for which these lessons were + originally prepared, to have all students prepare two + lessons in harmony as a test of their acquaintance with the + intervals and chords used in tuning. The lessons are not + difficult, and they embody only those principles which are + essential to the proper understanding of the key-board: the + intervals of the diatonic scale and the major common chord + in the twelve different keys, C, D, E, F, G, A, B, B-flat, + D-flat, E-flat, G-flat, and A-flat. In connection with the + harmony lessons, we use as a text-book "Clarke's + Harmony,"<a id="fnanchor_A" name="fnanchor_A"></a><a + href="#fn_A" class="fnanchor">[A]</a> and the student is + required to master the first two chapters and prepare + manuscripts upon each of the lessons. Below is a number + <span class='pagenum'><a name="Page_009" + id="Page_009"></a>[Pg 009]</span>of the most important + questions selected from those lessons upon which + manuscripts have been written: + </p> + <div class="blockquot sf"> + <p> + 1. Every white key on the piano represents an "absolute + pitch." By what names are these pitches known? How are + the black keys named? + </p> + <p> + 2. How many tones constitute the diatonic scale? Give + numerical names. + </p> + <p> + 3. Intervals are measured by steps and half-steps. How + many steps from 1 to 3 in the diatonic scale? 1 to 4? 1 + to 5? 3 to 5? 5 to 8? 1 to 8? + </p> + <p> + 4. Why is there no black key between E and F, and between + B and C? + </p> + <p> + 5. From 1 to 3 is called an interval of a third; from 3 + to 5, also a third; from 1 to 5, a fifth: they are so + called because they include, respectively, three and five + members of the diatonic scale. What is the interval 3 to + 6? 2 to 5? 5 to 8? 2 to 6? 1 to 8? + </p> + <p> + 6. Thirds are of two kinds: major (larger) thirds embrace + two whole-steps; minor (smaller) thirds embrace a step + and a half. What kind of a third is 1-3 in the diatonic + scale? 2-4? 3-5? 6-8? + </p> + <p> + 7. What do we mean by the term, Fundamental of a chord? + What is added to it to complete the common chord? + </p> + <p> + 8. What absolute pitches comprise the common chord of C? + What kind of interval between the first two members? What + between the first and last? What between the second and + last? + </p> + <p> + 9. What tones would you use if told to strike the common + chord of C in four-part, close harmony, using the + fundamental for the highest tone? + </p> + <p> + 10. How many keys (white and black) are there between + <span class='pagenum'><a name="Page_010" + id="Page_010"></a>[Pg 010]</span>the fundamental and the + third? How many between the third and the fifth? How many + between the fundamental and the fifth when the fifth is + played above the fundamental? + </p> + <p> + 11. How many keys (white and black) are there between two + keys comprising a perfect fourth? + </p> + <p> + 12. (Most important of all.) What keys of the piano + keyboard comprise the common chord founded upon G as the + fundamental? Upon F? Upon F♯? Upon G♯? Upon + B♭? Upon D♭? Upon E♭? Upon D? Upon E? + Upon A? Upon B? + </p> + </div> + <p> + If one is able to answer these questions correctly he is + qualified to begin the study of Piano Tuning. + </p> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_011" + id="Page_011"></a>[Pg 011]</span> + </p> + <h2> + <a name="LESSON_II" id="LESSON_II"></a>LESSON II. + </h2> + <hr style="width: 25%;" /> + <h3> + GENERAL CONSTRUCTION OF THE PIANO; SOMETHING OF ITS + EVOLUTION AND HISTORY. + </h3> + <p> + The piano of today is, unquestionably, the most perfect, + and consequently the most popular and beloved of all + musical instruments. + </p> + <div class="poem"> + <div class="stanza"> + <span class="i0">That enchanting Queen of the home,<br /> + </span> <span class="i2">Whose place in the hearts of the + family<br /> + </span> <span class="i0">Is as dear as though it could + speak<br /> + </span> <span class="i2">In words of joy and + sorrow,<br /> + </span> <span class="i0">Sadness or consolation;<br /> + </span> <span class="i2">Soothing, animating, + enrapturing,<br /> + </span> <span class="i0">Charming away the soul<br /> + </span> <span class="i2">From its worldly weight of + cares,<br /> + </span> <span class="i0">And wafting it softly<br /> + </span> <span class="i2">Into the realm of celestial + dreams.<br /> + </span> + </div> + </div> + <p> + The untiring efforts of genius for over a century have + succeeded in producing a musical instrument that falls + little short of perfection. Yet other inventions and + improvements are sure to come, for we are never content + with "good enough." + </p> + <p> + <span class='pagenum'><a name="Page_012" + id="Page_012"></a>[Pg 012]</span> + </p> + <p> + The student of these lessons may, in his practice, discover + defective mechanical action and by his ingenuity be able to + improve it; he may likewise see where an improvement can be + made in acoustic construction; where a better scale can be + drawn; or where different and perhaps new materials may be + used for the component parts of the instrument. The + possibilities are numerous along these lines, and in + addition to bestowing a favor upon the general public, the + man who has the originality to produce something new, + places himself beyond want. + </p> + <p> + The inevitable inference is that the piano is an evolution + of the harp principle. This instrument was known centuries + previous to the Christian era. From the best history + obtainable, we learn that about three hundred years ago, + the first effort was made to interpose a mechanical + contrivance between the performer and the strings whereby + it would only be necessary to strike the keys to produce + tone from the strings, thereby decreasing the difficulty in + finding the strings and picking them with the fingers, and + greatly increasing the possibilities in musical rendition. + </p> + <p> + History gives credit to Italy for the first productions of + this kind, about 1600 A.D., when the faculty <span + class='pagenum'><a name="Page_013" id="Page_013"></a>[Pg + 013]</span>of music was beginning to manifest itself more + boldly. Scientists saw that wonderful developments were + possible, and we have reason to believe that experiments + were made in England, France, Germany and all civilized + countries about this time, for the production of the + instrument which we call, in this day, a Pianoforte. + (<i>Piano e forte</i>: soft and loud.) + </p> + <p> + At this time communication between the different countries + was, of course, slow and uncertain, and experiments of this + kind were probably unknown outside of the immediate + neighborhood in which they were tried; therefore, much + valuable and interesting history has not come to light. + However, from the specimens which we have had the pleasure + of seeing, and some of which we have had the opportunity to + work on, we infer that about the same line of difficulties + presented themselves to all of these early experimenters, + most of which were not efficiently overcome until in the + last century, and the most important of which it fell to + the lot of American inventors to overcome. + </p> + <p> + Some of these early instruments were not even provided with + dampers for stopping the tone when the key was released; + consequently, when a number of <span class='pagenum'><a + name="Page_014" id="Page_014"></a>[Pg 014]</span>keys were + struck in succession, the tone continued from all, so long + as the strings would vibrate. The strings and sound-board + being very light, the sustaining qualities were meager + compared to those of the modern piano; consequently the + dampers were not so much missed as they would be if removed + from a modern upright or grand, which would surely render + them unfit for use. + </p> + <p> + In the first attempts at piano building, the difficulties + to be overcome may be enumerated as follows: The frames + were not strong enough to resist the tension of the + strings; they were made almost entirely of wood which + yields to the pull of the strings and is subject to + climatic changes; the scale was very imperfect, that is, + the length, tension and weight of the strings were not + properly proportioned, the result being a different quality + of tone from different portions of the keyboard; the + actions were either heavy and imperfect, or too light to + produce sufficient vibration; the proper point upon the + strings for the hammers to strike and for the dampers to + bear had not yet been ascertained; the preparation and + seasoning of the wood for the different parts of the + instrument had not received sufficient attention. + </p> + <p> + <span class='pagenum'><a name="Page_015" + id="Page_015"></a>[Pg 015]</span> + </p> + <p> + One cannot conceive how difficult it is to produce + something that has never existed, until he tries. The + requirements necessary to such results as are obtainable + from the modern piano are numerous and rigid and the result + of many costly experiments. + </p> + <p> + Probably the most important essential in piano building is + the production of a frame of such strength and stability + that the enormous tension of the strings is completely + resisted in all parts of the scale. In many of the cheaper + pianos of this day, the lack of this essential manifests + itself in an annoying degree to the piano tuner. In tuning, + the workman "brings up" his temperament in the middle of + the instrument; in most cases the temperament stands all + right. He next tunes the treble, then the bass; after doing + his work perfectly he will often find that the treble fell + somewhat while he was bringing up the bass; or, in a few + cases, he may find that the treble sharpened, thus showing + that there was yielding of the frame. Of course, this + defect might be overcome by using an extremely heavy metal + plate and wooden frame; but the commercial side of the + question, in this day, calls for lightness in the + instrument as a check to the expense of production, and, + consequently, pianos that <span class='pagenum'><a + name="Page_016" id="Page_016"></a>[Pg 016]</span>are "made + to sell" are often much too light to fulfil this + requirement. + </p> + <p> + In the upright piano, the back frame of wood is first made; + at the top of this is the pin-block, sometimes called the + wrest-plank. This is composed of several layers of wood + firmly glued together with the grain running in different + directions to prevent splitting and warping. Into this + plank the tuning pins are driven. The sound-board is fitted + firmly into this frame of wood below the pin-block. + </p> + <p> + Next, the strong metal plate is secured to the frame by + large bolts and screws. Openings are left in the plate for + the bridges, which project from the sound-board beyond the + metal plate; also for the tuning pins, action bracket + bolts, etc. + </p> + <p> + At the lower end of the plate, and just below the + bridges,<a id="fnanchor_B" name="fnanchor_B"></a><a + href="#fn_B" class="fnanchor">[B]</a> the hitchpins are + driven firmly into holes drilled to receive them. Their + purpose is to support the lower ends of the strings. The + bass strings are separate, and each has a loop with which + to fasten it to the hitchpin. In the treble, one piece of + wire forms two strings; the two ends are secured to the + <span class='pagenum'><a name="Page_017" + id="Page_017"></a>[Pg 017]</span>tuning pins above, and the + string is simply brought around the hitchpin. The bridges + communicating with the sound-board are at the lower end of + the sound-board. Notice, there is a portion of the length + of each string between the bridge and the hitchpin. + </p> + <div class="center"> + <img src="images/image016.jpg" + alt="Piano frame" title="Piano frame" /> + </div> + <p> + At the upper end of the strings, a "bearing-bar," situated + between the tuning pins and upper bridge, is attached to + the pin-block by screws which draw it inward; its function + is to hold the strings firmly in position. You will notice + that the lengths of the strings, above the bearing-bar, + vary considerably, even in the three strings comprising the + unison. (We will speak of the effect of this in tuning, + farther on.) + </p> + <p> + After that portion of the case is completed which forms the + key-bed or action frame, we are ready to set in the + </p> + <p class="center smcap"> + Action + </p> + <p> + By this is meant the keys and all those intricate parts + which convey the motion of the key to the hammers which + strike the strings, and the dampers which mute them. + </p> + <p> + The requisites of the action are as follows: + </p> + <p> + The keys must descend quickly and easily at the touch of + the performer, giving quick response. + </p> + <p> + <span class='pagenum'><a name="Page_018" + id="Page_018"></a>[Pg 018]</span> + </p> + <p> + The weight of the hammer must be properly proportioned to + the strings it causes to vibrate. + </p> + <p> + The hammer must rebound after striking the string. (Where + the hammer remains against the string, thereby preventing + vibration, the term "blocking" is used to designate the + fault.) + </p> + <p> + The action must be capable of quick repetition; that is, + when a key is struck a number of times in quick succession, + it must respond perfectly every time. + </p> + <p> + After striking and rebounding from the string, the hammer + should not fall to its lowest position where it rests when + not in use, as this would prevent quick repetition. For + catching the hammer at a short distance from the string, a + felted piece of wood suspended on a wire, called the back + check, rises when the key is depressed, and returns when + the key is released, allowing the hammer to regain its + resting position. + </p> + <p> + A damper, for stopping the tone of the string when a key is + released, must leave the string just before the hammer + strikes, and return the instant the key is released. + </p> + <p> + A means must be provided for releasing all the dampers from + the strings at the will of the performer. <span + class='pagenum'><a name="Page_019" id="Page_019"></a>[Pg + 019]</span>The loud pedal, as it is called, but more + properly, the damper pedal, accomplishes this end by + raising the dampers from the strings. + </p> + <p> + In the square and the grand piano, the action is under the + sound-board, while the strings are over it; so the hammers + are made to strike through an opening in the sound-board. + In the upright, the strings are between the action and the + sound-board; so no opening is necessary in the latter. + </p> + <p> + The "trap-action" consists of the pedals and the parts + which convey motion to the action proper. + </p> + <div class="center"> + QUESTIONS ON LESSON II. + </div> + <ol> + <li> + What have been some of the salient obstacles necessary to + overcome in producing the perfected piano? + </li> + <li> + Of what use are the dampers? Explain their mechanical + action. + </li> + <li> + Mention several of the qualities necessary to a good + action. + </li> + <li> + Describe the building of an upright piano. + </li> + <li> + Contrast the musical capacity and peculiar + characteristics of the piano with those of the organ, + which has the same keyboard. + </li> + </ol> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_020" + id="Page_020"></a>[Pg 020]</span> + </p> + <h2> + <a name="LESSON_III" id="LESSON_III"></a>LESSON III. + </h2> + <hr style="width: 25%;" /> + <h3> + TECHNICAL NAMES AND USES OF THE PARTS OF THE UPRIGHT PIANO + ACTION. + </h3> + <p> + In the practice of piano tuning, the first thing is to + ascertain if the action is in first-class condition. The + tuner must be able to detect, locate and correct the + slightest defect in any portion of the instrument. Any + regulating or repairing of the action should be attended to + before tuning the instrument; the latter should be the + final operation. As a thorough knowledge of regulating and + repairing is practically indispensable to the professional + tuner, the author has spared neither means, labor nor + research to make this part of the lessons very complete, + and feels sure that it will meet with the hearty approval + of most, if not all, students. The piano tuner who knows + nothing of regulating and repairing will miss many an + opportunity to earn extra money. + </p> + <p> + The illustration accompanying this lesson is from a + Wessell, Nickel and Gross Upright action. This <span + class='pagenum'><a name="Page_021" id="Page_021"></a>[Pg + 021]</span>firm, whose product is considered the acme of + perfection, makes nothing but actions. Most manufacturers + of pianos, of the present day, build the wooden frame, the + sound-board and the case only; the action, metal plate, + strings, tuning-pins, etc., being purchased from different + firms who make a specialty of the manufacture of these + parts. A few concerns, however, make every piece that + enters into the composition of the instruments bearing + their names. + </p> + <div class="center"> + <a href="images/original020.jpg"><img + src="images/image020.jpg" + alt="Upright piano action" + title="Upright piano action" /></a> + </div> + <p> + <i>Ky</i>, is the Key in its resting position. + </p> + <p> + <i>c</i>, wherever found, represents a cushion of felt or + soft leather upon which the different parts of the action + rest or come in contact with each other. Their purpose, as + is readily seen, is that of rendering the action noiseless + and easy of operation. + </p> + <p> + <i>Bnc R</i>, shows the end of the balance rail, extending + the entire length of the keyboard. + </p> + <p> + <i>B P</i>, is the balance pin. This is a perfectly round + pin driven firmly in the balance rail. The bottom of the + hole in the key fits closely around the balance pin; at the + top, it is the shape of a mortise, parallel with the key, + which allows the <span class='pagenum'><a name="Page_022" + id="Page_022"></a>[Pg 022]</span>key to move only in the + direction intended. The mortise in the wooden cap on top of + the key at this point is lined with bushing cloth which + holds the key in position laterally, and prevents looseness + and rattling, yet allows the key to move easily. + </p> + <p> + <i>L</i>, is the lead put in this portion of the key to + balance it, and to insure uniformity of "touch," and quick + and certain return of key to its rest position. As there is + more or less difference in the length of keys, and also in + the weight of the hammers operated by them, some keys are + leaded much more heavily than others. In some cases the + lead is inserted in the extreme back end of the key; in + others it is put near the balance rail according to the + requirement. In some actions the lead is omitted entirely; + but in the best actions it is almost invariably present. In + the action of the grand piano the keys are leaded in front + of the balance rail instead of back of it. This is due to + the fact that in the grand piano the hammer rests in a + horizontal position and its whole weight must be actually + lifted and the force of gravity overcome, <span + class='pagenum'><a name="Page_023" id="Page_023"></a>[Pg + 023]</span>while in the upright, the hammer rests in a + vertical position, only requiring to be thrown forward. + </p> + <p> + <i>G P</i>, is the guide pin, generally of oval shape, with + the longest diameter in line with the key. The hole in the + lower portion of the key, in which the guide pin works, is + bushed with bushing cloth and is made to fit so closely + that the key will not move laterally, yet not so tightly + that the key will not work easily. + </p> + <p> + <i>Bm</i>, is a wooden block called the bottom; sometimes + called the key-rocker. It is held in position by the two + screws shown in cut by which it can be adjusted or + regulated. + </p> + <p> + <i>E</i>, is the extension communicating the motion of the + key to the upper part of the action. There are various ways + in which the extension is connected to the bottom. In this + action, the extension is made round at the lower end and + fits snugly into a hole in the bottom upon a felt disc. + When the action is taken out, the extensions simply lift + out of the holes, and when it is put back it is necessary + to enter each one in its place. In other actions, the upper + side of the <span class='pagenum'><a name="Page_024" + id="Page_024"></a>[Pg 024]</span>bottom where the extension + rests has no hole but simply a felt covering upon which the + extension rests; in this case it is necessary to provide + what is called an extension guide which is hinged to the + extension guide rail shown in the cut at the left of the + extension. In actions of this kind, the extensions remain + in place at all times and the trouble of placing them + properly on the bottom when replacing the action is + obviated. Other methods also are employed which are readily + understood upon slight examination, but are essentially + similar to the above. Instead of the bottom, a capstan + screw is used in some actions as follows: + </p> + <p> + <i>Cpn</i>, is a capstan screw used in some actions in + place of the bottom. It is turned by inserting a pointed + instrument in one of the four holes, thus raising or + lowering the capstan in regulating. The lower end of the + extension is felted. In such actions the extension is + invariably provided with the extension guide. + </p> + <p> + <i>B</i>, is the metal action bracket. The bracket is one + solid piece of metal. There are generally four brackets in + the upright action. The brackets <span class='pagenum'><a + name="Page_025" id="Page_025"></a>[Pg 025]</span>rest on + supports in and at the sides of the keybed, and are secured + at the top by large bolts, + </p> + <p> + <i>BB</i>, which go through the metal plate and into the + wooden frame or pin block. At the top of each bracket is an + opening to receive this bolt and a thumbscrew (not shown in + the cut, being behind the hammer) which fastens the action + securely in position. + </p> + <p> + <i>M R</i>, is the main rail; so called because the main + constituents of the action are attached to it. (Everything + designated as "rail" in the action runs the entire length + of the action in one solid piece.) + </p> + <p> + <i>W</i>, is the wippen. Those pieces upon which or by + which the small letter <i>g</i> is shown are the flanges. + The one at the left of the wippen is called the wippen + flange. It is made fast to the main rail by a screw, and + upon it the wippen is hinged by means of a "center-pin" at + the lower end. The center-pin in the wippen is driven + through a hole in which it fits tightly and immovably in + the middle part, and it (the center-pin) is consequently + stationary in the wippen. The flange extends down at the + <span class='pagenum'><a name="Page_026" + id="Page_026"></a>[Pg 026]</span>sides of the wippen and + the holes in flange are made large enough to receive + bushing cloth in which the center-pin works freely but not + loosely. All flange joints are of this nature; some, + however, are provided with a means for tightening the + center-pin in the middle portion of the joint. + </p> + <p> + <i>j</i>, is the jack. The purpose of the jack is to + communicate the motion of the wippen to the hammer. The + precise adjustment of the jack and the adjacent parts upon + which it depends for its exact movements, play an important + part in regulating the "touch" of the piano, and will be + fully entered into in following lessons. + </p> + <p> + <i>js</i>, jack spring. Its purpose is to hold the jack + inward against the "nose" or "heel" of the hammer butt. + (See <i>Bt</i>, hammer butt.) + </p> + <p> + <i>Rr</i>, regulating rail. The <i>regulating button</i> is + shown attached to the rail by the regulating screw which is + turned by means of its ring on top of <i>Rr</i>. The + purpose of the regulating button is to throw the point of + the jack out of the nose of the hammer butt, and allow the + hammer to rebound from the string. If the button is too + <span class='pagenum'><a name="Page_027" + id="Page_027"></a>[Pg 027]</span>high, it does not throw or + trip the jack in time to prevent blocking. When the button + is too low, it disengages too soon, and much of the force + of the key is lost before it reaches the hammer. + </p> + <p> + <i>BR</i>, is the block rail, felted on the side next to + the jack which strikes against it when thrown from nose. + This rail is absent in some actions, in which case the back + of the jack is felted and strikes against the "back catch," + which is also felted on inner side. (The back catch has no + mark in the cut, but is explained below in connection with + the "back check.") + </p> + <p> + <i>BC</i>, is the back check which is simply a piece of + wood with a thick piece of felt glued to the inner face and + suspended on a wire. + </p> + <p> + <i>BCW</i>, back check wire supporting the back check, and + screwed to the wippen. The purpose of the back check is to + check the hammer by coming in contact with the "back catch" + (the backward projection of the butt), at a short distance + from the string in its return, and prevent the hammer from + falling entirely back to its rest position, thereby + preventing quick repetition. + </p> + <p> + <span class='pagenum'><a name="Page_028" + id="Page_028"></a>[Pg 028]</span> + </p> + <p> + <i>Bl</i>, bridle. This is a piece of tape about an eighth + of an inch wide with a piece of leather glued to the end + and a hole near the end for the point of the "stirrup" or + bridle wire. The cut shows where the bridle is fastened in + the hammer butt by being put into the hole in the butt, and + the back catch stem covered with glue and driven in by it + which precludes all possibility of its coming loose. The + bridle passes through a hole in the lower part of the back + catch. Its purpose is to assist the hammer to return + quickly by hanging to it with the weight of the wippen, + extension, jack, etc., when the key is released. Thus the + bridle becomes the main factor in the matter of quick + repetition. + </p> + <p> + <i>Bl W</i>, bridle wire, screwed into wippen, bent in the + shape of a buckle at top to hold bridle. + </p> + <p> + <i>Bt</i>, butt; or, more specifically, hammer butt. In + some cheap actions the butt is joined to its flange + <i>g</i>, by the means described under the head of wippen + flange; but in this action the center-pin is held firmly in + the butt by a small strip of brass containing a set screw; + somewhat obscure in the cut, but discernible. As <span + class='pagenum'><a name="Page_029" id="Page_029"></a>[Pg + 029]</span>explained elsewhere, all center-pins turn in the + flange and not in the middle part. + </p> + <p> + <i>HS</i>, hammer shank in rest position. + </p> + <p> + <i>H</i>, hammer showing wood body or head, and covering of + two layers of felt. + </p> + <p> + <i>H R</i>, hammer rail, resting on felt cushion, <i>c</i>, + glued to rail or bracket. The hammer rail is held in + position by the rod, shown under the hammer shank, which is + hinged to the bracket at the lower end, and which allows it + to be moved forward when the soft pedal is used. The soft + pedal communicates with this rail by a rod which moves it + forward and thereby shortens the stroke of the hammers and + produces a softer tone. + </p> + <p> + <i>sr</i>, spring rail screwed to the brackets. This rail + supports the light wire springs which assist the hammers in + returning to rest position. + </p> + <p> + <i>S</i>, string. + </p> + <p> + <i>D</i>, is the damper head secured to the damper wire by + a set screw. + </p> + <p> + <i>DL</i>, damper lever, working in damper flange <i>g</i>, + which is screwed to main rail. + </p> + <p> + <i>s</i>, spoon; so called from its shape. It is screwed + into <span class='pagenum'><a name="Page_030" + id="Page_030"></a>[Pg 030]</span>the wippen. When the key + is struck, the motion on the wippen throws the spoon + forward, pushing the lower end of damper lever forward, and + releasing the damper from its contact with the string. The + damper is held against the string by the wire spring which + is seen running from the damper flange to the top of the + damper lever. + </p> + <p> + <i>DR</i>, damper rod. This is a rod running from the left + or bass end of the action to the right as far as the + dampers are continued in the treble. It is acted upon by + the "loud" or damper pedal, which raises the outer + projection, and by being hinged to the main rail about the + same height as this projection, the entire rod is thrown + outward against the lower ends of the damper levers, + releasing all the dampers simultaneously. This being the + only office of the right pedal, it is readily seen that + this pedal does not increase the loudness, but simply + <i>sustains</i> any number of tones struck successively, + giving the effect of more volume. + </p> + <p> + The student should familiarize himself with all technical + terms used in this lesson, as they will be <span + class='pagenum'><a name="Page_031" id="Page_031"></a>[Pg + 031]</span>referred to frequently in the succeeding lessons + on repairing and regulating. + </p> + <div class="center"> + QUESTIONS ON LESSON III. + </div> + <p> + Without reference to anything but the cut, give technical + names for parts of action represented by the following + letters or abbreviations: + </p> + <ol> + <li> + Bnc R, c, G P, BP, Ky, L. + </li> + <li> + Bm, Cpn, E, W, j, js, g, and M R. + </li> + <li> + Rr, B C, B R, B C W, Bl, and Bl W. + </li> + <li> + Bt, H, H S, H R, and sr. + </li> + <li> + S, D, D L, D R, s, B, and B B. + </li> + <li> + Explain the purpose and movements of the jack. + </li> + <li> + Describe a flange and the joint of same. + </li> + <li> + Give names of the four flanges shown in cut. + </li> + <li> + What is the purpose of the back catch and back check? + </li> + <li> + Explain the mechanical action of the damper pedal, and + its effect when used; also, that of the soft pedal. + </li> + </ol> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_032" + id="Page_032"></a>[Pg 032]</span> + </p> + <h2> + <a name="LESSON_IV" id="LESSON_IV"></a>LESSON IV. + </h2> + <hr style="width: 25%;" /> + <h3> + ACTION OF SQUARE AND GRAND PIANOS. + </h3> + <p class="center smcap"> + Action of the Square Piano. + </p> + <p> + Up to about the year 1870, the square was the popular + piano. The grand has always been too expensive for the + great music-loving masses, and previous to this time the + upright had not been developed sufficiently to assert + itself as a satisfactory instrument. The numerous + objections to the square piano forced its manufacture to be + discontinued a few years after the introduction of the + improved new upright. Square pianos that come, at the + present day, under the hand of the tuner, are usually at + least fifteen years old, and more frequently twenty or + more. However, in some localities the tuner will meet + numbers of these pianos and he will find them a great + source of revenue, as they are almost invariably in need of + repair. + </p> + <p> + Compare the three cuts of actions in the study of this + lesson. + </p> + <p> + The main constituent parts of the square action are similar + in appearance to those of the upright; in <span + class='pagenum'><a name="Page_033" id="Page_033"></a>[Pg + 033]</span>fact, most of the parts are the same in name and + office. However, the parts are necessarily assembled very + differently. In the square action, the hammers strike in a + vertical direction, while in the upright they strike in a + horizontal direction; the motion of the key being the same + in both. + </p> + <p> + Of the three types, the square is the simplest action, as + many of the parts seen in the upright and grand are + entirely absent in the square. + </p> + <p> + Beginning with the key, it has its balance pin, guide pin, + cushions, etc., practically the same as in the other types. + </p> + <p> + The bottom, or key rocker, is reversed in the square; the + end transmitting the motion being nearest the performer. + </p> + <p> + The extension and wippen are absent in the square, as the + jack is attached directly to the bottom or key-rocker. + </p> + <p> + The back check is screwed to the key, and as the hammer + head rests against it after striking, the use of the + contrivance called the back catch in the upright is + unnecessary. + </p> + <p> + <span class='pagenum'><a name="Page_034" + id="Page_034"></a>[Pg 034]</span> + </p> + <div class="center"> + <a href="images/original035.jpg"><img + src="images/image035.png" + alt="Action of the Square Piano." + title="Action of the Square Piano." /></a> <p + class="caption">Action of the Square Piano.</p> + </div> + <div class="bb bt sf"> + <p class="center smcap"> + Action of the Square Piano. + </p> + <p> + A. Action Frame.<br /> + B's Indicate the Cushions, or Bushing, of felt, cloth or + leather.<br /> + C. Balance Rail.<br /> + D. Balance Pin. Round.<br /> + E. Mortised Cap for Balance Pin. Bushed.<br /> + F. Key.<br /> + G. Lead.<br /> + H. Back Check.<br /> + I. Bottom or Key Rocker.<br /> + J. Bottom Screws; used to regulate height of Jack.<br /> + K. Jack.<br /> + L. Jack Spring; concealed under Bottom.<br /> + M. Center Pin to Jack.<br /> + N. Hammer Rail.<br /> + O. Regulating Screw.<br /> + P. Regulating Button.<br /> + Q. Flange Rail.<br /> + R. Flange. Split.<br /> + S. Flange Rail Screw.<br /> + T. Flange Screw, to regulate jaws of flange.<br /> + U. Hammer Butt.<br /> + V. Center Pin.<br /> + W. Hammer Stem or Shank.<br /> + X. Hammer Head.<br /> + Y. Hammer Felt. Treble hammers sometimes capped with + buckskin in old instruments.<br /> + </p> + <p class="center smcap"> + Top Action of Square Piano. + </p> + <p> + 1. Damper Lifter Wire.<br /> + 2. Damper Lifter Buttons.<br /> + 3. Damper Felt.<br /> + 4. Damper Head.<br /> + 5. Damper Lever.<br /> + 6. Damper Leads.<br /> + 7. Shade, supported by wire stanchions, on top of which + are screwed shade buttons.<br /> + 8. Damper Rail. Tilted by Loud Pedal Rod which raises + all the dampers simultaneously.<br /> + 9. Damper Flange.<br /> + 10. Flange Screw.<br /> + 11. Damper Lever Center Pin.<br /> + </p> + <p class="center smcap"> + The Trap Action + </p> + <p> + consists of Pedals, Pedal Braces, Pedal Feet, Pedal Rods, + Roller Boards or Elbows, Studs, Plugs, Trap Springs, + Wires and Lifter Rods. + </p> + <p> + The cut is from the French action. Nearly all square + pianos in use at the present time are of this type. + </p> + </div> + <p> + <span class='pagenum'><a name="Page_035" + id="Page_035"></a>[Pg 035]</span><span class='pagenum'><a + name="Page_036" id="Page_036"></a>[Pg 036]</span>The hammer + rail in the square, in addition to serving its purpose as a + rest for the hammers, also serves the purpose of the + regulating rail, as you will see the regulating screw, with + its button, attached to it. This rail is stationary in the + square, not moving toward the strings and shortening the + stroke as it does in the upright when the soft pedal is + used. The soft pedal in the square piano simply interposes + a piece of felt between each hammer and its corresponding + string or strings. This felt being much softer than that of + the hammers, the tone is greatly subdued. + </p> + <p> + The mechanical arrangement of the dampers is very different + in the square from that in the upright. The dampers are + above the strings. Instead of springs to hold them against + the strings, they simply rest upon them with their weight. + In many old squares some of the dampers fall upon nodal + points, causing defective damping or harmonic after-tones. + </p> + <p> + The stationary parts of the square action are: action + frame, to which is secured the balance rail, balance pins + and guide pins, hammer rail, flange rail, and damper rail. + When the key is struck, the parts that move upward are: the + back end of the key, bottom, jack, hammer, back check, + damper wire and damper lever. The hammer falls back upon + the back check immediately after striking, and remains + <span class='pagenum'><a name="Page_037" + id="Page_037"></a>[Pg 037]</span>there until the key is + released, when all movable parts fall to rest position. + </p> + <p> + The action of the jack is the same in all types. + </p> + <p class="center smcap"> + Action of the Grand Piano. + </p> + <p> + After thoroughly going over the details of the action of + the square and upright pianos, there remains very little to + describe in the action of the grand. + </p> + <p> + The grand action partakes of the characteristics of both + the upright and the square, and is somewhat more + complicated than either. + </p> + <p> + The bottom and extension are almost identical with those of + the upright; the extension, however, is necessarily very + short. + </p> + <p> + The wippen is of different construction, and somewhat more + complicated in the grand. + </p> + <p> + The flange rail in the grand is made also to serve the + purpose of regulating rail, as the hammer rail is made to + do in the square. + </p> + <p> + The back check is identical with that of the square. + </p> + <p> + The dampers are the same in their working principles as + those of the square, but are generally different in + construction; yet, some squares have the same arrangement + of dampers as those shown in the cut of the grand action. + </p> + <p> + <span class='pagenum'><a name="Page_038" + id="Page_038"></a>[Pg 038]</span> + </p> + <p> + The soft pedal of the grand shifts the entire action to the + right so that the hammers strike only two and in some cases + only one of the strings. + </p> + <p> + The student should study the three types of actions from + the actions themselves, if possible. + </p> + <p> + <span class='pagenum'><a name="Page_039" + id="Page_039"></a>[Pg 039]</span> + </p> + <div class="center"> + <a href="images/original039.jpg"><img + src="images/image039.png" + alt="Action of the Grand Piano." + title="Action of the Grand Piano." /></a> + <p class="caption">Action of the Grand Piano.</p> + </div> + <div class="bb bt sf"> + <p class="center smcap"> + Action of the Grand Piano. + </p> + <p> + 1. Indicates the felt, cloth or leather, upon which the + various parts of the action rest, or fall + noiselessly.<br /> + 2. Key.<br /> + 3. Bottom; sometimes called Key Rocker.<br /> + 4. Extension; split at lower end to receive center pin + in Bottom.<br /> + 5. Wippen Support.<br /> + 6. Jack.<br /> + 7. Jack Spring.<br /> + 8. Flange and Regulating Rail.<br /> + 9. Regulating Screw, Button and Cushion.<br /> + 10. Escapement Lever.<br /> + 11. Regulating Screw in Hammer Flange, for Escapement + Lever.<br /> + 12. Check Wire, for Escapement Lever.<br /> + 13. Screw to regulate fall of Escapement Lever.<br /> + 14. Lever Flange, screwed to Flange Rail.<br /> + 15. Hammer Shank.<br /> + 16. Hammer.<br /> + 17. Back Check.<br /> + 18. Damper Lever, leaded.<br /> + 19. Damper Wire, screwed into upright.<br /> + 20. Damper Wire Guide, fastened to Sound-Board.<br /> + 21. Damper Head and Felt.<br /> + 0. Center Pins. Holes lined with Bushing Cloth.<br /> + </p> + </div> + <p> + <span class='pagenum'><a name="Page_040" + id="Page_040"></a>[Pg 040]</span> + </p> + <p class="center smcap"> + Instructions for Removing the Square and Grand Actions. + </p> + <p> + First, feel or look underneath the keyboard and see if + there are screws that go up into the action. In most of the + better grade instruments the action is fastened in this + way. If the screws have square heads, your tuning hammer + will fit them and bring them out; if common screws, a + screw-driver will suffice. Look through the opening in the + sound board where the hammers strike and see that they are + all down before pulling out the action, lest they break off + by catching on the under side of the sound board. This is + almost sure to happen if actions are out of order. + </p> + <p> + In most square pianos, the narrow board just below the keys + can be removed by being raised straight up, as it simply + sets over screw heads in the key frame. When this strip is + removed, a wire handle will be found in the middle of the + key frame by which to draw out the action. In some cases, + and especially in grands, this strip is secured by screws + found underneath the piano. In other pianos, the action is + held by screws in front of the key frame, which will be + revealed by the removal of the front strip, above referred + to. + </p> + <p> + Be especially careful in placing the action back into the + piano. As a rule, it is safe to keep the right (long) end + of the square action bearing against the right side of + entrance, being sure that one end of action does not get + ahead, which might cause some <span class='pagenum'><a + name="Page_041" id="Page_041"></a>[Pg 041]</span>of the + hammers to strike the props for which the openings are left + in the back extremities of action. + </p> + <p> + While the action is out, study carefully the purpose of + every part and its movements, referring to this and the + previous lesson until you have thoroughly mastered the + entire mechanism. Do not rest until you can name correctly + everything you see and know its use so well that you could + explain it satisfactorily to an inquirer. Sometimes the + tuner is asked a great many perplexing questions and is + expected to respond intelligently. + </p> + <p> + We have dealt with the three types of actions that are most + commonly found in the three types of pianos. The student + must bear in mind that there are numerous manufacturers of + actions, and that each has his peculiar method of + constructing his special action to bring about the desired + results, which are practically the same in all cases; and + consequently, while a variety of construction will confront + the beginner in piano regulating and repairing, he will + understand the construction and requirements of any action + that may demand his skill from the foregoing instruction, + if properly mastered. In this, as in all other mechanical + professions, one's inventive genius must often be <span + class='pagenum'><a name="Page_042" id="Page_042"></a>[Pg + 042]</span>summoned to assist in surmounting obstacles + which are sure to arise unexpectedly. + </p> + <p class="center"> + QUESTIONS ON LESSON IV. + </p> + <ol> + <li> + From a philosophical point of view, which do you consider + the easiest and most perfect of the three types of + actions? Also give reasons. + </li> + <li> + Considering the wippen and its attachments as one part, + how many parts move when a key is struck in the upright + piano? How many in the square? + </li> + <li> + Name the parts found in the upright action that are + absent in the square. + </li> + <li> + Describe the three methods by which soft tone is obtained + from use of soft pedal in the three types of actions. + </li> + <li> + What rail serves two purposes in the square action, and + what are they? What rail serves two purposes in the grand + action, and what are they? + </li> + </ol> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_043" + id="Page_043"></a>[Pg 043]</span> + </p> + <h2> + <a name="LESSON_V" id="LESSON_V"></a>LESSON V. + </h2> + <hr style="width: 25%;" /> + <h3> + REGULATING AND REPAIRING. + </h3> + <p class="center smcap"> + Faults in Pianos, aside from the Action, and their + Remedies. + </p> + <p> + One of the most common, and, at the same time, most + annoying conditions both to the owner of the piano and the + tuner, is the "sympathetic rattle." This trouble is most + usual in the square and the grand pianos and is generally + due to some loose substance lying on the sound board. The + rattle will be apparent only when certain keys are struck, + other tones being perfectly free from it. These tones cause + the sound board to vibrate in sympathy, so to speak, with + the weight of the intruding substance at the point where it + lies, and if it be moved the distance of six inches it will + sometimes cease to respond to these particular tones, but + may respond to others, or cease to cause any trouble. + </p> + <p> + The article may generally be found near the front of the + sound board under the top piece of the <span + class='pagenum'><a name="Page_044" id="Page_044"></a>[Pg + 044]</span>case, this being the place where it would most + likely fall. No special instrument is made for the purpose + of searching for such objects, but one can be easily + devised with which the tuner can feel all over the sound + board, and remove such articles as well as dust and dirt. + Secure a piece of rattan or good pliable hickory, and draw + it down to the width of half an inch, thin enough to bend + easily, and long enough to reach anywhere under the + stringing or metal plate. By putting a cloth over this + stick you can remove anything that comes in its way. Some + difficulty will be found, however, in getting under the + plate in some pianos. In case you cannot procure a suitable + piece of wood, a piece of clock spring will be found to + answer very well. We have taken from pianos such articles + as pencils, pieces of candy, dolls, pointers used by music + teachers, tacks, nails, pennies, buttons, pieces of broken + lamp chimneys, etc., etc., any one of which is sufficient + to render the piano unfit for use. The sound board of the + upright being vertical prevents its being subject to the + above difficulty. + </p> + <p> + A split in the sound board, in any style of piano, + sometimes causes trouble due to the vibrating edges <span + class='pagenum'><a name="Page_045" id="Page_045"></a>[Pg + 045]</span>of the board coming in contact with each other. + Insert the point of your screwdriver in the crack, holding + it there firmly; if the rattling stops, the difficulty is + discovered, and may be remedied by placing a screw or wedge + in the crack, or a wedge of wood, cork or rubber between + the sound board and iron plate or casing, if the location + of the trouble permits. While this method seems a + perfunctory one, it is nevertheless the best the tuner is + prepared to do, for it is next to impossible to glue a + crack in the sound board successfully outside of a regular + factory or repair shop, where the instrument may be taken + all apart and a new sound board put in or the old one + properly repaired. + </p> + <p> + Sometimes the sound board gets loose or unglued at the + edges, or the bridges or ribs come loose. Any part of the + piano where there is vibration or loose material may become + the source of the sympathetic rattle, as even parts of the + case vibrate with the tones struck; so you must examine the + panels, lock, hinges, soft pedal bar (in square), in fact + all parts of the case and woodwork for the location of the + trouble. Once found, the remedy will suggest itself. The + greatest difficulty is to locate the cause. Very <span + class='pagenum'><a name="Page_046" id="Page_046"></a>[Pg + 046]</span>frequently this will be found entirely outside + of the piano; a loose window glass, picture glass, lamp or + other article of furniture in the room may respond to a + particular tone or its octave. We have never found the + sympathetic rattle in the action; it has rattles, but not + of this character. Any other defect which may be found + under this head will only require the exercise of a little + mechanical ingenuity to suggest a remedy. + </p> + <p class="center"> + <span class="smcap">Regulating and Repairing the Upright + Action.</span><br /> + <span class="sf">(Use cut of upright action for reference + in following study.)</span> + </p> + <p> + We will begin with the key and take up each part of the + action in the succession in which motion is transmitted. + </p> + <p> + 1. <i>Key</i>. Keys stick; that is, after being struck, + they fail to come up quickly, if at all. First ascertain if + the trouble is really in the key, or in the upper part of + the action. To do this, lift the extension or wippen until + the upper part of the action is entirely free from the key, + so that you may test the key independently. Some keys are + leaded so that they will fall in front of the balance rail, + others so that they will fall back of it; in either case, + lift the low end and let go, to see if it will fall by its + own weight. If <span class='pagenum'><a name="Page_047" + id="Page_047"></a>[Pg 047]</span>it seems quite free, you + may know the trouble is not in the key; you will also find + that when you release the extension or wippen, it will not + fall readily, showing that the trouble lies in the upper + part. + </p> + <p> + If the trouble is found in the key, examine the guide pin. + See if it is placed in a direct line with the key. If so, + and it still binds, enlarge the hole by pressing the wood + back slightly with some wedge-shaped instrument, if you + have not a pair of the key pliers which are used for this + purpose. See that the cloth, with which the hole is bushed, + is not loose and wrinkled. Do not oil or grease the guide + pin unless such treatment has been previously resorted to, + as the polished pin will work more freely in the dry cloth. + Do not pinch hard on the pin with rough pliers and spoil + the polished surface. + </p> + <p> + Sometimes you will find one key warped so that it rubs on + the next, in which case, plane off a slight shaving to free + it. Sometimes changing the position of the guide pin will + straighten or level the key and make it work all right. + </p> + <p> + The balance pin is subject to some of the same difficulties + as the guide pin. See that it sets properly and is not + bound by the mortise. + </p> + <p> + <span class='pagenum'><a name="Page_048" + id="Page_048"></a>[Pg 048]</span> + </p> + <p> + Sometimes a splinter will be found on one side of a key + where the lead has been put in. A piece of any foreign + material between two keys generally causes both to stick. + </p> + <p> + Where the action is too deep, that is, the keys go down + farther than they ought, place cardboard washers under the + felt ones around the guide pin, or raise the felt strip + under back end of keys. + </p> + <p> + Where the action is too shallow, place thin washers under + those around the balance pin. When this is done, the whole + action must be regulated accordingly, as this alteration + will make a change in the working of the upper part of the + action. + </p> + <p> + 2. <i>The Bottom or Capstan</i>. This should be so adjusted + that when the key falls back to its rest position, the + point of the jack will just spring into its place in the + nose of the hammer butt. If held too high, the jack fails + to catch in the nose, and the key may be struck without + producing any effect on the hammer. When the bottom or + capstan is too low, the point of the jack will be some + distance below the notch, which will cause what is known as + lost motion, it being necessary to depress the key a + portion of its depth before the jack can act upon the <span + class='pagenum'><a name="Page_049" id="Page_049"></a>[Pg + 049]</span>hammer. Depress the key slowly, watching the + hammer, and the fault will be discovered. + </p> + <p> + After a piano has been used for some time, the keys that + are struck most frequently (those in the middle of the + instrument) will be found to have this fault. The felts + under the keys and those which are between the working + parts of the action become compressed or worn so that the + jack will be found to set so low that there will be lost + motion in the key. In this case, loosen one of the screws + in the bottom and turn the other down so as to move the + jack upward until nearly all lost motion is taken up. A + little play is generally necessary, but very little. In + case the action has a capstan, simply turn it upward. + </p> + <p> + 3. <i>Back Check</i>. Blocking is most usually caused by + the back check being too near the back catch, so that when + the key is struck, the back check holds the hammer against + the string. This should be seen after raising the bottom or + capstan as above referred to. It will be observed that when + this is done on account of the wear of the felts, the back + check will stand much nearer the back catch than it did + before, and will need bending back so as to give the hammer + plenty of "rebound." A steel instrument with <span + class='pagenum'><a name="Page_050" id="Page_050"></a>[Pg + 050]</span>properly shaped notches at the point, called a + regulator, is used for bending wires in regulating the + action. See that the wires stand as nearly in line as is + possible. In old actions that are considerably worn, + however, you will be obliged to alter some more than + others. + </p> + <p> + 4. <i>Bridle and Bridle Wire</i>. In putting in a new + bridle, it should be doubled over at the end and secured to + the hammer butt by a small tack. Be sure you get it exactly + the same length as the others; otherwise it will be + necessary to bend the bridle wire out of line. Some tuners + glue the bridle around the back catch stem, but the above + method is preferable. + </p> + <p> + The purpose of the bridle is to jerk the hammer back + quickly and the wire must be set, neither so far back as to + check the stroke of the hammer, nor so far forward that the + bridle is too slack to draw upon the hammer. + </p> + <p> + 5. <i>Jack</i>. The jack itself seldom gets out of order. + So long as its flange does not come unglued in the wippen, + or its spring get out of place or broken, or get tight in + its joint, it will need nothing. Its adjustment and action + is controlled by the bottom or capstan, and the regulating + button. + </p> + <p> + <span class='pagenum'><a name="Page_051" + id="Page_051"></a>[Pg 051]</span> + </p> + <p> + 6. <i>Regulating Button</i>. This button determines the + point in the stroke of the hammer where the jack flies off + from the nose of the butt. If the button is too high, the + jack does not fly off soon enough, and the result is, that + the hammer either blocks against the string or bounces from + the jack after the stroke has been made, striking the + string a second or third time from one stroke of the key. + The felt punching on the lower side of the button often + wears until this trouble prevails. Lower the button by + turning down the screw on top of the regulator rail; if + lowered too far, however, the action is weakened by causing + the jack to fly off too soon, without giving the hammer a + sufficient impulse. A regulating screwdriver is used for + this, but in its absence, a wire hook, similar to a shoe + buttoner, will turn the screw. + </p> + <p> + The block rail is properly adjusted at the factory and + requires no attention. + </p> + <p> + 7. <i>Hammer Butt</i>. The felts and leather on the heel of + the hammer butt wear out and must be replaced. The felt + cushion, that is lowest and farthest to the left (see + illustration), is the one that wears out first. The jack, + in returning to the notch, strikes <span class='pagenum'><a + name="Page_052" id="Page_052"></a>[Pg 052]</span>this + cushion, and in time wears it away so that the jack in + returning strikes the wood of the hammer butt, producing a + sharp click, which is very annoying, to say the least. This + click is heard at the instant the key rises to its rest + position. Sometimes, however, a similar click is produced + by the top of the key striking the board which is set over + the keys, due to the cloth being eaten off by moths, or a + pencil or some other article lying on the keys back of this + board. + </p> + <p> + The center pin in the butt of some cheap actions is not + held in the butt by metal clip and screw, and if it gets + loose so that it works out, must be replaced by a larger + pin. The size of center pins generally used in the factory, + is .050 of an inch in diameter; the size for repairing + should be .053. All of the best actions have the set screw + with which to make the pin fast in the butt. + </p> + <p> + Hammers stick when the center pin is too tight in the + flange. The bushing in the flange often expands. Some + tuners oil at the ends of the pin with kerosene or wet it + with alcohol, which is very good; but a better plan is to + shrink the bushing with a drop of water on each side so + that it will penetrate the bushing. After this is done, the + piano cannot be <span class='pagenum'><a name="Page_053" + id="Page_053"></a>[Pg 053]</span>used for a day or two, as + the water first swells the bushing, making all the hammers + stick; but when they are dry again, they will be found + free. This may seem a curious method, but you need not be + afraid of it; it is the most effective. + </p> + <p> + Before leaving the hammer butt, see that the hammer spring + is in its place. + </p> + <p> + 8. <i>Hammer Stem</i>. These sometimes warp, split, crack, + or come unglued at the butt or hammer. If twisted so far + that it does not strike properly on the strings, or that it + binds against the next hammer, the best thing is to put in + a new stem. If merely split or unglued, it may be repaired. + Sometimes a click is heard and it will seem impossible to + find the cause, the hammer and stem apparently perfect, but + a close examination will reveal a looseness in the stem + somewhere. + </p> + <p> + In putting in a new shank, drill or chip out the old one, + scrape the holes out clean, take your measure carefully, + and do not make the new shank too tight, but large enough + to fill the hole snugly. Apply glue to the ends of the + shank and also in the holes. Cedar is used in some makes, + but good maple is stronger, and is more generally used. + </p> + <p> + <span class='pagenum'><a name="Page_054" + id="Page_054"></a>[Pg 054]</span> + </p> + <p> + 9. <i>Hammers</i>. When too hard, soften with a felt pick. + Do not raise the felt up, but stick the pick in the felt + just back of the point and this will loosen it up and make + it softer and more elastic. Where the strings have worn + deep grooves, sandpaper them down nearly even and soften + the felt as above. + </p> + <p> + In regluing the felt to the head, glue only the back ends + of the felt, and clamp with strong rubber band till the + glue sets. Use tailor's chalk (fuller's earth) to clean + hammer felts. To harden or draw felts back in shape, place + a damp cloth over them, and then pass a hot iron over it. + </p> + <p> + 10. <i>Dampers</i>. Damper felt often gets hardened so that + when it comes against the vibrating string, it causes a + sort of buzzing sound. Loosen it up with the pick. + Imperfect damping can sometimes be corrected in the same + way. + </p> + <p> + The damper head sometimes turns round on its wire, leaving + one or two strings undamped. Tighten the set screw. See + that the dampers are in line; and that they will stop the + tone properly when the key is released. + </p> + <p> + Damper springs sometimes break. It is necessary to take out + the damper lever to put in a new one. + </p> + <p> + <span class='pagenum'><a name="Page_055" + id="Page_055"></a>[Pg 055]</span> + </p> + <p> + See that the spoons are in line and work properly. Press + the sustaining pedal down, and see if all the dampers are + in line; if not, bend the damper wires with the regulator + until they line up perfectly. + </p> + <p> + 11. <i>Damper Rod</i>. When the sustaining pedal squeaks, + look first to the pedal, then to the wooden rods leading up + to the damper rod. If the trouble is found in any of these, + or the springs, use sperm oil or vaseline. + </p> + <p> + Catch hold of the damper rod at the left behind the action + and work it. If it squeaks, you will have to take out the + action and oil the swings where they are hinged to the main + rail. + </p> + <p class="center"> + QUESTIONS ON LESSON V. + </p> + <ol> + <li> + If you should find a key sticking, how would you + determine the cause? + </li> + <li> + Name all the defects to which the key is subject. + </li> + <li> + Describe the proper adjustment of bottom or capstan. + </li> + <li> + Give two causes of blocking. + </li> + <li> + Give the purpose of the regulating button, and its proper + adjustment. + </li> + </ol> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_056" + id="Page_056"></a>[Pg 056]</span> + </p> + <h2> + <a name="LESSON_VI" id="LESSON_VI"></a>LESSON VI. + </h2> + <hr style="width: 25%;" /> + <h3> + REGULATING AND REPAIRING.(Continued.) + </h3> + <p class="center smcap"> + The Square Action. + </p> + <p> + 1. <i>The key</i> in the square piano is subject to the + same troubles as that of the upright, and requires the same + treatment. However, the keys being much longer are more + liable to cause trouble by warping. + </p> + <p> + 2. <i>Bottom or Key Rocker</i>. Unlike in the upright + action, the jack is attached directly to the bottom; but, + lowering or raising the bottom has the same effect in both + cases. The screws regulating the height of the jack can be + gotten at with a proper screwdriver. If you have to take + out the key in order to regulate the bottom, first take + particular notice of the conditions in respect to the + operation of the jack on the hammer. Work the key slowly, + to discover if there is lost motion. Decide which way the + bottom must go and how far, so that you will not have to + remove and replace the key more than once <span + class='pagenum'><a name="Page_057" id="Page_057"></a>[Pg + 057]</span>or twice to adjust it. In taking out the key, + remove the board which is set edgewise over the keys + immediately back of where the fingers strike, by taking out + the screw at each end. Lift the hammer with the finger + until the jack falls out of place; then by lifting the key + off the balance pin it can be drawn out. The back check + will sometimes rub so hard against the regulating button + that it will be bent somewhat, and must be adjusted after + the key is replaced. + </p> + <p> + The bottom is often found to have shrunken; it rattles at + every stroke of the key. This can generally be stopped by + simply turning the back screw down until tight, which can + be done without taking the key out. This will rarely be + found to alter the jack enough to cause it to fail to + return to the notch in the butt. After doing this, however, + it is well to examine for such a condition. + </p> + <p> + A sluggish motion of the jack is often found in old square + pianos caused by the swelling of the wood, at the point + where the jack is hinged to the bottom, or by the center + pin's becoming foul from oxide. This will cause the jack to + fail at times to operate on the hammer, especially in quick + repetition. The <span class='pagenum'><a name="Page_058" + id="Page_058"></a>[Pg 058]</span>key is struck with no + response. Take out the bottom entirely, and with the + fingers press the sides of the bottom inward; at the same + time, work the jack back and forth. This will generally + free it if the jack-spring is all right. + </p> + <p> + 3. <i>Jack</i>. As in the upright, the behavior of the jack + depends entirely upon the surrounding members. A very + common occurrence in the square piano is a broken + jack-spring. This spring is concealed in a groove on the + under side of the bottom, with a linen thread leading + around the end of the jack and held fast by a wooden plug. + If the spring is found to be long enough, drive out the + plug, attach a new thread to the spring, and fasten as + before. If a new spring is needed, one may be made by + wrapping some small wire round a piece of music wire of the + right size. + </p> + <p> + 4. <i>The back check, hammer stem and regulating button</i> + are subject to the same faults as their counterparts in the + upright, which may be remedied in the same way. Bridles and + hammer springs are not needed in the square, as the weight + of the hammer, moving in a vertical direction, is + sufficient to bring it to its rest position. + </p> + <p> + <span class='pagenum'><a name="Page_059" + id="Page_059"></a>[Pg 059]</span> + </p> + <p> + 5. <i>Hammers</i>, when made of felt, will of course + require the same treatment as those in the upright. In many + old squares the hammers are built up of buckskin. If this + becomes beaten down hard, it is well to cap the hammer with + a new soft piece of buckskin, gluing only at the back ends. + </p> + <p> + 6. <i>Butts and Flanges</i>. A click just as the key comes + up, indicates that the felt cushion, against which the jack + rests, is worn out and must be replaced. + </p> + <p> + In all square actions the center pin, in the butt, is held + by friction alone, but rarely gets loose; if it should be + found loose, put in a larger pin. + </p> + <p> + The flange, shown in the cut, is what is called a split + flange. By the set screw <b>T</b>, the jaws can be + regulated so that they neither clamp the center pin so + tightly as to make the action sluggish nor so loosely as to + let the hammer wabble. + </p> + <p> + If the bushing cloth is found to be badly worn, it is + better to put in new, which must be done neatly, or the + result will not be satisfactory. + </p> + <p> + Hammer flanges, like all other wooden parts, shrink away + from the screw heads and allow the hammer to drift to one + side or rattle. While the <span class='pagenum'><a + name="Page_060" id="Page_060"></a>[Pg 060]</span>action is + in the piano, strike the keys to see if there are any that + strike improperly. Mark the keys so as to indicate just + what the trouble is, so that you will know how to remedy it + when the action is out. If the hammers are set so close + that they rub against each other, you may have to cut off a + slight shaving of felt, but this is rarely necessary; for + if properly placed, there is generally room for all; yet + sometimes the expansion of the felt or warping of the shank + makes cutting necessary. + </p> + <p> + 7. <i>Dampers</i>. The dampers in the square action depend + entirely upon their weight for their efficiency in damping + the strings and returning after being raised by the key. + Often, after the key is struck, the damper will not return + to its place and the string is undamped. This is generally + found to be caused by the wire sticking in the hole through + which it passes, the wire being rusty or bent or some + foreign substance being in the hole round the wire. The + bushing cloth in the hole may be in such condition as to + retard the free passage of the damper wire, in which case + the wire may be heated with a match and run up and down a + few times through the hole, which will free it. The damper + may not <span class='pagenum'><a name="Page_061" + id="Page_061"></a>[Pg 061]</span>fall readily on account of + a sluggish joint in the flange. Work it back and forth as + far as it will go a few times; if necessary, take it off + the damper rail and look for the cause of the trouble. + </p> + <p> + Damper flanges get loose on the damper rail and work to one + side, causing defective damping and rattling. See that they + are all tight, and in their places. + </p> + <p> + Damper lifter buttons sometimes hold the damper off the + string. See that the top button falls so low that the + damper lever does not touch it when the key is released. + This is accomplished by altering the lower button. Examine + the damper felts to see if they are moth-eaten, or have + become hardened or in any way impaired. Notice the + adjustment of the shade; that it is not too low or too + high. The purpose of the shade is to prevent the damper + levers from flying up; but it should be high enough so that + the levers do not touch it when the key is depressed + gently. + </p> + <p> + Defective damping is one of the most annoying conditions, + and when one is employed to regulate a piano thoroughly and + put it in order, he should see that no key is left in which + this occurs. Strike each <span class='pagenum'><a + name="Page_062" id="Page_062"></a>[Pg 062]</span>key and + immediately let it up to see if it stops the sound quickly, + or, in other words, damps perfectly; if it does not, find + the cause and regulate until satisfactory. + </p> + <p> + 8. <i>The grand action</i> being, in principle, practically + the same as that of the square and the upright, containing + the same mechanism as is found in those actions, it is + needless to give special instructions concerning it; as the + previous work has given the pupil a thorough knowledge of + the requirements of all actions, their common faults, and + proper methods of regulating to bring about satisfactory + results. Let us merely remark: Study thoroughly the + behavior of every component part of each action that comes + under your observation; understand what each part is for, + why it is there, and how it works or should work properly + to fill its office. Then regulate and try for results. If + you have natural mechanical genius, a little experience + will prepare you to do all regulating and repairing with + skill and quickness. + </p> + <p> + <span class='pagenum'><a name="Page_063" + id="Page_063"></a>[Pg 063]</span> + </p> + <p class="center smcap"> + Miscellaneous repairs. + </p> + <p> + A few miscellaneous difficulties, common to all styles of + actions, are occasionally met with and need to be + rectified. + </p> + <p> + 1. <i>Broken Hammer Shank</i>. Glue the ends, lay a nicely + fitting piece of wood, well coated with glue, on each side + and wrap with binding wire. If it is broken off up so close + to the hammer as not to permit this, drill a hole through + the hammer head in line with the center of the shank, with + a small-sized screwdriver such as watchmakers use, and run + the wire through this and around the shank, drawing it + firm; glue as before; when dry it will be as strong as + ever. When the shank is broken off close to the butt, the + same treatment will sometimes answer, but the strain here + is so much greater that it is sometimes necessary to put in + a new shank. In fact, it is always better to do so. + </p> + <p> + 2. <i>Flanges, damper heads</i>, and all small wooden parts + are liable to break or come unglued. The watchmaker's + screwdriver, the binding wire and the glue must always be + at hand for these emergencies. These breaks are generally + in places where <span class='pagenum'><a name="Page_064" + id="Page_064"></a>[Pg 064]</span>wrapping is not + permissible, and you are compelled to drill. Keep the + screwdriver well sharpened and the drilling is easy. + </p> + <p> + 3. <i>Ivories</i>. When unglued, scrape the old glue off, + apply glue to both surfaces and clamp with an ivory clamp + or rubber band until the glue is firm. Apply the same + treatment to ebony sharps. + </p> + <p> + 4. <i>Leads</i> in the keys and the dampers of the square + piano get loose and rattle. Hammer them just enough to + tighten; too much might split the key. + </p> + <p> + 5. <i>Friction</i>. Where different materials, such as wood + and felt, would rub together they are covered with black + lead to lubricate them. The point of the jack where it + comes in contact with the butt, the toe of the jack which + strikes the regulating button, and the long wooden capstan + which takes the place of the extension and works directly + on the under side of the wippen, which is covered with + felt, are black-leaded. When a key squeaks and goes down + reluctantly, the trouble can usually be traced to these + places; especially to the wooden capstan, the black lead + having worn away. Use powdered black lead on these parts. + </p> + <p> + <span class='pagenum'><a name="Page_065" + id="Page_065"></a>[Pg 065]</span> + </p> + <p> + There are many things in this kind of work that require + only the exercise of "common sense." These we have omitted + to mention, treating only of those things the student does + not know intuitively. + </p> + <p class="center"> + QUESTIONS ON LESSON VI. + </p> + <ol> + <li> + When a key snaps or clicks at the instant it is let up, + give two or more conditions that might cause it. + </li> + <li> + When a key simply rattles, what parts of the action would + you examine for the trouble? + </li> + <li> + When a key is struck and there is no response, what may + be the cause? + </li> + <li> + Give two causes for defective damping in a square piano. + </li> + <li> + Give cause of and remedy for a squeaking key. + </li> + </ol> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_066" + id="Page_066"></a>[Pg 066]</span> + </p> + <h2> + <a name="LESSON_VII" id="LESSON_VII"></a>LESSON VII. + </h2> + <hr style="width: 25%;" /> + <h3> + THE STUDY AND PRACTICE OF PIANO TUNING. + </h3> + <p> + Before commencing the systematic study of piano tuning, we + want to impress the student with a few important facts that + underlie the great principles of scale building and general + details of the art. + </p> + <p> + If you have followed the suggestions, and thoroughly + mastered the work up to this point you should now have some + idea of the natural and artificial phenomena of musical + tones; you should have a clear knowledge at least of the + fundamental principles of harmony and the technical terms + by which we designate intervals and their relation to each + other; a knowledge of the general and specific construction + of the different types of pianos and their actions, and the + methods employed to put them in perfect working condition + mechanically. This admitted, we are ready to consider the + art of tuningone, <span class='pagenum'><a name="Page_067" + id="Page_067"></a>[Pg 067]</span>the appreciation of which + is in direct proportion to the understanding of it. Let us + now view this art for a moment in its past, present and + future phases. + </p> + <p> + You may be a little surprised at what we are about to tell + you, but it is a fact, gleaned from long experience in + traveling and observation, that many, verily, the majority + of pretending tuners have not so much practical knowledge + of a piano as you should now have. We have no doubt that + you, if you have a musical ear, could, without further + instruction, improve an instrument that was extremely out + of tune. You could detect and improve a tone which you + should find extremely sharp or flat; you could detect and + improve a unison that might be badly out, and you might + produce an entire scale in which none of the chords would + be unbearably rasping. But this is not enough. You should + aspire to perfection, and not stop short of it. + </p> + <p> + It may seem to us who are musicians with thorough knowledge + of the simpler laws of music, that a scale of eight tones + is a simple affair; simply a natural consequence; the + inevitable arrangement; but a historical investigation will + prove our mistake. We <span class='pagenum'><a + name="Page_068" id="Page_068"></a>[Pg 068]</span>will not + go into the complexities of musical history; suffice it to + say that the wisest philosophers who lived prior to the + fourteenth century had no idea of a scale like that we have + at the present day. + </p> + <p> + In piano tuning, as in other arts, many theories and + conjectures have been advanced regarding the end to be + sought and the means by which to gain it. There must be a + plana system by which to work. The question is: What plan + will insure the most perfect results with the least amount + of labor? In Piano Tuning, this plan is called the + Temperament. + </p> + <p> + Webster defines the word thus: "A system of compromises in + the tuning of pianofortes, organs," etc. Later on we will + discuss fully what these compromises are, and why they + exist; for it is in them that the tuner demonstrates his + greatest skill, and to them that the piano owes its + surpassing excellence as a musical instrument, and, + consequently, its immense popularity. For the present, the + term "temperament" may be considered as meaning the plan or + pattern from which the tuner works. + </p> + <p> + No subject of so great importance in the whole realm of + musical science has been so strangely neglected as the + method of setting a temperament. <span class='pagenum'><a + name="Page_069" id="Page_069"></a>[Pg 069]</span>Even + musicians of high learning, in other respects, give little + attention to scale building, and hence they differ widely + on this topic. There can be but one "best way" of doing a + thing, and that best way should be known and followed by + the profession; but, strange to say, there are a half dozen + systems of setting the temperament in vogue at the present + time. The author has, in his library, a book on + "Temperament" which, if followed, would result in the + production of a scale in which every chord would be + unbalanced, harsh and unbearable. This is mentioned merely + to call attention to the fact that great differences of + opinion exist among scientific men regarding this important + subject. + </p> + <p> + In the author's practice, he was curious to try the + different methods, and has tuned by all the systems of + temperament in vogue at the present, or that have ever been + used extensively. His experience has proved that all but + one is hampered with uncertainty, difficulty of execution + or imperfection in some respect. + </p> + <p> + A system which will positively insure the strictest + uniformity of difference in pitch of any given interval in + all the keys, and that makes use of the fewest <span + class='pagenum'><a name="Page_070" id="Page_070"></a>[Pg + 070]</span>intervals in tuning and the easiest onesthose in + which a discrepancy is most readily perceived by the ear, + is the best system to adopt and follow. Such a system is + the one followed by the author for years with the most + satisfying results. He does not claim any high honor by + this statement, but does claim that, while his system + differs but slightly from some of the others, it is more + certain to produce the best results, is the simplest to + understand, is the easiest to follow, and, consequently, is + the best. + </p> + <p> + To become a piano tuner of the highest skill, many things + are necessary; but what may be lacking at the outset may be + acquired by study and practice. More depends upon the ear + than upon anything else; but no person, however talented, + has a sufficiently acute perception to tune perfectly + without some culture. Some practice in tuning is necessary + to bring the ear to that acuteness of perception so + indispensable in certain portions of the instrument. It may + also be said that no extraordinary talent for music is + absolutely necessary, since many of the best tuners are not + musicians in any sense of the word. Patience and + perseverance, associated with conscientiousness and an + insatiable desire to <span class='pagenum'><a + name="Page_071" id="Page_071"></a>[Pg 071]</span>excel, are + among the foremost requirements. Having these it only + remains to gain a thorough knowledge of every detail of the + work; a little practice will bring skill and dexterity. + </p> + <p> + Finally, we would impress the student with the strenuous + importance of thoroughly mastering the lessons which + immediately follow. You should be inspired with the utmost + confidence, both in yourself and in the possibilities of + the profession to those who merit a reputation. And, while + this lesson contains little technical instruction, if by + its study the pupil is impressed with the maxims herein + presented, and is inspired to make earnest effort in his + future work, both in acquiring and in practicing the art of + Piano Tuning, the author will feel that its mission is, by + no means, the least significant one in the course. + </p> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_072" + id="Page_072"></a>[Pg 072]</span> + </p> + <h2> + <a name="LESSON_VIII" id="LESSON_VIII"></a>LESSON VIII. + </h2> + <hr style="width: 25%;" /> + <h3> + THE TEMPERAMENT. + </h3> + <p> + Some tuners favor the term, "laying the bearings," others + say "setting the temperament." The former is more + commonplace, as it merely suggests the idea of laying a + number of patterns by which all others are to be measured. + The latter term is extremely comprehensive. A lucid + definition of the word "temperament," in the sense in which + it is used here, would require a discourse of considerable + length. The following statements will elicit the full + meaning of the term: + </p> + <p> + The untutored would, perhaps, not think of setting a + temperament to tune by. He would likely begin at some + unfavorable point, and tune by various intervals, relying + wholly upon his conception of pitch for the accuracy of the + tones tuned, the same as a violinist in tuning his four + strings. To be sure, pitch has to be reckoned as a rude + guide in setting <span class='pagenum'><a name="Page_073" + id="Page_073"></a>[Pg 073]</span>the tones; but if pitch + alone were the guide we would never attain to any degree of + perfection in scale forming. We could never adjust our + tones to that delicate fineness so much appreciated, which + gives to the instrument its surpassing brilliancy. + </p> + <p> + <b>Beats, Waves, Pulsations.</b> To obtain absolute + accuracy the tuner is guided by beats, waves or pulsations. + These three words refer to one and the same thing, a + phenomenon that occurs in certain intervals when two tones + are sounded together that are not in exact tune. These + terms must not be confounded with the term "sound wave" or + "vibrations" so often used in discussions on the theory of + sound. However, we think the student is thoroughly familiar + with these terms. The rate of vibration of two tones not in + a favorable ratio, may produce the phenomenon known as + "beats, waves, or pulsations." Vibrations may exist either + with or without pulsations. + </p> + <p> + These pulsations are most perceptible in the unison, the + octave and the fifth. They are more easily perceived in the + unison than in the octave, and more easily in the octave + than in the fifth. They are also perceptible in the perfect + fourth, the major and <span class='pagenum'><a + name="Page_074" id="Page_074"></a>[Pg 074]</span>minor + third and some other intervals, but on account of their + obscurity, and because these intervals are unnecessary in + tuning they have long since been abandoned in "temperament + making" (with the exception of the perfect fourth) by most + tuners, although a few still make use of it. We do not say + that the fourth is unsafe to tune by, but you will see + later on why it is not best to make use of it. + </p> + <p> + <i>The Fischer System</i> or method of "setting the + temperament" has these advantages: It uses but two kinds of + intervals: the fifth and octave; by employing two whole + octaves in place of one or one and a half, nearly all of + the middle section of strings is brought up in pitch which + insures that the temperament will stand better while the + remaining strings are being tuned; and the alternate tuning + of the fifth and octave makes the system exceedingly easy + to learn, enabling the tuner to work with less mental + strain. Also the two-octave system gives a greater compass + for testing, thus insuring greater accuracy. + </p> + <p> + If you have access to a piano, it will now be well for you + to begin training the ear to perceive the pulsations. If + you cannot use a piano, you can train very well by the use + of a mandolin, guitar, violin, <span class='pagenum'><a + name="Page_075" id="Page_075"></a>[Pg 075]</span>zither, or + any stringed instrument. An instrument with metal strings, + however, is better, as the vibrations are more perfect. + </p> + <p> + You will, of course, know that the front top panel of the + case has to be removed to give access to the tuning pins, + and that you should have a regular tuning hammer and set of + mutes to begin with. The panel is held in place in various + ways: sometimes with buttons, sometimes with pins set in + slots, and sometimes with patent fastenings; but a little + examination will reveal how it may be removed. + </p> + <p> + To produce a tone of a certain pitch, the string must be of + the right thickness and length. These items are decided by + the scale draughtsman in the factory; if incorrect, the + tuner can do nothing to improve them. + </p> + <p> + To produce the correct pitch, the string must be of the + right tension, which is brought about by winding one end of + the string around the tuning pin until the proper degree of + tension is reached. This must be decided by the ear of the + tuner. Two strings of equal thickness and equal length + produce the same tone when brought to the same tension; the + result being known as "unison." A defect in the unison + <span class='pagenum'><a name="Page_076" + id="Page_076"></a>[Pg 076]</span>being the easiest way in + which to detect the beats, we advise that the student + practice on it first. + </p> + <p> + After taking out the panel, the first thing to do is to + place your rubber mute between two trios of strings (if the + piano is an upright which usually has three strings to a + note) so that only two strings sound when the key is + struck. Select some key near the middle of the keyboard. + Strike the key strongly and hold it down. If the two + sounding strings give forth a smooth, unwavering tonea tone + that sounds as if it came from one string, the unison is + perfect. If you find it so, remove the mute and place it on + the other side of the trio of strings. If the piano has + been tuned recently by an expert, you may have to continue + your search over several keys before you find an imperfect + unison; but you will rarely find a piano in such perfect + tune that it will not contain some defective unisons. + However, if you do not succeed in finding a defective + unison, select a key near the middle of the key-board, + place your mute so that but two strings sound, and with + your tuning hammer loosen one of the strings very slightly. + Now you will notice a throbbing, beating sound, very unlike + the tone produced when the strings were <span + class='pagenum'><a name="Page_077" id="Page_077"></a>[Pg + 077]</span>in exact unison. See if you can count the beats. + If you have lowered the tension too much, the beats will be + too rapid to permit counting. Now with a steady and gradual + pull, with the heel of the hand against some stationary + part, bring the string up slowly. You will notice these + waves become slower and slower. When they become quite + slow, stop and count, or wave the hand in time with the + pulsations. After practicing this until you are sure your + ear has become accustomed to the beats and will recognize + them again, you may proceed to perfect the unison. Bring + the string up gradually as before, and when the unison is + reached you will hear one single, simple, musical tone, as + though it were from a single string. Never have more than + two strings sounding at once. You might go over the entire + key-board now and correct all the unisons if the scale is + yet fairly good. See which string is, in your opinion, the + nearest to correctness with respect to the scale, and tune + the other one, or two, as the case may be, to it. If the + scale is badly out of symmetry, you will not get very good + results without setting a temperament; but the tones will + sound better individually. This experiment is more for + practice than for improving the piano. + </p> + <p> + <span class='pagenum'><a name="Page_078" + id="Page_078"></a>[Pg 078]</span> + </p> + <p> + <i>The cause</i> of the waves in a defective unison is the + alternate recurring of the periods when the condensations + and rarefactions correspond in the two strings and then + antagonize. This is known in physics as "interference of + sound-waves." + </p> + <p> + <b>The Octave.</b> When perfectly tuned, the upper tone of + the octave has exactly double the number of vibrations of + the lower. If the lower tone vibrates 1000 per second, the + upper will vibrate 2000. Of course, the ear cannot + ascertain in any way the number of vibrations per second; + we use these figures for scientific demonstration only. + However, there is an instrument called the Siren which is + constructed for the purpose of ascertaining the number of + vibrations per second of any given tone, and which is + delicately accurate in its work. By its assistance we know, + definitely, a great many things regarding our musical scale + of which we would otherwise be ignorant. But, while we + cannot, by the ear, ascertain these numbers, we can, by the + "interference of sound-waves" above referred to, ascertain, + to the most delicate point, when the relative vibration of + two strings is mathematically exact, if they are tuned to a + unison, octave, fifth, etc. + </p> + <p> + <span class='pagenum'><a name="Page_079" + id="Page_079"></a>[Pg 079]</span> + </p> + <p> + Practice now on tuning the octave. Find an octave in which + the upper tone is flat. Mute all but one string in the + lower tone to make sure of getting a pure tone, then select + one string (the middle one if a piano has three strings) of + the upper octave and proceed to pull it up gradually until + all beats disappear. This being done, bring up the unisons. + </p> + <p> + <b>The Fifth.</b> In our system, when we speak of a fifth, + we mean a fifth upward. The fifth to C is G, to G is D, and + so on. + </p> + <p> + The vibration of the fifth is one and a half times that of + its fundamental. If a certain F vibrates 100, the C, a + fifth above, will vibrate 150, if tuned so that no waves + are heard; but for reasons which will be fully explained + later, the fifth cannot be tuned with mathematical + precision. On account of certain peculiarities in our + tempered scale, the fifth must always be left somewhat + flatter than perfect. This fact is always learned with some + astonishment by beginners. + </p> + <p> + In your practice on tuning the fifth, first tune it + perfectly, so that no waves are perceptible; then flat it + so that there are very slow waves; less than one per + second. Some authorities say there should be three beats in + five seconds; but the tuner must learn <span + class='pagenum'><a name="Page_080" id="Page_080"></a>[Pg + 080]</span>to determine this by his own judgment. The + tempering of the fifth will be treated exhaustively in + subsequent lessons. + </p> + <p> + We advise that you confine your practice to the unison + until you are sure you have a clear conception of its + peculiarities in all portions of the key-board, except the + extreme lower and upper octaves; do not try these yet. Do + not begin to practice on the octave until you are very + familiar with the beats in the unison. By gradual progress + you will avoid confusing the ear, each step being + thoroughly mastered before advancing to the next. Remember, + there is nothing that is extremely difficult in learning to + tune if you but understand what has to be done, go about it + systematically, and have plenty of patience. + </p> + <p> + In this lesson we give you our system of setting the + temperament; that is, the succession in which the different + tones of the temperament are tuned. We advise, however, + that you do not attempt to set a temperament until after + studying Lesson IX, which enters into the theory of + temperament, testing, etc. + </p> + <p> + Two octaves are used for the temperament: an octave above, + and an octave below middle C. Middle C can be told by its + being, the C nearest the name <span class='pagenum'><a + name="Page_081" id="Page_081"></a>[Pg 081]</span>of the + piano on the name board. In other words, it is the fifth C + from the highest C, and the fourth from the lowest in the + modern piano, which has seven and a third octaves. + </p> + <p> + The diagram illustrates the two octaves of the key-board, + and shows how each key is designated in giving the system + of temperament. + </p> + <p> + <b>Pitch.</b> The Piano Manufacturers' Association has + established what is known as "international pitch." + Tuning-forks made to this pitch are marked "C-517.3," + meaning that our 3C vibrates 517.3 per second. Concert + pitch is nearly a half step higher than this. Some + manufacturers still tune their instruments to this higher + pitch. + </p> + <p> + If it is desired to tune a piano to a certain pitch, say + concert pitch, tune the C that is an octave above middle C + by a concert pitch tuning-fork or pipe. If, however, the + piano is too much below that, it is not safe to bring it up + to it at one tuning. But, say it will permit tuning to + concert pitch; after this C (3C) is well laid, tune middle + C (2C) by it, then tune the C octave below middle C (1C) to + middle C. Having 1C for a starting point, proceed by tuning + a fifth up, then its octave, then a fifth, then an <span + class='pagenum'><a name="Page_082" id="Page_082"></a>[Pg + 082]</span>octave, always tuning the octave whichever way + is necessary to keep within the two octaves. + </p> + <p> + The simplicity of this system can be readily seen; yet for + the use of beginners, we give on the following page the + whole succession of intervals as they are taken in setting + the temperament. + </p> + <div class="center"> + <div class="figcenter" style="width: 400px;"> + <span class="smcap">Diagram of the Two Octaves Used in + "Temperament," and of the Succession in Which They Are + Tuned<br /> + <br /> + </span> <img src="images/image082.png" width="400" + height="65" alt="Octaves used in 'Temperament'" + title="Octaves used in 'Temperament'" /> + </div> + </div> + <p> + Middle C begins second octave; known by the asterisk (*) + under it. + </p> + <h3> + THE FISCHER SYSTEM OF SETTING TEMPERAMENT. + </h3> + <p> + First, tune 3C by tuning pipe, or as directed. + </p> + <p> + By this, tune 2C, and by 2C tune 1C; then tune as follows: + </p> + <div class="center"> + <table> + <tr> + <td>By</td> + <td>1C</td> + <td>tune</td> + <td>1G</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1G</td> + <td class="center">"</td> + <td>2G</td> + <td>Â Â octave above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1G</td> + <td class="center">"</td> + <td>2D</td> + <td>fifth above, + </td> + </tr> + <tr> + <td class="center">"</td> + <td>2D</td> + <td class="center">"</td> + <td>1D</td> + <td>Â Â octave below,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1D</td> + <td class="center">"</td> + <td>1A</td> + <td>fifth above,<span class='pagenum'><a name="Page_083" + id="Page_083"></a>[Pg 083]</span> + </td> + </tr> + <tr> + <td class="center">"</td> + <td>1A</td> + <td class="center">"</td> + <td>2A</td> + <td>Â Â octave above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1A</td> + <td class="center">"</td> + <td>2E</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>2E</td> + <td class="center">"</td> + <td>1E</td> + <td>Â Â octave below,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1E</td> + <td class="center">"</td> + <td>1B</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1B</td> + <td class="center">"</td> + <td>2B</td> + <td>Â Â octave above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1B</td> + <td class="center">"</td> + <td>2F♯</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>2F♯</td> + <td class="center">"</td> + <td>1F♯</td> + <td>Â Â octave below,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1F♯</td> + <td class="center">"</td> + <td>2C♯</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>2C♯</td> + <td class="center">"</td> + <td>1C♯</td> + <td>Â Â octave below,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1C♯</td> + <td class="center">"</td> + <td>1G♯</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1G♯</td> + <td class="center">"</td> + <td>2G♯</td> + <td>Â Â octave above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1G♯</td> + <td class="center">"</td> + <td>2D♯</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>2D♯</td> + <td class="center">"</td> + <td>1D♯</td> + <td>Â Â octave below,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1D♯</td> + <td class="center">"</td> + <td>1A♯</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1A♯</td> + <td class="center">"</td> + <td>2A♯</td> + <td>Â Â octave above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1A♯(B♭)</td> + <td class="center">"</td> + <td>2F</td> + <td>fifth above,</td> + </tr> + <tr> + <td class="center">"</td> + <td>2F</td> + <td class="center">"</td> + <td>1F</td> + <td>Â Â octave below,</td> + </tr> + <tr> + <td class="center">"</td> + <td>1F</td> + <td class="center">try</td> + <td>2C</td> + <td>fifth above.</td> + </tr> + </table> + </div> + <p> + You will observe this last fifth brings you back to the + starting-point (C). It is called the "wolf," from the + howling of its beats when the tuner has been inaccurate or + the piano fails to stand. + </p> + <p class="center"> + QUESTIONS ON LESSON VIII. + </p> + <ol> + <li> + What is the cause of the beats or pulsations? + </li> + <li> + Have you practiced tuning the unison? <span + class='pagenum'><a name="Page_084" id="Page_084"></a>[Pg + 084]</span> + </li> + <li> + Can you distinguish the beats clearly? + </li> + <li> + Have you practiced tuning the octave? + </li> + <li> + Do you thoroughly understand the system of setting the + temperament as set forth in this lesson? + </li> + </ol> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_085" + id="Page_085"></a>[Pg 085]</span> + </p> + <h2> + <a name="LESSON_IX" id="LESSON_IX"></a>LESSON IX. + </h2> + <hr style="width: 25%;" /> + <h3> + SPECIFIC INSTRUCTIONS IN TEMPERAMENT SETTING. + </h3> + <p> + <b>Pitch.</b> It is a matter of importance in tuning an + instrument that it be tuned to a pitch that will adapt it + to the special use to which it may be subjected. As + previously explained, there are at present two different + pitches in use, international pitch and concert pitch, the + latter being about a half-step higher than the former. The + tuner should carry with him a tuning pipe or fork tuned to + 3C in one or the other of these pitches. The special uses + to which pianos are subjected are as follows: + </p> + <p> + 1st, As a concert piano. In the opera house, music hall, + and occasionally in the church, or even in a private + dwelling, the piano is used along with orchestral + instruments. All orchestral instruments are supposed to be + tuned to concert pitch. The stringed instruments can, of + course, be tuned to any pitch; but the brass and wood-wind + instruments <span class='pagenum'><a name="Page_086" + id="Page_086"></a>[Pg 086]</span>are not so adjustable. The + brass instruments are provided with a tuning slide and + their pitch can be lowered somewhat, but rarely as much as + a half-step, while the clarinet should not be varied from + its fixed pitch if it can be avoided. It is desirable, + then, that all pianos used with orchestra should be tuned + to concert pitch if possible. + </p> + <p> + 2d, As an accompaniment for singing. Some persons use their + pianos mainly for accompanying. It may be that singers + cannot sing high, in which case they are better pleased if + the piano is tuned to international pitch, while others, + especially concert singers, have their pianos at a higher + pitch. Where a piano is used in the home to practice by, + and the singer goes out to various places to sing with + other instruments, we have always advised to have the piano + tuned as near concert pitch as it would bear, for the + reason that if one practices with an instrument tuned to + concert pitch he may feel sure of reaching the pitch of any + instrument he may be called upon to sing with elsewhere. + </p> + <p> + The great majority of pianos are left entirely to the + tuner's judgment in regard to pitch. The tuner knows, or + should know, to what pitch to tune the <span + class='pagenum'><a name="Page_087" id="Page_087"></a>[Pg + 087]</span>piano to insure the best results. The following + suggestions will be found entirely safe to follow in + deciding the question of the pitch to which to tune: + </p> + <p> + Ascertain if the piano is used with orchestra, and if + clarinets and cornets are used. If so, and the piano is not + too much below concert pitch, and bids fair to stand the + tension, draw your 3C up to concert pitch and proceed to + lay your temperament. If the piano is nearly as low as + international pitch, do not try to bring it up at one + tuning to concert unless the owner demands it, when you may + explain that it will not stand in tune long. The slightest + alteration possible, in the pitch of an instrument, insures + the best results, so far as standing in tune is concerned. + </p> + <p> + If everything be left to your judgment, as it generally is, + and the instrument is for general, rather than special use, + set your temperament at such a pitch as will require the + least possible alteration. This may be arrived at in the + following way: Ascertain which portion of the instrument + has fallen the most. The overstrung bass strings generally + stand better than any other, and in most cases you will + find the C which is two octaves below middle C <span + class='pagenum'><a name="Page_088" id="Page_088"></a>[Pg + 088]</span>to be higher (relatively) than any other C in + the piano. If so, take it as a basis and tune by perfect + octaves up to 3C. + </p> + <p> + The supposition is, that all strings in an instrument + gradually grow flatter; and in a well-balanced instrument + they should do so; but the fact is, that in certain cases + some of the strings will grow sharper. The cause is this: + The tension of the strings on one side of a brace in the + metal plate or frame is greater than on the other side; and + if there is any yielding of the structure, the result is + that the overpowered strings are drawn tighter. This + condition, however, is rare in the better grade of pianos. + Here is a rule which is safe, and will prove satisfactory + in ninety-nine per cent. of your practice where no specific + pitch is prescribed: + </p> + <p> + Take the three Cs included in the temperament and the C + that is an octave below 1C, and try each of them with its + octave until you ascertain which is the sharpest with + respect to the others; then, bring the others up to it. You + now have your pitch established in the Cs and can begin on + 1C and proceed to set the temperament. Before applying this + rule, it is well to try 3C with tuning pipe or fork to + <span class='pagenum'><a name="Page_089" + id="Page_089"></a>[Pg 089]</span>see if the piano is below + international pitch. We would not advise tuning any modern + piano below international pitch. Aim to keep within the + bounds of the two prescribed pitches; never higher than + concert, nor lower than international. If, however, you + should be called on to tune an old instrument that has + become extremely low, with very rusty strings, and perhaps + with some of them broken, that by all appearances will not + stand even international pitch, you may be compelled to + leave it somewhat below. + </p> + <p> + <b>The Continuous Mute.</b> Do not try to set a temperament + without a continuous mute. Its purpose is to mute all + outside (1st and 3d<a id="fnanchor_C" + name="fnanchor_C"></a><a href="#fn_C" + class="fnanchor">[C]</a>) strings of all the trios included + in the temperament so that none but the middle strings + sound when struck by the hammers. The advantage of this can + be seen at once. The tuner tunes only the middle strings in + setting the temperament and thereby avoids the confusion of + hearing more than two strings at once. The continuous mute + is then removed and the outside strings tuned to the + middle. Without the continuous <span class='pagenum'><a + name="Page_090" id="Page_090"></a>[Pg 090]</span>mute, he + would be obliged to tune all three of the strings of the + unison before he could tune another interval by it, and it + would not be so safe to tune by as a single string, as + there might be a slight discrepancy in the unison giving + rise to waves which would confuse the ear. The tuner should + hear but two strings at once while setting a temperament; + the one he is tuning by and the one he is tuning. A + continuous mute is a strip of muting felt of the proper + thickness to be pushed in between the trios of strings. + Simply lay it across a portion of the strings and with a + screwdriver push it in between the trios just above where + the hammers strike. In the square piano, which has but two + strings to a key, the continuous mute cannot be used and + you will be obliged to tune both strings in unison before + leaving to tune another interval. This is one of the + reasons why the square piano does not, as a rule, admit of + as fine tuning as the upright. + </p> + <p> + It is presumed that you are now familiar with the + succession of tones and intervals used in setting the + temperament. Fix these things in your mind and the system + is easy to understand and remember. Keep within the bounds + of the two octaves laid out <span class='pagenum'><a + name="Page_091" id="Page_091"></a>[Pg 091]</span>in Lesson + X. Tune all fifths upward; that is, tune all fifths by + their fundamentals. For example, starting on 1C, use it as + fundamental, and by it, tune its fifth, which is G; then, + having G tuned, use it as fundamental, and by it tune its + fifth, which is D, and so on through. After tuning a fifth, + always tune its octave either above or below, whichever way + it lies within the bounds of the two octaves. After going + through one or two experiments in setting temperament you + will see the simplicity of this system and will, perhaps, + not be obliged to refer to the diagram any more. + </p> + <p> + For various reasons, it is better to try your experiments + on an upright piano, and the better the piano, the more + satisfactory will be the result of the experiment. You + should have no hesitancy or timidity in taking hold of a + good piano, as you cannot damage it if you use good + judgment, follow instructions, and work carefully. The + first caution is, be very careful that you draw a string + but slightly sharper than it is to be left. Rest the heel + of the hand against some stationary part of the piano and + pull very slowly, and in a direct right angle with the + tuning pin so as to avoid any tendency to bend or <span + class='pagenum'><a name="Page_092" id="Page_092"></a>[Pg + 092]</span>spring the pin. We would advise now that you + find an upright piano that is badly out of tune, if you + have none of your own, and proceed to set a temperament. + </p> + <p> + The following instructions will suffice for your first + experiments, and by them you may be able to get fairly good + results; however, the theory of temperament, which is more + thoroughly entered into in Lesson XII, must be studied + before you can have a thorough understanding of the causes + and effects. + </p> + <p> + After deciding, as per instructions on pitch which C you + will tune first, place the tuning hammer (using the star + head if pins are square) on the pin with the handle + extending upwards or inclined slightly to the right. (The + star head, which will fit the pin at eight different + angles, enables the tuner to select the most favorable + position.) To raise the pitch, you will, of course, pull + the hammer to the right. In order to make a string stand in + tune, it is well to draw it very slightly above the pitch + at which it is to remain, and settle it back by striking + the key repeatedly and strongly, and at the same time + bearing gently to the left on the tuning hammer. The exact + amount of over-tension must be learned by practice; <span + class='pagenum'><a name="Page_093" id="Page_093"></a>[Pg + 093]</span>but it should be so slight as to be barely + perceptible. Aim to get the string tuned with the least + possible turning of the hammer. The tension of the string + should be evenly distributed over its entire length; that + is, over its vibrating middle and its "dead ends" beyond + the bridges. Therefore it is necessary to strike the key + strongly while tuning so as to make the string draw through + the bridges. By practice, you will gain control of the + hammer and become so expert that you can feel the strings + draw through the bridges and the pins turn in the block. + </p> + <p> + Having now tuned your three Cs, you will take 1C as a + starting point, and by it, tune 1G a perfect fifth above. + Tune it perfect by drawing it gradually up or down until + all pulsations disappear. Now after making sure you have it + perfect, flatten it until you can hear slow, almost + imperceptible waves; less rapid than one per second. This + flattening of the fifth is called tempering, and from it + comes the word "temperament." The fact that the fifth must + always be tuned a little flatter than perfect, is a matter + which always causes some astonishment when first learned. + It seems, to the uninitiated, that every interval should be + made perfect; but it is <span class='pagenum'><a + name="Page_094" id="Page_094"></a>[Pg 094]</span>impossible + to make them so, and get a correct scale, as we shall see + later on. + </p> + <p> + Now tune 2G by the 1G just tuned, to a perfect octave. + Remember that all octaves should be left perfectall waves + tuned out. Now try 2G with 2C. If your octaves are perfect, + this upper fifth will beat a little faster than the lower + one, but the dissonance should not be so great as to be + disagreeable. Proceed to your next fifth, which is 2D, then + its octave, 1D, then its fifth and so on as per directions + on the system card. You can make no chord trials until you + have tuned E, an interval of a major third from C. + </p> + <p> + Having tuned 2E, you can now make your first trial: the + chord of C. If you have tempered your fifths correctly, + this chord will come out in pleasing harmony, and yet the E + will be somewhat sharper than a perfect major third to C. + Now, just for experiment, lower 2E until all waves + disappear when sounded with 2C. You now have a perfect + major third. Upon sounding the chord, you will find it more + pleasing than before; but you cannot leave your thirds + perfect. Draw it up again to its proper temperament with A, + and you will notice it has very <span class='pagenum'><a + name="Page_095" id="Page_095"></a>[Pg 095]</span>pronounced + beats when sounded with C. Proceed with the next step, + which is that of tuning 1B, fifth to 1E. When tuned, try it + as a major third in the chord of G. At each step from this + on, try the note just tuned as a major third in its proper + chord. Remember, the third always sounds better if lower + than you dare to leave it; but, on the other hand, it must + not be left so sharp as to be at all unpleasant when heard + in the chord. As to the position of the chord for these + trials, the second position, that is, with the third the + highest, is the most favorable, as in this position you can + more easily discern excessive sharpness of the third, which + is the most common occurrence. When you have gone through + the entire system and arrived at the last fifth, 1F-2C, you + should find it nearly as perfect as the rest, but you will + hardly be able to do so in your first efforts. Even old + tuners frequently have to go over their work a second or + third time before all fifths are properly tempered. By this + system, however, you cannot go far wrong if you test each + step as directed, and your first chord comes up right. If + the first test, G-C-E, proves that there is a false member + in the chord, do not proceed with the system, but go over + the first seven steps <span class='pagenum'><a + name="Page_096" id="Page_096"></a>[Pg 096]</span>until you + find the offending members and rectify. Do not be + discouraged on account of failures. No one ever set a + correct temperament at the first attempt. + </p> + <p class="center"> + QUESTIONS ON LESSON IX. + </p> + <ol> + <li> + Define the terms, "International Pitch," and "Concert + Pitch." + </li> + <li> + How would you arrive at the most favorable pitch at which + to tune a piano, if the owner did not suggest any certain + pitch? + </li> + <li> + What is the advantage in using the continuous mute? + </li> + <li> + Tell what is necessary in the tuning of a string to + insure it to stand well? + </li> + <li> + What would result in the major third C-E, if all the + fifths, up to E, were tuned perfect? + </li> + </ol> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_097" + id="Page_097"></a>[Pg 097]</span> + </p> + <h2> + <a name="LESSON_X" id="LESSON_X"></a>LESSON X. + </h2> + <hr style="width: 25%;" /> + <h3> + THEORY OF THE TEMPERAMENT. + </h3> + <p> + The instructions given in Lessons VIII and IX cover the + subject of temperament pretty thoroughly in a way, and by + them alone, the student might learn to set a temperament + satisfactorily; but the student who is ambitious and + enthusiastic is not content with a mere knowledge of how to + do a thing; he wants to know why he does it; why certain + causes produce certain effects; why this and that is + necessary, etc. In the following lessons we set forth a + comprehensive demonstration of the theory of Temperament, + requirements of the correct scale and the essentials of its + mathematics. + </p> + <p> + <b>Equal Temperament.</b> Equal temperament is one in which + the twelve fixed tones of the chromatic scale<a + id="fnanchor_D" name="fnanchor_D"></a><a href="#fn_D" + class="fnanchor">[D]</a> are equidistant. Any chord will be + as harmonious in one key as in another. + </p> + <p> + <span class='pagenum'><a name="Page_098" + id="Page_098"></a>[Pg 098]</span> + </p> + <p> + <b>Unequal Temperament.</b> Unequal temperament was + practiced in olden times when music did not wander far from + a few keys which were favored in the tuning. You will see, + presently, how a temperament could be set in such a way as + to favor a certain key (family of tones) and also those + keys which are nearly related to it; but, that in favoring + these keys, our scale must be constructed greatly to the + detriment of the "remote" keys. While a chord or + progression of chords would sound extremely harmonious in + the favored keys, they would be so unbalanced in the remote + keys as to render them extremely unpleasant and almost + unfit to be used. In this day, when piano and organ music + is written and played in all the keys, the unequal + temperament is, of course, out of the question. But, + strange to say, it is only within the last half century + that the system of equal temperament has been universally + adopted, and some tuners, even now, will try to favor the + flat keys because they are used more by the mass of players + who play little but popular music, which is mostly written + in keys having flats in the signature. + </p> + <p> + Upon the system table you will notice that the first five + tones tuned (not counting the octaves) are <span + class='pagenum'><a name="Page_099" id="Page_099"></a>[Pg + 099]</span>C, G, D, A and E; it being necessary to go over + these fifths before we can make any tests of the complete + major chord or even the major third. Now, just for a proof + of what has been said about the necessity of flattening the + fifths, try tuning all these fifths perfect. Tune them so + that there are absolutely no waves in any of them and you + will find that, on trying the chord G-C-E, or the major + third C-E, the E will be very much too sharp. Now, let your + E down until perfect with C, all waves disappearing. You + now have the most perfect, sweetest harmony in the chord of + C (G, C, E) that can be produced; all its members being + absolutely perfect; not a wave to mar its serene purity. + But, now, upon sounding this E with the A below it, you + will find it so flat that the dissonance is unbearable. Try + the minor chord of A (A-C-E) and you will hear the rasping, + throbbing beats of the too greatly flattened fifth. + </p> + <p> + So, you see, we are confronted with a difficulty. If we + tune our fifths perfect (in which case our fourths would + also be perfect), our thirds are so sharp that the ear will + not tolerate them; and, if we tune our thirds low enough to + banish all beats, our fifths are intolerably flat. + </p> + <p> + <span class='pagenum'><a name="Page_100" + id="Page_100"></a>[Pg 100]</span> + </p> + <p> + The experiment above shows us beautifully the prominent + inconsistency of our scale. We have demonstrated, that if + we tune the members of the chord of C so as to get + absolutely pure harmony, we could not use the chord of A on + account of the flat fifth E, which did duty so perfectly as + third in the chord of C. + </p> + <p> + There is but one solution to this problem: Since we cannot + tune either the fifth or the third perfect, we must + compromise, we must strike the happy medium. So we will + proceed by a method that will leave our fifths flatter than + perfect, but not so much as to make them at all + displeasing, and that will leave our thirds sharper than + perfect, but not intolerably so. + </p> + <p> + We have, thus far, spoken only of the octave, fifth and + third. The inquisitive student may, at this juncture, want + to know something about the various other intervals, such + as the minor third, the major and minor sixth, the + diminished seventh, etc. But please bear in mind that there + are many peculiarities in the tempered scale, and we are + going to have you fully and explicitly informed on every + point, if you will be content to absorb as little at a time + as you <span class='pagenum'><a name="Page_101" + id="Page_101"></a>[Pg 101]</span>are prepared to receive. + While it may seem to us that the tempered scale is a very + complex institution when viewed as a specific arrangement + of tones from which we are to derive all the various kinds + of harmony, yet, when we consider that the chromatic scale + is simply a series of twelve half-stepstwelve perfectly + similar intervalsit seems very simple. + </p> + <p> + Bear in mind that the two cardinal points of the system of + tuning are: + </p> + <ol> + <li> + All octaves shall be tuned perfect. + </li> + <li> + All fifths shall be tuned a little flatter than perfect. + </li> + </ol> + <p> + You have seen from Lesson VIII that by this system we begin + upon a certain tone and by a circle of twelve fifths cover + every chromatic tone of the scale, and that we are finally + brought around to a fifth, landing upon the tone upon which + we started. + </p> + <p> + So you see there is very little to remember. Later on we + will speak of the various other intervals used in harmony: + not that they form any prominent part in scale forming, for + they do not; but for the purpose of giving the learner a + thorough understanding of all that pertains to the + establishing of a correct equal temperament. + </p> + <p> + <span class='pagenum'><a name="Page_102" + id="Page_102"></a>[Pg 102]</span> + </p> + <p> + If the instruction thus far is understood and carried out, + and the student can properly tune fifths and octaves, the + other intervals will take care of themselves, and will take + their places gracefully in any harmony in which they are + called upon to take part; but if there is a single instance + in which an octave or a fifth is allowed to remain untrue + or untempered, one or more chords will show it up. It may + manifest itself in one chord only. A tone may be untrue to + our tempered scale, and yet sound beautifully in certain + chords, but there will always be at least one in which it + will "howl." For instance, if in the seventh step of our + system, we tune E a little too flat, it sounds all the + better when used as third in the chord of C, as we have + shown in the experiment mentioned on page 94 of this + lesson. But, if the remainder of the temperament is + accurate, this E, in the chord in which E acts as tonic or + fundamental, will be found to be too flat, and its third, G + sharp, will demonstrate the fact by sounding too sharp. + </p> + <p> + The following suggestions will serve you greatly in + testing: When a third sounds disagreeably sharp, one or + more fifths have not been sufficiently flattened.<a + id="fnanchor_E" name="fnanchor_E"></a><a href="#fn_E" + class="fnanchor">[E]</a> <span class='pagenum'><a + name="Page_103" id="Page_103"></a>[Pg 103]</span> While it + is true that thirds are tuned sharp, there is a limit + beyond which we cannot go, and this excessive sharpness of + the third is the thing that tuners always listen for. + </p> + <p> + The fundamental sounds better to the ear when too sharp. + The reason for this is the same as has already been + explained above; namely, if the fundamental is too sharp + the third will be less sharp to it, and, therefore, nearer + perfect. + </p> + <p> + After you have gone all over your temperament, test every + member of the chromatic scale as a fundamental of a chord, + as a third, and as a fifth. For instance: try middle C as + fundamental in the chord of C (G-C-E or E-G-C or C-E-G). + Then try it as third in the chord A flat (E flat-A flat-C + or C-E flat-A flat or A flat-C-E flat). Then try it as + fifth in the chord of F (C-F-A or A-C-F or F-A-C). Take G + likewise and try it as fundamental in the chord of G in its + three positions, then try it as a <span class='pagenum'><a + name="Page_104" id="Page_104"></a>[Pg 104]</span>third in + the chord of E flat, then as fifth in the chord of C. In + like manner try every tone in this way, and if there is a + falsely tempered interval in the scale you will be sure to + find it. + </p> + <p> + You now understand that the correctness of your temperament + depends entirely upon your ability to judge the degree of + flatness of your fifths; provided, of course, that the + strings stand as tuned. We have told you something about + this, but you may not be able at once to judge with + sufficient accuracy to insure a good temperament. Now, we + have said, let the fifths beat a little more slowly than + once a second; but the question crops up, How am I to judge + of a second of time? The fact is that a second of time is + quickly learned and more easily estimated, perhaps, than + any other interval of time; however, we describe here a + little device which will accustom one to estimate it very + accurately in a short time. The pendulum oscillates by an + invariable law which says that a pendulum of a certain + length will vibrate always in a corresponding period of + time, whether it swings through a short arc or a long one. + A pendulum thirty-nine and a half inches long will vibrate + seconds by a single swing; one nine and <span + class='pagenum'><a name="Page_105" id="Page_105"></a>[Pg + 105]</span>seven-eighths inches long will vibrate seconds + at the double swing, or the to-and-fro swing. You can + easily make one by tying any little heavy article to a + string of either of these lengths. Measure from the center + of such heavy article to the point of contact of the string + at the top with some stationary object. This is a sure + guide. Set the pendulum swinging and count the vibrations + and you will soon become quite infallible. Having acquired + the ability to judge a second of time you can go to work + with more confidence. + </p> + <p> + Now, as a matter of fact, in a scale which is equally + tempered, no two fifths beat exactly alike, as the lower a + fifth, the slower it should beat, and thus the fifths in + the bass are hardly perceptibly flat, while those in the + treble beat more rapidly. For example, if a certain fifth + beat once a second, the fifth an octave higher will beat + twice a second, and one that is two octaves higher will + beat four times a second, and so on, doubling the number of + beats with each ascending octave. + </p> + <p> + In a subsequent lesson, in which we give the mathematics of + the temperament, these various ratios will be found + accurately figured out; but for the <span + class='pagenum'><a name="Page_106" id="Page_106"></a>[Pg + 106]</span>present let us notice the difference between the + actual tempered scale and the exact mathematical scale in + the point of the flattening of the fifth. Take for example + 1C, and for convenience of figuring, say it vibrates 128 + per second. The relation of a fundamental to its fifth is + that of 2 to 3. So if 128 is represented as 2, we think of + it as 2 times 64. Then with another 64 added, we have 192, + which represents 3. In other words, a fundamental has just + two-thirds of the number of vibrations per second that its + fifth has, in the exact scale. This would mean a fifth in + which there would be no beats. Now in the tempered scale we + find that G vibrates 191.78 instead of 192; so we can + easily see how much variation from the mathematical + standard there is in this portion of the instrument. It is + only about a fourth of a vibration. This would mean that, + in this fifth we would hear the beats a little slower than + one per second. Take the same fifth an octave higher and + take 2C as fundamental, which has 256 for its vibration + number. The G, fifth above, should vibrate 384, but in the + tempered scale it beats but 383.57, almost half a vibration + flat. This would give nearly 2 beats in 3 seconds. + </p> + <p> + <span class='pagenum'><a name="Page_107" + id="Page_107"></a>[Pg 107]</span> + </p> + <p> + These figures simply represent to the eye the ratios of + these sounds, and it is not supposed that a tuner is to + attain to such a degree of accuracy, but he should strive + to arrive as near it as possible. + </p> + <p> + It is well for the student to practice temperament setting + and regular tuning now if he can do so. After getting a + good temperament, proceed to tune by octaves upward, always + testing the tone tuned as a fifth and third until his ear + becomes sufficiently true on the octave that testing + otherwise is unnecessary. Tune the overstrung bass last and + your work is finished. If your first efforts are at all + satisfactory you should be greatly encouraged and feel + assured that accuracy will reward continued practice. + </p> + <p class="center"> + QUESTIONS ON LESSON X. + </p> + <ol> + <li> + What is meant by the term "equal temperament"? + </li> + <li> + What is meant by the term "unequal temperament"? + </li> + <li> + Webster defines the term "temperament" thus: "A system of + compromises in the tuning of pianofortes, organs, etc." + Explain fully what these compromises are. <span + class='pagenum'><a name="Page_108" id="Page_108"></a>[Pg + 108]</span> + </li> + <li> + In testing chords to ascertain if temperament is correct, + what is the main thing to listen for as a guide? + </li> + <li> + In what three chords would you try the tone A, in testing + your temperament? + </li> + <li> + With what results have you demonstrated the experiments + in this and the previous lesson? + </li> + </ol> + <hr style="width: 65%;" /> + <p> + <span class='pagenum'><a name="Page_109" + id="Page_109"></a>[Pg 109]</span> + </p> + <h2> + <a name="LESSON_XI" id="LESSON_XI"></a>LESSON XI. + </h2> + <hr style="width: 25%;" /> + <h3> + THE TECHNIQUE OR MODUS OPERANDI OF PIANO TUNING. + </h3> + <p> + At this juncture, it is thought prudent to defer the + discussion of scale building and detail some of the + requirements connected with the technical operations of + tuning. We do this here because some students are, at this + stage, beginning to tune and unless instructed in these + things will take hold of the work in an unfavorable way + and, perhaps, form habits that will be hard to break. + Especially is this so in the matter of setting the mutes or + wedges. As to our discussion of scale building, we shall + take that up again, that you may be more thoroughly + informed on that subject. + </p> + <p> + Some mechanics do more work in a given time than others, do + it as well or better, and with less exertion. This is + because they have method or system in their work so that + there are no movements <span class='pagenum'><a + name="Page_110" id="Page_110"></a>[Pg 110]</span>lost. + Every motion is made to count for the advancement of the + cause. Others go about things in a reckless way, taking no + thought as to time and labor-saving methods. + </p> + <p> + In spite of any instruction that can be given, the beginner + in piano tuning will not be able to take hold of his work + with the ease and the grace of the veteran, nor will he + ever be able to work with great accuracy and expedition + unless he has a systematic method of doing the various + things incident to his profession. + </p> + <p> + In this lesson, as its subject implies, we endeavor to tell + you just how to begin and the way to proceed, step by step, + through the work, to obtain the best results in the + shortest time, with the greatest ease and the least + confusion. + </p> + <p class="center smcap"> + Manipulation of the Tuning Hammer. + </p> + <p> + It may seem that the tightening of a string by turning a + pin, around which it is wound, by the aid of an instrument + fitting its square end, is such a simple operation that it + should require no skill. Simply tightening a string in this + manner is, to be sure, a simple matter; but there is a + definite degree of tension at which the <i>vibrating + section</i> of the string <span class='pagenum'><a + name="Page_111" id="Page_111"></a>[Pg 111]</span>must be + left, and it should be left in such a condition that the + tension will remain invariable, or as near so as is + possible. The only means given the tuner by which he is to + bring about this condition are his tuning hammer and the + key of the piano, with its mechanism, whereby he may strike + the string he is tuning. + </p> + <p> + The purpose of the tuning hammer is that of altering the + tension. The purpose of striking the string by means of the + key is twofold: first, to ascertain the pitch of the + string, and second, to equalize the tension of the string + over its entire length. Consider the string in its three + sections, viz.: lower dead end (from hitch pin to lower + bridge), vibrating section (section between the bridges), + and upper dead end (from upper bridge to tuning pin). + </p> + <p> + When placing the hammer on the tuning pin and turning to + the right, it is evident that the increased tension will be + manifest first in the upper dead end. In pianos having + agraffes or upper bridges with a tightly screwed bearing + bar which makes the strings draw very hard through the + bridge, some considerable tension may be produced in the + upper dead end before the string will draw through the + bridge and increase the tension in the vibrating middle. In + <span class='pagenum'><a name="Page_112" + id="Page_112"></a>[Pg 112]</span>other pianos the strings + "render" very easily over the upper bridge, and the + slightest turn of the hammer manifests an alteration of + pitch in the vibrating section. As a rule, strings "render" + much more easily through the upper, than the lower bridge. + There are two reasons for this: One is, that the + construction of the lower bridge is such as to cause a + tendency in this direction, having two bridge-pins which + stand out of line with the string and bear against it in + opposite directions; the other is that the lower bridge is + so much farther from the point where the hammer strikes the + string that its vibration does not help it through as it + does at the upper bridge. + </p> + <p> + Now, the thing desired is to have the tension equally + distributed over the entire length of the string. Tension + should be the same in the three different sections. This is + of paramount importance. If this condition does not obtain, + the piano will not stand in tune. Yet, this is not the only + item of importance. The tuning pin must be properly "set," + as tuners term it. + </p> + <p> + By "setting the pins," we mean, leaving it so balanced with + respect to the pull of the string that it will neither + yield to the pull of the string nor tend to <span + class='pagenum'><a name="Page_113" id="Page_113"></a>[Pg + 113]</span>draw it tighter. Coming now to the exact + manipulation of the tuning hammer, there are some important + items to consider.<a id="fnanchor_F" + name="fnanchor_F"></a><a href="#fn_F" + class="fnanchor">[F]</a> Now, if the tuning hammer is + placed upon the tuning pin with the handle straight upward, + and it is pulled backward (from the tuner) just a little, + before it is turned to the right, the tension will be + increased somewhat before the pin is turned, as this + motion, slight as it may seem, pulls the pin upward enough + to draw the string through the upper bridge an + infinitesimally small distance, but enough to be + perceptible to the ear. Now if the hammer were removed, the + tendency of the pin would be to yield to the pull of the + string; but if the pin is turned enough to take up such + amount of string as was pulled through the bridge, and, as + it is turned, is allowed to yield downward toward the pull + of the string, it will resume its balance and the string + will stand at that pitch, provided it has been "rendered" + properly over the bridges. + </p> + <p> + We set forth these details that you may have a thorough + understanding of what is meant by setting the pins, and + while it is not always advisable to <span + class='pagenum'><a name="Page_114" id="Page_114"></a>[Pg + 114]</span>follow this method in tuning, there are some + pianos that will stand more satisfactorily when treated in + this way. This method is recommended where the string has + become rusty at the upper bridge, as it is loosened at the + bridge before it is started to wind around the pin which + prevents it breaking at that point. We believe that ninety + per cent. of strings break right where they start around + tuning pin. A very good way to draw a string up is to give + the hammer an alternate up and down motion, pulling the + handle lightly to you, then from you, as you draw it up; + not enough to bend or break the pin or to crush the wood + around the pin, but just enough to make the string take on + its increased tension equally. + </p> + <p> + In regard to the lower bridge, the strings will rarely + "render" through them properly unless brought to a tension + a little higher than it is desired they shall be left. If + this is done, a few sharp blows of key will generally make + them equalize all right; then press the hammer gently to + the left, not enough to turn the pin in the socket, but to + settle it back to a well-balanced position. After a little + practice the tuner can generally guess precisely how much + <span class='pagenum'><a name="Page_115" + id="Page_115"></a>[Pg 115]</span>over-tension to allow. If + the pin is left slightly sprung downward, its tendency will + be to spring upward, thereby sharpening the string; so be + careful to leave the pins in perfect balance, or as tuners + say, "properly set." + </p> + <p> + The foregoing, while applicable to the whole scale, is not + so urgent in the over-strung bass. The strings are so heavy + and the tension is so great that they will generally + "render" quite freely over the bridges, and it is only + necessary to bring them up to pitch, handling the hammer in + such a manner as to leave the pins well balanced; but it is + not necessary to give them over-tension and beat them down + again; in fact it is not advisable, as a rule. At all + times, place the hammer on the pin as far as it will go, + and strike the key while drawing a string up. + </p> + <p> + In tuning the square piano, it is not possible to set the + hammer upon the pin with the handle in line with, and + beyond the string, as is the rule in the upright. Where the + square has the square pin, the hammer (with star head) can + always be set with the handle to the right of the string + somewhat, but usually almost in line with the string and + almost directly over it, and the manipulation of the hammer + <span class='pagenum'><a name="Page_116" + id="Page_116"></a>[Pg 116]</span>is much the same, though + the tuner is at a greater disadvantage, the pins being + farther from him and he has not such a good rest for his + hand. Many old squares have the oblong pin. In this case, + use the double hammer head. On the one side the hole in the + head is made with the longer diameter in line with the + handle, and on the other side the hole is made with the + longer diameter at right angles with the handle; so that if + you cannot get a favorable position with one end you can + with the other. + </p> + <p> + We have said nothing about which hand to use in striking + the keys and in wielding the hammer, but it is customary to + handle the hammer with the right hand and it is always + advisable for two very good reasons: It gives the tuner a + much more favorable position at the instrument; and, as the + right hand is more used in ordinary every-day operations + and is more trained in applying degrees of force and + guiding tools, it is more easily trained to manipulate the + hammer properly. Training the hand in the skilful use of + the hammer is of the utmost importance and comes only by + continued practice, but when it is trained, one can + virtually "feel" the tones with the hammer. + </p> + <p> + <span class='pagenum'><a name="Page_117" + id="Page_117"></a>[Pg 117]</span> + </p> + <p> + At first, the young tuner is almost invariably discouraged + by his slow progress. He must remember that, however fine + his ear and however great his mechanical ability, he has + much to acquire by training in both, and he must expect to + be two or three times longer in finishing off a job of + tuning at the outset than will be necessary after he has + had a few months' practice. You can be your own trainer in + these things if you will do a little rational thinking and + be content to "hasten slowly." And as to using the left + hand, we would not advise it in any event. + </p> + <p class="center smcap"> + Setting the Mutes or Wedges in the Upright. + </p> + <p> + As stated in a previous lesson, the mutes should be so + placed that only two strings are heard at one time: the one + the tuner is tuning, and the one he is tuning by. It is + true that this is an easy matter, but it is also true that + very few tuners know how to do it in a way to save time and + avoid placing the mutes two or more times in the same + place. By using a little inventive genius during early + practice the author succeeded in formulating a system of + muting by which he accomplished the ends as stated <span + class='pagenum'><a name="Page_118" id="Page_118"></a>[Pg + 118]</span>above, and assures the reader that a great deal + of time can be saved by following it. + </p> + <p> + After removing the muffler or any other instrumental + attachment which may be in the piano in the way of placing + the mutes, the first thing to do is to place the continuous + mute so that all the outside strings of the trios are + damped. The temperament is then set by tuning the middle + strings, of the twenty-five trios comprised in the + two-octave temperament as demonstrated in a previous + lesson. After satisfying yourself by trials or test that + the temperament is true, you then remove the continuous + mute and proceed to bring the outside strings in unison + with the middle one. Now, your 1C is sometimes found to be + the first pair in the over-strung bass, which usually has + two strings to a key, while in other pianos, 1C is the + first trio in the treble stringing, and in many cases it is + the second trio in the treble. For illustration, we will + say it is the second in the treble. In speaking of the + separate strings of a trio we will number them 1st, 2d, and + 3d, from left to right, as in foot-note, page 89, Lesson + IX. Setting the mutes in bringing up the unisons in the + temperament is exceedingly simple. + </p> + <p> + <span class='pagenum'><a name="Page_119" + id="Page_119"></a>[Pg 119]</span> + </p> + <p> + The following diagram will, we think, demonstrate clearly + the method employed: + </p> + <div class="center"> + <div class="figcenter" style="width: 600px;"> + <img src="images/image119.jpg" width="600" height="173" + alt="Use of continuous mute" + title="Use of continuous mute" /> + </div> + </div> + <p> + The upper row of O's represents the upper row of tuning + pins. To these are attached the first string of each + unison. To the middle row are attached the second or middle + strings, and to the lower row are attached the third + strings. The diagonal lines represent the three strings of + the unison (trio). The asterisk on the middle one indicates + that it has been tuned. + </p> + <p> + But one mute is used in tuning these unisons. It is + inserted between the trios in the order indicated by the + figures 1, 2, 3, etc. When inserted in place 1, between + unisons B and C, it will mute the first string of C; so the + first string of the trio to tune is always the third. Then + place your mute in place 2 and tune the first string of C. + Then, without moving your mute, bring up third string of + C♯, <span class='pagenum'><a name="Page_120" + id="Page_120"></a>[Pg 120]</span>then third string of D and + so on. By this method, you tune two strings every time you + reset your mute. + </p> + <p> + When through with the temperament, the next step is usually + that of tuning the bass; but while we are in the treble we + will proceed to give the method of setting the mutes in the + upper treble beyond the temperament. All three strings have + yet to be tuned here, and we have to use two mutes. The + unisons are tuned in regular succession upward the same as + in the example above. The mute that is kept farthest to the + left, is indicated by the letter A, and the one kept to the + right, by the letter B, as in diagram below. + </p> + <div class="center"> + <div class="figcenter" style="width: 600px;"> + <img src="images/image120.jpg" width="600" height="80" + alt="Use of two mutes" title="Use of two mutes" /> + </div> + </div> + <p> + The mutes are first placed in the places indicated by the + figures 1 and 2, thereby muting first and third strings of + the first unison beyond the temperament, which is + 3C♯. The middle string of this unison is now tuned by + its octave below. (If you have left imperfect unisons in + your temperament, rendering it difficult to tune octaves by + them, it will be well to <span class='pagenum'><a + name="Page_121" id="Page_121"></a>[Pg 121]</span>replace + your continuous mute so as to tune from a single string.) + Having tuned the middle string of C♯, move mute B to + place 3 and tune third string of C♯. Then, move mute + A to place 2 and tune first string of C♯. Your mutes + are now already set for tuning the middle string of D. + After this is done, proceed to move mute B first, then mute + A; tuning middle string, then third, then first, moving + step by step as indicated in example above until the last + unison is reached. By this system you tune three strings + every time the mutes are set twice. + </p> + <p> + The over-strung bass usually has but two strings to a + unison and only one mute is needed. In the extreme low or + contra-bass, pianos have but one string, in tuning which + the mute is discarded. Set the mute as indicated by the + figures 1, 2, 3, etc., in the diagram below, always tuning + the string farthest to the right by its octave above; then + move the mute to its next place and tune the left string by + the right. Here, again, you tune two strings every time you + reset your mute. The I's represent bass strings. + </p> + <div class="center"> + <div class="figcenter" style="width: 600px;"> + <img src="images/image121.jpg" width="600" height="85" + alt="Tuning the Bass" title="Tuning the Bass" /> + </div> + </div> + <p> + <span class='pagenum'><a name="Page_122" + id="Page_122"></a>[Pg 122]</span> + </p> + <p class="center smcap"> + Setting the Mutes in the Square Piano. + </p> + <p> + In setting the temperament in the square piano, simply mute + the string farthest to the left and tune the one to the + right until the temperament is finished, then set the mutes + in the bass the same as in the upright. In tuning the + treble, if the piano has three strings, the same system is + used as has been described for the upright. When the piano + has but two strings to a unison, as is usually the case, + employ the system described for the bass of the upright, + but reversed, as you are proceeding to the right instead of + to the left. + </p> + <p> + Remove the shade before beginning to tune a square piano, + and if necessary, lay the dampers back and trace the + strings to their pins so as to mark them. Certain pins are + marked to guide the tuner in placing his hammer. The way we + have always marked them is as follows: + </p> + <p> + Mark both pins of each pair of C strings with white crayon. + Mark only one pin of each pair of G's. Knowing the + intervals of the other keys from the marked ones, you can + easily calculate correctly, <span class='pagenum'><a + name="Page_123" id="Page_123"></a>[Pg 123]</span>upon which + pin to set your hammer to tune any string desired. For + instance, if you are striking D♯, next above middle + C, you calculate that, as D♯ is the third chromatic + interval from middle C, you are to set the hammer on one or + the other of the pins belonging to the third pair to the + right of the pair marked as middle C. B would be first pair + to the left, F♯ would be first pair to the left of + the marked G, and so on. It is usually necessary to mark + only those pairs near the middle of the piano, but we + advise the beginner to mark throughout the scale, as by so + doing he may avoid breaking a string occasionally by + pulling on some other than the one he is sounding. This + will occur in your early practice if you do not use + caution. And for safety, some tuners always mark + throughout. + </p> + <p class="center"> + QUESTIONS ON LESSON XI. + </p> + <ol> + <li> + By what means is the tuner enabled to make the strings + draw through the bridges and equalize the tension + throughout their entire length? + </li> + <li> + State conditions that may result from a tuning pin's not + being properly set. <span class='pagenum'><a + name="Page_124" id="Page_124"></a>[Pg 124]</span> + </li> + <li> + In this system of muting, state definitely which string + is tuned first after the continuous mute is removed. + Which second? Which third? + </li> + <li> + After the unisons are finished in the temperament, which + string is tuned next, if we go immediately from the + temperament to the over-strung bass? Which second? Which + third? + </li> + <li> + Upon beginning to tune the treble beyond the temperament, + which string is tuned first? Which second? Which third? + </li> + <li> + (a) How many mutes are used in tuning outside the strings + of the temperament?<br /> + (b) In what proportion is the number of times the mute + is changed to the number of strings tuned? + </li> + <li> + (a) How many mutes are used in tuning the treble beyond + the temperament?<br /> + (b) In what proportion is the number of times the mute + is changed to the number of strings tuned? + </li> + <li> + Which pairs of pins are marked in the square piano to + guide the tuner in placing his hammer? Also, how are they + marked? <span class='pagenum'><a name="Page_125" + id="Page_125"></a>[Pg 125]</span> + </li> + <li> + Having marked your pins as instructed, how would you find + the pins belonging to a pair of strings struck by F on + key-board? How those struck by G♯? + </li> + <li> + Tell what you can of the requirements necessary to insure + that a piano will stand in tune. + </li> + </ol> + <hr style="width: 65%;" /> + <p><span class='pagenum'><a name="Page_126" + id="Page_126"></a>[Pg 126]</span></p> + <h2> + <a name="LESSON_XII" id="LESSON_XII"></a>LESSON XII. + </h2> + <hr style="width: 25%;" /> + <h3> + MATHEMATICS OF THE TEMPERED SCALE. + </h3> + <p> + One of the first questions that arises in the mind of the + thinking young tuner is: Why is it necessary to temper + certain intervals in tuning? We cannot answer this question + in a few words; but you have seen, if you have tried the + experiments laid down in previous lessons, that such + deviation is inevitable. You know that practical scale + making will permit but two pure intervals (unison and + octave), but you have yet to learn the scientific reasons + why this is so. To do this, requires a little mathematical + reasoning. + </p> + <p> + In this lesson we shall demonstrate the principles of this + complex subject in a clear and comprehensive way, and if + you will study it carefully you may master it thoroughly, + which will place you in possession of a knowledge of the + art of which few tuners of the present can boast. + </p> + <p> + In the following demonstrations of relative pitch numbers, + we adopt a pitch in which middle C has 256 vibrations per + second. This is not a pitch <span class='pagenum'><a + name="Page_127" id="Page_127"></a>[Pg 127]</span>which is + used in actual practice, as it is even below international + (middle C 258.65); but is chosen on account of the fact + that the various relative pitch numbers work out more + favorably, and hence, it is called the "Philosophical + Standard." Below are the actual vibration numbers of the + two pitches in vogue; so you can see that neither of these + pitches would be so favorable to deal with mathematically. + </p> + <p> + International—3C–517.3. + Concert—3C–540. + </p> + <p> + (Let us state here that the difference in these pitches is + less than a half-step, but is so near that it is generally + spoken of as being just a half-step.) + </p> + <p> + Temperament denotes the arrangement of a system of musical + sounds in which <i>each one</i> will form a serviceable + interval with <i>any one</i> of the others. Any given tone + must do duty as the initial or key-note of a major or of a + minor scale and also as any other member; thus: + </p> + <div class="center"> + <table> + <tr> + <td>C must</td> + <td>serve as</td> + <td>1,</td> + <td>in the</td> + <td>key of</td> + <td>C</td> + <td>major or</td> + <td>C</td> + <td>minor.</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td>2,</td> + <td class="center">"</td> + <td class="center">"</td> + <td>B♭</td> + <td class="center">"</td> + <td>B♭</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td>3,</td> + <td class="center">"</td> + <td class="center">"</td> + <td>A♭</td> + <td class="center">"</td> + <td>A</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td>4,</td> + <td class="center">"</td> + <td class="center">"</td> + <td>G</td> + <td class="center">"</td> + <td>G</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td>5,</td> + <td class="center">"</td> + <td class="center">"</td> + <td>F</td> + <td class="center">"</td> + <td>F</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td>6,</td> + <td class="center">"</td> + <td class="center">"</td> + <td>E♭</td> + <td class="center">"</td> + <td>E</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td>7,</td> + <td class="center">"</td> + <td class="center">"</td> + <td>D♭</td> + <td class="center">"</td> + <td>C♯</td> + <td class="center">"</td> + </tr> + </table> + </div> + <p> + <span class='pagenum'><a name="Page_128" + id="Page_128"></a>[Pg 128]</span>Likewise, all other tones + of the instrument must be so stationed that they can serve + as <i>any member</i> of <i>any scale</i>, major or minor. + </p> + <p> + This is rendered necessary on account of the various + modulations employed in modern music, in which every + possible harmony in every key is used. + </p> + <p class="center smcap"> + Rationale of the Temperament. + </p> + <p> + Writers upon the mathematics of sound tell us, experience + teaches us, and in previous lessons we have demonstrated in + various ways, that if we tune all fifths perfect up to the + seventh step (see diagram, pages 82, 83) the last E + obtained will be too sharp to form a major third to C. In + fact, the third thus obtained is so sharp as to render it + offensive to the ear, and therefore unfit for use in + harmony, where this interval plays so conspicuous a part. + To remedy this, it becomes necessary to tune each of the + fifths a very small degree flatter than perfect. The E thus + obtained will not be so sharp as to be offensive to the + ear; yet, if the fifth be properly altered or tempered, the + third will still be sharper than perfect; for if the fifths + were flattened enough to render the thirds perfect, they + (the fifths) would become offensive. Now, it is a fact, + that the third will bear greater <span class='pagenum'><a + name="Page_129" id="Page_129"></a>[Pg 129]</span>deviation + from perfect consonance than the fifth; so the compromise + is made somewhat in favor of the fifth. If we should + continue the series of perfect fifths, we will find the + same defect in all the major thirds throughout the scale. + </p> + <p> + We must, therefore, flatten each fifth of the complete + circle, C-G-D-A-E-B-F♯-C♯-G♯ or + A♭-E♭-B♭-F-C, successively in a very + small degree; the depression, while it will not materially + impair the consonant quality of the fifths, will produce a + series of somewhat sharp, though still agreeable and + harmonious major thirds. + </p> + <p> + We wish, now, to demonstrate the cause of the foregoing by + mathematical calculation, which, while it is somewhat + lengthy and tedious, is not difficult if followed + progressively. First, we will consider tone relationship in + connection with relative string length. Students who have + small stringed instruments, guitar, violin, or mandolin, + may find pleasure in demonstrating some of the following + facts thereupon. + </p> + <p> + One-half of any string will produce a tone exactly an + octave above that yielded by its entire length. Harmonic + tones on the violin are made by <span class='pagenum'><a + name="Page_130" id="Page_130"></a>[Pg 130]</span>touching + the string lightly with the finger at such points as will + cause the string to vibrate in segments; thus if touched + exactly in the middle it will produce a harmonic tone an + octave above that of the whole string. + </p> + <p> + Two-thirds of the length of a string when stopped produces + a tone a fifth higher than that of the entire string; + one-third of the length of a string on the violin, either + from the nut or from the bridge, if touched lightly with + the finger at that point, produces a harmonic tone an + octave higher than the fifth to the open tone of that + string, because you divide the string into three vibrating + segments, each of which is one-third its entire length. + Reason it thus: If two-thirds of a string produce a fifth, + one-third, being just half of two-thirds, will produce a + tone an octave higher than two-thirds. For illustration, if + the string be tuned to 1C, the harmonic tone produced as + above will be 2G. We might go on for pages concerning + harmonics, but for our present use it is only necessary to + show the general principles. For our needs we will discuss + the relative length of string necessary to produce the + various tones of the diatonic scale, showing ratios of the + intervals in the same. + </p> + <p> + <span class='pagenum'><a name="Page_131" + id="Page_131"></a>[Pg 131]</span> + </p> + <p> + In the following table, 1 represents the entire length of a + string sounding the tone C. The other tones of the + ascending major scale require strings of such fractional + length as are indicated by the fractions beneath them. By + taking accurate measurements you can demonstrate these + figures upon any small stringed instrument. + </p> + <div class="center"> + <table cellspacing="5"> + <tr> + <td class="center smcap">Fundamental</td> + <td class="center smcap">Major<br />Second</td> + <td class="center smcap">Major<br />Third</td> + <td class="center smcap">Perfect<br />Fourth</td> + <td class="center smcap">Perfect<br />Fifth</td> + <td class="center smcap">Major<br />Sixth</td> + <td class="center smcap">Major<br />Seventh</td> + <td class="center smcap">Octave</td> + </tr> + <tr> + <td class="center smcap">C</td> + <td class="center smcap">D</td> + <td class="center smcap">E</td> + <td class="center smcap">F</td> + <td class="center smcap">G</td> + <td class="center smcap">A</td> + <td class="center smcap">B</td> + <td class="center smcap">C</td> + </tr> + <tr> + <td class="center smcap">1</td> + <td class="center smcap">8/9</td> + <td class="center smcap">4/5</td> + <td class="center smcap">3/4</td> + <td class="center smcap">2/3</td> + <td class="center smcap">3/5</td> + <td class="center smcap">8/15</td> + <td class="center smcap">1/2</td> + </tr> + </table> + </div> + <p> + To illustrate this principle further and make it very + clear, let us suppose that the entire length of the string + sounding the fundamental C is 360 inches; then the segments + of this string necessary to produce the other tones of the + ascending major scale will be, in inches, as follows: + </p> + <div class="center"> + <table cellspacing="10"> + <tr> + <td class="center">C</td> + <td class="center">D</td> + <td class="center">E</td> + <td class="center">F</td> + <td class="center">G</td> + <td class="center">A</td> + <td class="center">B</td> + <td class="center">C</td> + </tr> + <tr> + <td class="center">360</td> + <td class="center">320</td> + <td class="center">288</td> + <td class="center">270</td> + <td class="center">240</td> + <td class="center">216</td> + <td class="center">192</td> + <td class="center">180</td> + </tr> + </table> + </div> + <p> + Comparing now one with another (by means of the ratios + expressed by their corresponding numbers) the intervals + formed by the tones of the above scale, it will be found + that they all preserve their original <span + class='pagenum'><a name="Page_132" id="Page_132"></a>[Pg + 132]</span>purity except the minor third, D-F, and the + fifth, D-A. The third, D-F, presents itself in the ratio of + 320 to 270 instead of 324 to 270 (which latter is + equivalent to the ratio of 6 to 5, the true ratio of the + minor third). The third, D-F, therefore, is to the true + minor third as 320 to 324 (reduced to their lowest terms by + dividing both numbers by 4, gives the ratio of 80 to 81). + Again, the fifth, A-F, presents itself in the ratio of 320 + to 216, or (dividing each term by 4) 80 to 54; instead of 3 + to 2 (=81 to 54multiplying each term by 27), which is the + ratio of the true fifth. Continuing the scale an octave + higher, it will be found that the sixth, F-D, and the + fourth, A-D, will labor under the same imperfections. + </p> + <p> + The comparison, then, of these ratios of the minor third, + D-F, and the fifth, D-A, with the perfect ratios of these + intervals, shows that each is too small by the ratio + expressed by the figures 80 to 81. This is called, by + mathematicians, the <i>syntonic comma</i>. + </p> + <p> + As experience teaches us that the ear cannot endure such + deviation as a whole comma in any fifth, it is easy to see + that some tempering must take place even in such a simple + and limited number of sounds as the above series of eight + tones. + </p> + <p> + <span class='pagenum'><a name="Page_133" + id="Page_133"></a>[Pg 133]</span> + </p> + <p> + The necessity of temperament becomes still more apparent + when it is proposed to combine every sound used in music + into a connected system, such that each individual sound + shall not only form practical intervals with all the other + sounds, but also that each sound may be employed as the + root of its own major or minor key; and that all the tones + necessary to form its scale shall stand in such relation to + each other as to satisfy the ear. + </p> + <p> + The chief requisites of any system of musical temperament + adapted to the purposes of modern music are: + </p> + <p> + 1. That all octaves must remain perfect, each being divided + into twelve semitones. + </p> + <p> + 2. That each sound of the system may be employed as the + root of a major or minor scale, without increasing the + number of sounds in the system. + </p> + <p> + 3. That each consonant interval, according to its degree of + consonance, shall lose as little of its original purity as + possible; so that the ear may still acknowledge it as a + perfect or imperfect consonance. + </p> + <p> + Several ways of adjusting such a system of temperament have + been proposed, all of which may be classed under either the + head of equal or of unequal temperament. + </p> + <p> + <span class='pagenum'><a name="Page_134" + id="Page_134"></a>[Pg 134]</span> + </p> + <p> + The principles set forth in the following propositions + clearly demonstrate the reasons for tempering, and the + whole rationale of the system of equal temperament, which + is that in general use, and which is invariably sought and + practiced by tuners of the present. + </p> + <p class="center smcap"> + Proposition I. + </p> + <p> + If we divide an octave, as from middle C to 3C, into three + major thirds, each in the perfect ratio of 5 to 4, as C-E, + E-G♯ (A♭), A♭-C, then the C obtained from + the last third, A♭-C, will be too flat to form a + perfect octave by a small quantity, called in the theory of + harmonics a <i>diesis</i>, which is expressed by the ratio + 128 to 125. + </p> + <p> + <span class="smcap">Explanation</span>. The length of the + string sounding the tone C is represented by unity or 1. + Now, as we have shown, the major third to that C, which is + E, is produced by <span class="sf">4/5</span> of its + length. + </p> + <p> + In like manner, G♯, the major third to E, will be + produced by <span class="sf">4/5</span> of that segment of + the string which sounds the tone E; that is, G♯ will + be produced by <span class="sf">4/5</span> of <span + class="sf">4/5</span> ( <span class="sf">4/5</span> + multiplied by <span class="sf">4/5</span>) which equals + <span class="sf">16/25</span> of the entire length of the + string sounding the tone C. + </p> + <p> + <span class='pagenum'><a name="Page_135" + id="Page_135"></a>[Pg 135]</span> + </p> + <p> + We come, now, to the last third, G♯ (A♭) to C, + which completes the interval of the octave, middle C to 3C. + This last C, being the major third from the A♭, will + be produced as before, by <span class="sf">4/5</span> of + that segment of the string which sounds A♭; that is, + by <span class="sf">4/5</span> of <span + class="sf">16/25</span>, which equals <span + class="sf">64/125</span> of the entire length of the + string. Keep this last fraction, <span + class="sf">64/125</span>, in mind, and remember it as + representing the segment of the entire string, which + produces the upper C by the succession of three perfectly + tuned major thirds. + </p> + <p> + Now, let us refer to the law which says that a perfect + octave is obtained from the exact half of the length of any + string. Is <span class="sf">64/125</span> an exact half? + No; using the same numerator, an exact half would be <span + class="sf">64/128</span>. + </p> + <p> + Hence, it is clear that the octave obtained by the + succession of perfect major thirds will differ from the + true octave by the ratio of 128 to 125. The fraction, <span + class="sf">64/125</span>, representing a longer segment of + the string than <span class="sf">64/128</span> (½), + it would produce a flatter tone than the exact half. + </p> + <p> + It is evident, therefore, that <i>all major thirds must be + tuned somewhat sharper than perfect</i> in a system of + equal temperament. + </p> + <p> + <span class='pagenum'><a name="Page_136" + id="Page_136"></a>[Pg 136]</span> + </p> + <p> + The ratio which expresses the value of the <i>diesis</i> is + that of 128 to 125. If, therefore, the octaves are to + remain perfect, which they must do, <i>each major third + must be tuned sharper than perfect by one-third part of the + diesis</i>. + </p> + <p> + The foregoing demonstration may be made still clearer by + the following diagram which represents the length of string + necessary to produce these tones. (This diagram is exact in + the various proportional lengths, being about one + twenty-fifth the actual length represented.) + </p> + <div class="center"> + <div class="figcenter" style="width: 600px;"> + <img src="images/image136.jpg" width="600" height="230" + alt="" + title="Relationship of Length of String to Tone" /> + </div> + </div> + <p> + This diagram clearly demonstrates that the last C obtained + by the succession of thirds covers a segment of the string + which is <span class="sf">18/25</span> longer than an exact + half; nearly three-fourths of an inch too long, 30 inches + being the exact half. + </p> + <p> + <span class='pagenum'><a name="Page_137" + id="Page_137"></a>[Pg 137]</span> + </p> + <p> + To make this proposition still better understood, we give + the comparison of the actual vibration numbers as follows: + </p> + <div class="center"> + <div class="figcenter" style="width: 400px;"> + <img src="images/image137.png" width="400" height="178" + alt="" title="Actual vibration numbers" /> + </div> + </div> + <p> + We think the foregoing elucidation of Proposition I + sufficient to establish a thorough understanding of the + facts set forth therein, if they are studied over carefully + a few times. If everything is not clear at the first + reading, go over it several times, as this matter is of + value to you. + </p> + <p class="center"> + QUESTIONS ON LESSON XII. + </p> + <ol> + <li> + Why is the pitch, C-256, adopted for scientific + discussion, and what is this pitch called? + </li> + <li> + The tone G forms the root (1) in the key of G. What does + it form in the key of C? What in F? What in D? <span + class='pagenum'><a name="Page_138" id="Page_138"></a>[Pg + 138]</span> + </li> + <li> + What tone is produced by a <span class="sf">2/3</span> + segment of a string? What by a <span + class="sf">1/2</span> segment? What by a <span + class="sf">4/5</span> segment? + </li> + <li> + (a) What intervals must be tuned absolutely + perfect?<br /> + (b) In the two intervals that must be tempered, the + third and the fifth, which will bear the greater + deviation? + </li> + <li> + What would be the result if we should tune from 2C to 3C + by a succession of perfect thirds? + </li> + <li> + Do you understand the facts set forth in Proposition I, + in this lesson? + </li> + </ol> + <hr style="width: 65%;" /> + <p><span class='pagenum'><a name="Page_139" + id="Page_139"></a>[Pg 139]</span></p> + <h2> + <a name="LESSON_XIII" id="LESSON_XIII"></a>LESSON XIII. + </h2> + <hr /> + <h3> + RATIONALE OF THE TEMPERAMENT.<br /> + <span class="sf">(Concluded from Lesson XII.)</span> + </h3> + <p class="center smcap"> + Proposition II. + </p> + <p> + That the student of scientific scale building may + understand fully the reasons why the tempered scale is at + constant variance with exact mathematical ratios, we + continue this discussion through two more propositions, No. + II, following, demonstrating the result of dividing the + octave into four minor thirds, and Proposition III, + demonstrating the result of twelve perfect fifths. The + matter in Lesson XII, if properly mastered, has given a + thorough insight into the principal features of the subject + in question; so the following demonstration will be made as + brief as possible, consistent with clearness. + </p> + <p> + Let us figure the result of dividing an octave into four + minor thirds. The ratio of the length of string sounding a + fundamental, to the length necessary to sound its minor + third, is that of 6 to 5. In other <span class='pagenum'><a + name="Page_140" id="Page_140"></a>[Pg 140]</span>words, + <span class="sf">5/6</span> of any string sounds a tone + which is an exact minor third above that of the whole + string. + </p> + <p> + Now, suppose we select, as before, a string sounding middle + C, as the fundamental tone. We now ascend by minor thirds + until we reach the C, octave above middle C, which we call + 3C, as follows: + </p> + <p class="center sf"> + Middle C-E♭;Â Â E♭-F♯;Â Â F♯-A;Â Â A-3C. + </p> + <p> + Demonstrate by figures as follows:Let the whole length of + string sounding middle C be represented by unity or 1. + </p> + <table cellspacing="5"> + <tr> + <td>E♭ will be sounded by 5/6 of the string</td> + <td>5/6</td> + </tr> + <tr> + <td>F♯, by 5/6 of the E♭ segment; that is, by + 5/6 of 5/6 of the entire string, which equals</td> + <td>25/36</td> + </tr> + <tr> + <td>A, by 5/6 of 25/36 of entire string, which equals</td> + <td>125/216</td> + </tr> + <tr> + <td>3C, by 5/6 of 125/216 of entire string, which equals</td> + <td>625/1296</td> + </tr> + </table> + <p> + Now bear in mind, this last fraction, <span + class="sf">625/1296</span>, represents the segment of the + entire string which should sound the tone 3C, an exact + octave above middle C. Remember, our law demands an exact + half of a string by which to sound its octave. How much + does it vary? Divide the denominator (1296) by 2 and place + the result over it for a numerator, and <span + class='pagenum'><a name="Page_141" id="Page_141"></a>[Pg + 141]</span>this gives <span class="sf">648/1296</span>, + which is an exact half. Notice the comparison. + </p> + <table cellspacing="5"> + <tr> + <td>3C obtained from a succession of exact minor thirds,</td> + <td>625/1296</td> + </tr> + <tr> + <td>3C obtained from an exact half of the string</td> + <td>648/1296</td> + </tr> + </table> + <p> + Now, the former fraction is smaller than the latter; hence, + the segment of string which it represents will be shorter + than the exact half, and will consequently yield a sharper + tone. The denominators being the same, we have only to find + the difference between the numerators to tell how much too + short the former segment is. This proves the C obtained by + the succession of minor thirds to be too short by <span + class="sf">23/1296</span> of the length of the whole + string. + </p> + <p> + If, therefore, all octaves are to remain perfect, it is + evident that <i>all minor thirds must be tuned flatter than + perfect</i> in the system of equal temperament. + </p> + <p> + The ratio, then, of 648 to 625 expresses the excess by + which the true octave exceeds four exact minor thirds; + consequently, each minor third must be flatter than perfect + by one-fourth part of the difference between these + fractions. By this means the dissonance is evenly + distributed so that it is not noticeable in the various + chords, in the major and <span class='pagenum'><a + name="Page_142" id="Page_142"></a>[Pg 142]</span>minor + keys, where this interval is almost invariably present. (We + find no record of writers on the mathematics of sound + giving a name to the above ratio expressing variance, as + they have to others.) + </p> + <p class="center smcap"> + Proposition III. + </p> + <p> + Proposition III deals with the perfect fifth, showing the + result from a series of twelve perfect fifths employed + within the space of an octave. + </p> + <p> + <span class="smcap">Method</span>. Taking 1C as the + fundamental, representing it by unity or 1, the G, fifth + above, is sounded by a <span class="sf">2/3</span> segment + of the string sounding C. The next fifth, G-D, takes us + beyond the octave, and we find that the D will be sounded + by <span class="sf">4/9</span> (<span class="sf">2/3</span> + of <span class="sf">2/3</span> equals <span + class="sf">4/9</span>) of the entire string, which fraction + is less than half; so to keep within the bounds of the + octave, we must double this segment and make it sound the + tone D an octave lower, thus: <span class="sf">4/9</span> + times 2 equals <span class="sf">8/9</span>, the segment + sounding the D within the octave. + </p> + <p> + We may shorten the operation as follows: Instead of + multiplying <span class="sf">2/3</span> by <span + class="sf">2/3</span>, giving us <span + class="sf">4/9</span>, and then multiplying this answer by + 2, let us double the fraction, <span class="sf">2/3</span>, + which equals <span class="sf">4/3</span>, and use it as a + multiplier when it becomes necessary to double the segment + to keep within the octave. + </p> + <p> + <span class='pagenum'><a name="Page_143" + id="Page_143"></a>[Pg 143]</span> + </p> + <p> + We may proceed now with the twelve steps as follows: + </p> + <p> + Steps + </p> + <div class="center"> + <table> + <tr> + <td>1.</td> + <td>1C</td> + <td>to</td> + <td>1G</td> + <td colspan="5"></td> + <td>segment</td> + <td>2/3</td> + <td>for</td> + <td>1G</td> + </tr> + <tr> + <td>2.</td> + <td>1G</td> + <td class="center">"</td> + <td>1D</td> + <td>Multiply</td> + <td>2/3</td> + <td>by</td> + <td>4/3,</td> + <td>gives</td> + <td>segment</td> + <td>8/9</td> + <td class="center">"</td> + <td>1D</td> + </tr> + <tr> + <td>3.</td> + <td>1D</td> + <td class="center">"</td> + <td>1A</td> + <td class="center">"</td> + <td>8/9</td> + <td class="center">"</td> + <td>2/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>16/27</td> + <td class="center">"</td> + <td>1A</td> + </tr> + <tr> + <td>4.</td> + <td>1A</td> + <td class="center">"</td> + <td>1E</td> + <td class="center">"</td> + <td>16/27</td> + <td class="center">"</td> + <td>4/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>64/81</td> + <td class="center">"</td> + <td>1E</td> + </tr> + <tr> + <td>5.</td> + <td>1E</td> + <td class="center">"</td> + <td>1B</td> + <td class="center">"</td> + <td>64/81</td> + <td class="center">"</td> + <td>2/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>128/243</td> + <td class="center">"</td> + <td>1B</td> + </tr> + <tr> + <td>6.</td> + <td>1B</td> + <td class="center">"</td> + <td>1F♯</td> + <td class="center">"</td> + <td>128/243</td> + <td class="center">"</td> + <td>4/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>512/729</td> + <td class="center">"</td> + <td>1F♯</td> + </tr> + <tr> + <td>7.</td> + <td>1F♯</td> + <td class="center">"</td> + <td>1C♯</td> + <td class="center">"</td> + <td>512/729</td> + <td class="center">"</td> + <td>4/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>2048/2187</td> + <td class="center">"</td> + <td>1C♯</td> + </tr> + <tr> + <td>8.</td> + <td>1C♯</td> + <td class="center">"</td> + <td>1G♯</td> + <td class="center">"</td> + <td>2048/2187</td> + <td class="center">"</td> + <td>2/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>4096/6561</td> + <td class="center">"</td> + <td>1G♯</td> + </tr> + <tr> + <td>9.</td> + <td>1G♯</td> + <td class="center">"</td> + <td>1D♯</td> + <td class="center">"</td> + <td>4096/6561</td> + <td class="center">"</td> + <td>4/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>16384/19683</td> + <td class="center">"</td> + <td>1D♯</td> + </tr> + <tr> + <td>10.</td> + <td>1D♯</td> + <td class="center">"</td> + <td>1A♯</td> + <td class="center">"</td> + <td>16384/19683</td> + <td class="center">"</td> + <td>2/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>32768/59049</td> + <td class="center">"</td> + <td>1A♯</td> + </tr> + <tr> + <td>11.</td> + <td>1A♯</td> + <td class="center">"</td> + <td>1F</td> + <td class="center">"</td> + <td>32768/59049</td> + <td class="center">"</td> + <td>4/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>131072/177147</td> + <td class="center">"</td> + <td>1F</td> + </tr> + <tr> + <td>12.</td> + <td>1F</td> + <td class="center">"</td> + <td>2C</td> + <td class="center">"</td> + <td>131072/177147</td> + <td class="center">"</td> + <td>2/3</td> + <td class="center">"</td> + <td class="center">"</td> + <td>262144/531441</td> + <td class="center">"</td> + <td>2C</td> + </tr> + </table> + </div> + <p> + Now, this last fraction should be equivalent to <span + class="sf">1/2</span>, when reduced to its lowest terms, if + it is destined to produce a true octave; but, using this + numerator, 262144, a half would be expressed by <span + class="sf">262144/524288</span>, the segment producing the + true octave; so the fraction <span + class="sf">262144/531441</span>, which represents the + segment for 2C, obtained by the circle of fifths, being + evidently less than <span class="sf">1/2</span>, this + segment will yield a tone somewhat sharper than the true + octave. The two denominators are taken in this case to show + the ratio of the variance; so the octave obtained from the + circle of <span class='pagenum'><a name="Page_144" + id="Page_144"></a>[Pg 144]</span>fifths is sharper than the + true octave in the ratio expressed by 531441 to 524288, + which ratio is called the <i>ditonic comma</i>. This comma + is equal to one-fifth of a half-step. + </p> + <p> + We are to conclude, then, that if octaves are to remain + perfect, and we desire to establish an equal temperament, + the above-named difference is best disposed of by dividing + it into twelve equal parts and depressing each of the + fifths one-twelfth part of the ditonic comma; thereby + dispersing the dissonance so that it will allow perfect + octaves, and yet, but slightly impair the consonance of the + fifths. + </p> + <p> + We believe the foregoing propositions will demonstrate the + facts stated therein, to the student's satisfaction, and + that he should now have a pretty thorough knowledge of the + mathematics of the temperament. That the equal temperament + is the only practical temperament, is confidently affirmed + by Mr. W.S.B. Woolhouse, an eminent authority on musical + mathematics, who says: + </p> + <p> + "It is very misleading to suppose that the necessity of + temperament applies only to instruments which have fixed + tones. Singers and performers on perfect instruments must + all temper their intervals, <span class='pagenum'><a + name="Page_145" id="Page_145"></a>[Pg 145]</span>or they + could not keep in tune with each other, or even with + themselves; and on arriving at the same notes by different + routes, would be continually finding a want of agreement. + The scale of equal temperament obviates all such + inconveniences, and continues to be universally accepted + with unqualified satisfaction by the most eminent + vocalists; and equally so by the most renowned and + accomplished performers on stringed instruments, although + these instruments are capable of an indefinite variety of + intonation. The high development of modern instrumental + music would not have been possible, and could not have been + acquired, without the manifold advantages of the tempered + intonation by equal semitones, and it has, in consequence, + long become the established basis of tuning." + </p> + <p class="center smcap"> + Numerical Comparison of the Diatonic Scale with the + Tempered Scale. + </p> + <p> + The following table, comparing vibration numbers of the + diatonic scale with those of the tempered, shows the + difference in the two scales, existing between the thirds, + fifths and other intervals. + </p> + <p> + <span class='pagenum'><a name="Page_146" + id="Page_146"></a>[Pg 146]</span> + </p> + <p> + Notice that the difference is but slight in the lowest + octave used which is shown on the left; but taking the + scale four octaves higher, shown on the right, the + difference becomes more striking. + </p> + <div class="center"> + <table cellspacing="5"> + <tr> + <td></td> + <td class="smcap">Diatonic.</td> + <td class="smcap">Tempered.</td> + <td colspan="2"></td> + <td class="smcap">Diatonic.</td> + <td class="smcap">Tempered.</td> + </tr> + <tr> + <td>C</td> + <td>32.</td> + <td>32.</td> + <td></td> + <td>C</td> + <td>512.</td> + <td>512.</td> + </tr> + <tr> + <td>D</td> + <td>36.</td> + <td>35.92</td> + <td></td> + <td>D</td> + <td>576.</td> + <td>574.70</td> + </tr> + <tr> + <td>E</td> + <td>40.</td> + <td>40.32</td> + <td></td> + <td>E</td> + <td>640.</td> + <td>645.08</td> + </tr> + <tr> + <td>F</td> + <td>42.66</td> + <td>42.71</td> + <td></td> + <td>F</td> + <td>682.66</td> + <td>683.44</td> + </tr> + <tr> + <td>G</td> + <td>48.</td> + <td>47.95</td> + <td></td> + <td>G</td> + <td>768.</td> + <td>767.13</td> + </tr> + <tr> + <td>A</td> + <td>53.33</td> + <td>53.82</td> + <td></td> + <td>A</td> + <td>853.33</td> + <td>861.08</td> + </tr> + <tr> + <td>B</td> + <td>60.</td> + <td>60.41</td> + <td></td> + <td>B</td> + <td>960.</td> + <td>966.53</td> + </tr> + <tr> + <td>C</td> + <td>64.</td> + <td>64.</td> + <td></td> + <td>C</td> + <td>1024.</td> + <td>1024.</td> + </tr> + </table> + </div> + <p> + Following this paragraph we give a reference table in which + the numbers are given for four consecutive octaves, + calculated for the system of equal temperament. Each column + represents an octave. The first two columns cover the tones + of the two octaves used in setting the temperament by our + system. + </p> + <p class="center sf"> + TABLE OF VIBRATIONS PER SECOND. + </p> + <div class="center"> + <table cellspacing="5"> + <tr> + <td>C</td> + <td>128.</td> + <td>256.</td> + <td>512.</td> + <td>1024.</td> + </tr> + <tr> + <td>C♯</td> + <td>135.61</td> + <td>271.22</td> + <td>542.44</td> + <td>1084.89</td> + </tr> + <tr> + <td>D</td> + <td>143.68</td> + <td>287.35</td> + <td>574.70</td> + <td>1149.40</td> + </tr> + <tr> + <td>D♯</td> + <td>152.22</td> + <td>304.44</td> + <td>608.87</td> + <td>1217.75</td> + </tr> + <tr> + <td>E</td> + <td>161.27</td> + <td>322.54</td> + <td>645.08</td> + <td>1290.16</td> + </tr> + <tr> + <td>F</td> + <td>170.86</td> + <td>341.72</td> + <td>683.44</td> + <td>1366.87</td> + </tr> + <tr> + <td>F♯</td> + <td>181.02</td> + <td>362.04</td> + <td>724.08</td> + <td>1448.15<span class='pagenum'><a name="Page_147" + id="Page_147"></a>[Pg 147]</span></td> + </tr> + <tr> + <td>G</td> + <td>191.78</td> + <td>383.57</td> + <td>767.13</td> + <td>1534.27</td> + </tr> + <tr> + <td>G♯</td> + <td>203.19</td> + <td>406.37</td> + <td>812.75</td> + <td>1625.50</td> + </tr> + <tr> + <td>A</td> + <td>215.27</td> + <td>430.54</td> + <td>861.08</td> + <td>1722.16</td> + </tr> + <tr> + <td>A♯</td> + <td>228.07</td> + <td>456.14</td> + <td>912.28</td> + <td>1824.56</td> + </tr> + <tr> + <td>B</td> + <td>241.63</td> + <td>483.26</td> + <td>966.53</td> + <td>1933.06</td> + </tr> + <tr> + <td>C</td> + <td>256.</td> + <td>512.</td> + <td>1024.</td> + <td>2048.</td> + </tr> + </table> + </div> + <p> + Much interesting and valuable exercise may be derived from + the investigation of this table by figuring out what + certain intervals would be if exact, and then comparing + them with the figures shown in this tempered scale. To do + this, select two notes and ascertain what interval the + higher forms to the lower; then, by the fraction in the + table below corresponding to that interval, multiply the + vibration number of the lower note. + </p> + <p> + <span class="smcap">Example</span>. Say we select the first + C, 128, and the G in the same column. We know this to be an + interval of a perfect fifth. Referring to the table below, + we find that the vibration of the fifth is 3/2 of, or 3/2 + times, that of its fundamental; so we simply multiply this + fraction by the vibration number of C, which is 128, and + this gives 192 as the exact fifth. <span class='pagenum'><a + name="Page_148" id="Page_148"></a>[Pg 148]</span>Now, on + referring to the above table of equal temperament, we find + this G quoted a little less (flatter), viz., 191.78. To + find a fourth from any note, multiply its number by 4/3, a + major third, by 5/4, and so on as per table below. + </p> + <p class="center sf"> + TABLE SHOWING RELATIVE VIBRATION OF INTERVALS BY IMPROPER + FRACTIONS. + </p> + <div class="center"> + <table cellspacing="5"> + <tr> + <td>The</td> + <td>relation</td> + <td>of the</td> + <td>Octave to a</td> + <td>Fundamental</td> + <td>is expressed by</td> + <td>2/1</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Fifth to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>3/2</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Fourth to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>4/3</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Major Third to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>5/4</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Minor Third to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>6/5</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Major Second to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>9/8</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Major Sixth to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>5/3</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Minor Sixth to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>8/5</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Major Seventh to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>15/8</td> + </tr> + <tr> + <td class="center">"</td> + <td class="center">"</td> + <td class="center">"</td> + <td>Minor Second to a</td> + <td class="center">"</td> + <td class="center">"</td> + <td>16/15</td> + </tr> + </table> + </div> + <p class="center"> + QUESTIONS ON LESSON XIII. + </p> + <ol> + <li> + State what principle is demonstrated in Proposition II. + </li> + <li> + State what principle is demonstrated in Proposition III. + </li> + <li> + What would be the vibration per second of an exact (not + tempered) fifth, from C-512? + </li> + <li> + Give the figures and the process used in finding the + vibration number of the <i>exact</i> major third to + C-256. <span class='pagenum'><a name="Page_149" + id="Page_149"></a>[Pg 149]</span> + </li> + <li> + If we should tune the whole circle of twelve fifths + exactly as detailed in Proposition III, how much too + sharp would the last C be to the first C tuned? + </li> + </ol> + <hr style="width: 65%;" /> + <p><span class='pagenum'><a name="Page_150" + id="Page_150"></a>[Pg 150]</span></p> + <h2> + <a name="LESSON_XIV" id="LESSON_XIV"></a>LESSON XIV. + </h2> + <hr /> + <h3> + MISCELLANEOUS TOPICS PERTAINING TO THE PRACTICAL WORK OF + TUNING. + </h3> + <p> + <b>Beats.</b> The phenomenon known as "beats" has been but + briefly alluded to in previous lessons, and not + analytically discussed as it should be, being so important + a feature as it is, in the practical operations of tuning. + The average tuner hears and considers the beats with a + vague and indefinite comprehension, guessing at causes and + effects, and arriving at uncertain results. Having now + become familiar with vibration numbers and ratios, the + student may, at this juncture, more readily understand the + phenomenon, the more scientific discussion of which it has + been thought prudent to withhold until now. + </p> + <p> + In speaking of the unison in Lesson VIII, we stated that + "the cause of the waves in a defective unison is the + alternate recurring of the periods when the condensations + and the rarefactions correspond <span class='pagenum'><a + name="Page_151" id="Page_151"></a>[Pg 151]</span>in the two + strings, and then antagonize." This concise definition is + complete; but it may not as yet have been fully + apprehended. The unison being the simplest interval, we + shall use it for consideration before taking the more + complex intervals into account. + </p> + <p> + Let us consider the nature of a single musical tone: that + it consists of a chain of sound-waves; that each sound-wave + consists of a condensation and a rarefaction, which are + directly opposed to each other; and that sound-waves travel + through air at a specific rate per second. Let us also + remark, here, that in the foregoing lessons, where + reference is made to vibrations, the term signifies + sound-waves. In other words, the terms, "vibration" and + "sound-wave," are synonymous. + </p> + <p> + If two strings, tuned to give forth the same number of + vibrations per second, are struck at the same time, the + tone produced will appear to come from a single source; one + sweet, continuous, smooth, musical tone. The reason is + this: The condensations sent forth from each of the two + strings occur exactly together; the rarefactions, which, of + course, alternate with the condensations, are also + simultaneous. <span class='pagenum'><a name="Page_152" + id="Page_152"></a>[Pg 152]</span>It necessarily follows, + therefore, that the condensations from each of the two + strings travel with the same velocity. Now, while this + condition prevails, it is evident that the two strings + assist each other, making the condensations more condensed, + and, consequently, the rarefactions more rarefied, the + result of which is, the two allied forces combine to + strengthen the tone. + </p> + <p> + In opposition to the above, if two strings, tuned to + produce the same tone, could be so struck that the + condensation of one would occur at the same instant with + the rarefaction of the other, it is readily seen that the + two forces would oppose, or counteract each other, which, + if equal, would result in absolute silence.<a + id="fnanchor_G" name="fnanchor_G"></a><a href="#fn_G" + class="fnanchor">[G]</a> + </p> + <p> + <span class='pagenum'><a name="Page_153" + id="Page_153"></a>[Pg 153]</span> + </p> + <p> + If one of the strings vibrates 100 times in a second, and + the other 101, there will be a portion of time during each + second when the vibrations will coincide, and likewise a + portion of time when they will antagonize each other. The + periods of coincidence and of antagonism pass by + progressive transition from one to the other, and the + portion of time when exactitude is attained is + infinitesimal; so there will be two opposite effects + noticed in every second of time: the one, a progressive + augmentation of strength and volume, the other, a gradual + diminution of the same; the former occurring when the + vibrations are coming into coincidence, the latter, when + they are approaching the point of antagonism. Therefore, + when we speak of one beat per second, we mean that there + will be one period of augmentation and one period of + diminution in one second. Young tuners sometimes get + confused and accept one beat as being two, taking the + period of augmentation for one beat and likewise the period + of diminution. This is most likely to occur in the lower + fifths of the temperament where the beats are very slow. + </p> + <p> + Two strings struck at the same time, one tuned an octave + higher than the other, will vibrate in the <span + class='pagenum'><a name="Page_154" id="Page_154"></a>[Pg + 154]</span>ratio of 2 to 1. If these two strings vary from + this ratio to the amount of <i>one</i> vibration, they will + produce <i>two</i> beats. Two strings sounding an interval + of the fifth vibrate in the ratio of 3 to 2. If they vary + from this ratio to the amount of <i>one</i> vibration, + there will occur <i>three</i> beats per second. In the case + of the major third, there will occur <i>four</i> beats per + second to a variation of <i>one</i> vibration from the true + ratio of 5 to 4. You should bear this in mind in + considering the proper number of beats for an interval, the + vibration number being known. + </p> + <p> + It will be seen, from the above facts in connection with + the study of the table of vibration numbers in Lesson XIII, + that all fifths do not beat alike. The lower the vibration + number, the slower the beats. If, at a certain point, a + fifth beats once per second, the fifth taken an octave + higher will beat twice; and the intervening fifths will + beat from a little more than once, up to nearly twice per + second, as they approach the higher fifth. Vibrations per + second double with each octave, and so do beats. + </p> + <p> + By referring to the table in Lesson XIII, above referred + to, the exact beating of any fifth may be ascertained as + follows: + </p> + <p> + <span class='pagenum'><a name="Page_155" + id="Page_155"></a>[Pg 155]</span> + </p> + <p> + Ascertain what the vibration number of the <i>exact</i> + fifth would be, according to the instructions given beneath + the table; find the difference between this and the + <i>tempered</i> fifth given in the table. Multiply this + difference by 3, and the result will be the number of beats + or fraction thereof, of the tempered fifth. The reason we + multiply by 3 is because, as above stated, a variation of + one vibration per second in the fifth causes three beats + per second. + </p> + <p> + <i>Example.</i>Take the first fifth in the table, C-128 to + G-191.78, and by the proper calculation (see example, page + 147, Lesson XIII) we find the exact fifth to this C would + be 192. The difference, then, found by subtracting the + smaller from the greater, is .22 ( <span + class="sf">22/100</span>). Multiply .22 by 3 and the result + is .66, or about two-thirds of a beat per second. + </p> + <p> + By these calculations we learn that the fifth, C-256 to + G-383.57, should have 1.29 beats: nearly one and a third + per second, and that the highest fifth of the temperament, + F-341.72 to C-512, should be 1.74, or nearly one and + three-quarters. By remembering these figures, and + endeavoring to temper as nearly according to them as + possible, the tuner will find that his temperament will + come up most <span class='pagenum'><a name="Page_156" + id="Page_156"></a>[Pg 156]</span>beautifully. This is one + of the features that is overlooked or entirely unknown to + many fairly good tuners; their aim being to get all fifths + the same. + </p> + <p> + <b>Finishing up the Temperament.</b> If your last trial, + F-C, does not prove a correct fifth, you must consider how + best to rectify. The following are the causes which result + in improper temperament: + </p> + <ol> + <li> + Fifths too flat. + </li> + <li> + Fifths not flat enough. + </li> + <li> + Some fifths correctly tempered and others not. + </li> + <li> + Some fifths sharper instead of flatter than perfect; a + condition that must be watched with vigilance. + </li> + <li> + Some or all of the strings tuned fall from the pitch at + which they were left. + </li> + </ol> + <p> + From a little reflection upon these causes, it is seen that + the last trial may prove a correct fifth and yet the + temperament be imperfect. If this is the case, it will be + necessary to go all over the temperament again. Generally, + however, after you have had a little experience, you will + find the trouble in one of the first two causes above, + unless it be a piano wherein, the strings fall as in Cause + 5. This latter <span class='pagenum'><a name="Page_157" + id="Page_157"></a>[Pg 157]</span>cause can be ascertained + in cases only where you have started from a tuning pipe or + fork. Sometimes you may find that the temperament may be + corrected by the alteration of but two or three tones; so + it is always well to stop and examine carefully before + attempting the correction. A haphazard attempt might cause + much extra work. + </p> + <p> + In temperament setting by our system, if the fifths are + properly tempered and the octaves are left perfect, the + other intervals will need no attention, and will be found + beautifully correct when used in testing. + </p> + <p> + The mistuned or tempered intervals are as follows: + </p> + <div class="center"> + <table cellspacing="5"> + <tr> + <td class="smcap">Intervals Flattened.</td> + <td class="smcap">Intervals Sharpened.</td> + </tr> + <tr> + <td>The Fifth, slightly.</td> + <td>The Fourth, slightly.</td> + </tr> + <tr> + <td>The Minor Third, considerably.</td> + <td>The Major Third, greatly.</td> + </tr> + <tr> + <td>The Minor Sixth, considerably.</td> + <td>The Major Sixth, greatly.</td> + </tr> + </table> + </div> + <p> + <b>Tuning the Treble.</b> In tuning the treble, which is + always tuned by exact octaves, from their corresponding + tones within the temperament, the ear will often accept an + octave as true before its pitch has been sufficiently + raised. Especially is <span class='pagenum'><a + name="Page_158" id="Page_158"></a>[Pg 158]</span>this true + in the upper octaves. After tuning a string in the treble + by its octave in the temperament, test it as a fifth. For + instance, after tuning your first string beyond the + temperament, 3C♯, test it as a fifth to 2F♯. If + you are yet uncertain, try it as a major third in the chord + of A. The beats will serve you as a guide in testing by + fifths, up to about an octave and a half above the highest + tone of the temperament; but beyond this point they become + so rapid as to be only discernible as degrees of roughness. + The beats will serve as a guide in tuning <i>octaves</i> + higher in the treble than the point at which the beats of + the <i>fifth</i> become unavailable; and in tuning + <i>unisons</i>, the beats are discernible almost to the + last tone. + </p> + <p> + The best method to follow in tuning the treble may be + summed up as follows: Tune the first octave with the beats + as guides both in the octave and in testing it by the + fifth. If yet uncertain, test by chords. Above this octave, + rely somewhat upon the beats in the octave, still use the + fifth for testing, but listen for the pitch in the extreme + upper tones and not so much for the beats except in + bringing up unisons, in which the beats are more prominent. + </p> + <p> + <span class='pagenum'><a name="Page_159" + id="Page_159"></a>[Pg 159]</span> + </p> + <p> + In the extreme upper tones, the musical ear of the tuner is + tried to the utmost. Here, his judgment of correct harmonic + relation is the principal or only guide, while in the + middle octaves the beats serve him so faithfully, his + musical qualifications being brought into requisition only + as a rough guide in determining pitch of the various + intervals. To tune by the beats requires a sharp ear and + mental discernment; to tune by pitch requires a fine + musical ear and knowledge of the simpler laws of harmony. + </p> + <p> + As stated above, the tuner will fail in many cases to tune + his high octaves sharp enough. Rarely, if ever, will a + tuner with a good ear leave the upper tones too sharp. Now, + there is one more fact which is of the utmost importance in + tuning the treble: it is the fact that the extreme upper + octave and a half must be tuned slightly sharper than + perfect; if the octaves are tuned perfect, the upper tones + of the instrument will sound flat when used in scale and + arpeggio passages covering a large portion of the + key-board. Begin to sharpen your octaves slightly from + about the seventeenth key from the last; counting both + black and white. In other words, begin to sharpen from the + last A♭ but one, in the standard <span + class='pagenum'><a name="Page_160" id="Page_160"></a>[Pg + 160]</span>scale of seven and a third octaves of which the + last key is C. Sharpen but slightly, and increase the + degree of sharpening but little as you proceed. + </p> + <p> + <b>Tuning the Bass.</b> In tuning the bass, listen for the + beats only, in bringing up the octaves. It is sometimes + well to try the string tuned, with its fifth, but the + octave in the bass should suffice, as the vibrations are so + much slower here that if you listen acutely the octave + beats will guide you. + </p> + <p> + It is not necessary to pull the strings higher than the + pitch at which they are to stand. Learn to pull them up + gradually and in a way that will "render" the string over + the bridges, which is an easy thing to do, the strings + being so much heavier here than elsewhere. Never leave a + bass string the slightest amount too sharp. As flatness is + so obnoxious in the treble, just so is sharpness in the + bass, so if there must be any variation in any bass tone + let it be flat; but aim at perfect octaves throughout the + bass. + </p> + <p> + <b>False Waves.</b> We say "false waves" for want of a + better name. You will find a string occasionally that will + give forth waves or beats so similar to the real ones that + it takes a practiced ear to distinguish the difference. + Where a unison contains a string <span class='pagenum'><a + name="Page_161" id="Page_161"></a>[Pg 161]</span>of this + kind, select some other string by which to tune the + interval, and leave the bad string until the last; you may + then find difficulty in being able to tell when you have it + in unison. The cause may be a twisted string, a fault in + the string by imperfect drawing of the wire, or in the + construction of the sound-board. + </p> + <p> + In the low bass tones, a kind of false waves are always + present, and will annoy the tuner long after he has been in + regular practice. They are, however, of a different nature + from the true waves in that they are of a metallic timbre + and of much greater rapidity than the latter. Close + attention will generally enable the tuner to distinguish + between them. They are caused by what is known as + "harmonics" or "over-tones"; the string vibrating in + fractional segments. + </p> + <p> + False waves will occur in an annoying degree when the tuner + sets a mute on a nodal point in the string; it will cause + the muted string to sound a real harmonic tone. This does + not happen in the upright, as the mutes are set so near the + end of the string as to preclude this possibility. In the + square, however, it very frequently happens, as there are + so many nodes between the dampers and the bridge, <span + class='pagenum'><a name="Page_162" id="Page_162"></a>[Pg + 162]</span>where the tuner sets his mutes. If, for + instance, he is tuning an octave and has his mute set + precisely in the middle of the vibrating segment, in place + of muting the string it sounds its own octave, which will + disturb the ear in listening for the tone from the one free + string. Move the mute either way until it is found to mute + the string entirely. + </p> + <p class="center"> + QUESTIONS ON LESSON XIV. + </p> + <ol> + <li> + Explain the cause of the beats. + </li> + <li> + How many <i>beats</i> per second in a unison of two + strings, one tuned to 100, the other to 101 vibrations + per second? + </li> + <li> + How many beats per second in an octave, the lower tone of + which is tuned to 100, the upper to 201 vibrations per + second? + </li> + <li> + How many beats per second in a fifth, the fundamental of + which is tuned to 100, the fifth to 151? + </li> + <li> + The fifth, 2F-3C, when properly tempered, should beat + 1¾ times per second. How often should a fifth, an + octave higher, beat? + </li> + </ol> + <hr style="width: 65%;" /> + <p><span class='pagenum'><a name="Page_163" + id="Page_163"></a>[Pg 163]</span></p> + <h2> + <a name="LESSON_XV" id="LESSON_XV"></a>LESSON XV. + </h2> + <hr /> + <h3> + MISCELLANEOUS TOPICS PERTAINING TO THE PRACTICAL WORK OF + TUNING, REGULATING, AND REPAIRING. + </h3> + <p> + <b>Comparison of the Different Systems.</b> Up to this + time, we have given no account of any system of tuning + except the one recommended. For the purpose of making the + student more thoroughly informed we detail here several + different systems which have been devised and practiced by + other tuners. It is a matter of history that artisans in + this profession and leaders in musical science have + endeavored to devise a system of temperament having all the + desirable qualifications. + </p> + <p> + The aims of many have been to invent a system which uses + the fewest number of tones; working under the impression + that the fewer the tones used in the temperament, the + easier the tuner's work. These have reduced the compass of + the temperament to the twelve semi-tones from middle C to B + above; or from F below, to E above middle C. <span + class='pagenum'><a name="Page_164" id="Page_164"></a>[Pg + 164]</span>This system requires the tuner to make use of + both fourths and fifths. Not only does he have to use these + two kinds of intervals in tuning, but he has to tune by + fourths up and fourths down, and, likewise, by fifths up + and fifths down. When tuning a fifth upward, he flattens + it; and when tuning a fifth downward he sharpens the lower + tone; when tuning a fourth upward, he sharpens it; when + tuning a fourth downward, he flattens the lower tone. + </p> + <p> + It is readily seen that by a system of this kind the + tuner's mind is constantly on a strain to know how to + temper the interval he is tuning, and how much to temper + it, as fourths require a different degree of tempering from + the fifths; and he is constantly changing from an interval + upward to one downward; so, this system must be stamped as + tedious and complicated, to say the least. Yet this system + is much followed in factories for rough tuning, and also by + many old professional tuners. + </p> + <p> + The table on the following page gives the succession of + intervals generally taken by tuners employing this system + using the tones within the F octave mentioned above. Middle + C is obtained in the usual way, from the tuning fork. + </p> + <p> + <span class='pagenum'><a name="Page_165" + id="Page_165"></a>[Pg 165]</span> + </p> + <p class="center"> + SYSTEM A. + </p> + <div class="center"> + <table cellspacing="5"> + <tr> + <td>By middle</td> + <td>C</td> + <td>tune</td> + <td>F</td> + <td>fifth below.</td> + <td>Temper</td> + <td>sharp.</td> + </tr> + <tr> + <td>By</td> + <td>F</td> + <td class="center">"</td> + <td>B♭ (A♯)</td> + <td>Â Â fourth above.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td>C</td> + <td class="center">"</td> + <td>G</td> + <td>Â Â fourth below.</td> + <td class="center">"</td> + <td>flat</td> + </tr> + <tr> + <td class="center">"</td> + <td>G</td> + <td class="center">"</td> + <td>D</td> + <td>fifth above.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td>D</td> + <td class="center">"</td> + <td>A</td> + <td>Â Â fourth below.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td>A</td> + <td class="center">"</td> + <td>E</td> + <td>fifth above.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td>E</td> + <td class="center">"</td> + <td>B</td> + <td>Â Â fourth below.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td>B</td> + <td class="center">"</td> + <td>F♯</td> + <td>Â Â fourth below.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td>F♯</td> + <td class="center">"</td> + <td>C♯</td> + <td>fifth above.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td>C♯</td> + <td class="center">"</td> + <td>G♯</td> + <td>Â Â fourth below.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td class="center">"</td> + <td>G♯</td> + <td class="center">"</td> + <td>D♯</td> + <td>fifth above.</td> + <td class="center">"</td> + <td class="center">"</td> + </tr> + <tr> + <td>Then try</td> + <td>D♯</td> + <td>with</td> + <td>A♯</td> + <td colspan="3">previously tuned for "wolves."</td> + </tr> + </table> + </div> + <p> + We think a little study and trial of this system will + produce the conviction that it is a very difficult and + precarious one, and that it has every disadvantage but one, + namely, that it uses the smallest possible number of tones, + which is really of little value, and does not compensate + for the difficulty encountered and the uncertainty of the + results. + </p> + <p> + Another system which has many advantages over the above, is + one which employs fifths only and covers a compass of an + octave and a half. This system is similar to ours in that + it employs fifths in the same succession as far as + G♯, the most of them, however, being an octave + higher. From this G♯ <span class='pagenum'><a + name="Page_166" id="Page_166"></a>[Pg 166]</span>there is a + break in the succession, and the tuner goes back to middle + C from which he started and tunes by fifths downward until + he reaches the G♯ at which he left off. This system + employs the tones from F below middle C to C, octave above. + Below is the succession, starting upon 3C, whose pitch is + determined as usual. + </p> + <p class="center"> + SYSTEM B. + </p> + <div class="center"> + <table cellspacing="5"> + <tr> + <td class="center">By</td> + <td>3C</td> + <td class="center">tune</td> + <td>2C</td> + <td>Â Â octave below.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2C</td> + <td class="center">"</td> + <td>2G</td> + <td>fifth above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2G</td> + <td class="center">"</td> + <td>1G</td> + <td>Â Â octave below.</td> + </tr> + <tr> + <td class="center">"</td> + <td>1G</td> + <td class="center">"</td> + <td>2D</td> + <td>fifth above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2D</td> + <td class="center">"</td> + <td>2A</td> + <td>fifth above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2A</td> + <td class="center">"</td> + <td>1A</td> + <td>Â Â octave below.</td> + </tr> + <tr> + <td class="center">"</td> + <td>1A</td> + <td class="center">"</td> + <td>2E</td> + <td>fifth above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2E</td> + <td class="center">"</td> + <td>2B</td> + <td>fifth above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2B</td> + <td class="center">"</td> + <td>1B</td> + <td>Â Â octave below.</td> + </tr> + <tr> + <td class="center">"</td> + <td>1B</td> + <td class="center">"</td> + <td>2F♯</td> + <td>fifth above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2F♯</td> + <td class="center">"</td> + <td>1F♯</td> + <td>Â Â octave below.</td> + </tr> + <tr> + <td class="center">"</td> + <td>1F♯</td> + <td class="center">"</td> + <td>2C♯</td> + <td>fifth above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2C♯</td> + <td class="center">"</td> + <td>2G♯</td> + <td>fifth above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2G♯</td> + <td class="center">"</td> + <td>1G♯</td> + <td>Â Â octave below.</td> + </tr> + <tr> + <td colspan="5" class="center"><hr /></td> + </tr> + <tr> + <td class="center">By</td> + <td>2C</td> + <td class="center">tune</td> + <td>1F</td> + <td>fifth below. Temper sharp.</td> + </tr> + <tr> + <td class="center">"</td> + <td>1F</td> + <td class="center">"</td> + <td>2F</td> + <td>Â Â octave above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2F</td> + <td class="center">"</td> + <td>1B♭</td> + <td>fifth below. Temper sharp.</td> + </tr> + <tr> + <td class="center">"</td> + <td>1B♭</td> + <td class="center">"</td> + <td>2B♭</td> + <td>Â Â octave above.</td> + </tr> + <tr> + <td class="center">"</td> + <td>2B♭</td> + <td class="center">"</td> + <td>2E♭</td> + <td>fifth below. Temper sharp.</td> + </tr> + <tr> + <td class="center">Now by</td> + <td>2E♭</td> + <td class="center">try</td> + <td>1A♭ (G♯)</td> + <td>fifth below for the "wolf."</td> + </tr> + <tr> + <td colspan="5"> + Note that this last trial brings you back to the last + tone tuned before the break. + </td> + </tr> + </table> + </div> + <p> + <span class='pagenum'><a name="Page_167" + id="Page_167"></a>[Pg 167]</span> + </p> + <p> + This system is used by a great number of very successful + tuners, and it has but one appreciable disadvantage, which + is that involved in changing from fifths upward to fifths + downward. This difficulty is easily overcome, if it were + all there is to encounter; but in practice, we find that + after tuning the intervals in the above succession down to + the last step in the first series, middle C will often have + changed pitch somewhat, and the last five tones with their + octaves tuned from it will not be in true harmony with the + intervals tuned in the first series. For this reason it is + better to go on through, as in our system, tuning by fifths + upward, and if there is any change of pitch in the first + tones tuned, they may be more easily corrected by going + over them in the same way as at the start; also, the amount + of difficulty in locating discrepancies is greatly + lessened. + </p> + <p class="center"> + SYSTEM C. + </p> + <p> + The following system is one that is followed by many good + tuners of the present day and has many advantages. To use + this system successfully, however, one must be familiar + with the number of beats necessary in each interval used. + </p> + <p> + <span class='pagenum'><a name="Page_168" + id="Page_168"></a>[Pg 168]</span> + </p> + <div class="blockquot sf"> + <p class="center"> + Take 1F as a standard. + </p> + <p> + By 1F, tune 2C, fifth above.<br /> + By 1F, tune 1Bm, fourth above.<br /> + By 1F, tune 1A, major third above.<br /> + By 1F, tune 2D, sixth above.<br /> + By 1F, tune 1Am, minor third above.<br /> + By 1F, tune 2F, octave above.<br /> + By 2C or 2D, tune 1G, fourth or fifth below.<br /> + By 1G, 1A or 2C, tune 2E, sixth, fifth or third + above.<br /> + By 1G or 2E, tune 1B, third above or fourth below.<br /> + By 1A or A♯, tune 2C♯, major or minor third + above.<br /> + By 1A♭, 1B♭ or 1B, tune 2E♭, fifth, + fourth or major third above.<br /> + By 1B♭, 1B, 2C♯ or 2E♭, tune + 1F♯, major third, fourth, fifth or sixth below. + </p> + </div> + <p> + As each step is taken in this system, the tone tuned is + tested with any or all of the tones previously tuned. + </p> + <p> + You will notice that six tones are tuned by the first + standard, F. Therefore, if any error is left in any one of + the intervals it exists in this only and is not transmitted + to other tones, if corrected before such other tones are + used to tune by. + </p> + <p> + The numerous tests possible, early in the system, and the + small compass used, one octave, may be said to be the chief + advantages of the system. + </p> + <p> + <span class='pagenum'><a name="Page_169" + id="Page_169"></a>[Pg 169]</span> + </p> + <p> + The intervals used are the minor and major third, perfect + fourth and fifth, and major sixth. The thirds and sixths + beat from about 7 to nearly 12 per second. The exact number + of beats for each step in the system may be calculated from + the "Table of Vibration Numbers" in Lesson XIII. For + instance, take middle C (2C) at 256, and its major third, + 2E. The exact third, determined by multiplying 256 by 5/4, + is found to be 320. By reference to the table, we find the + tempered third vibrates 322.54. The difference then is 2.54 + vibrations per second, and, knowing that a difference of + one vibration from the exact major third produces 4 beats, + we simply multiply 2.54 by 4 and we have 10.16, the number + of beats we should hear per second when this third is + tempered correctly. Other intervals may be figured out in + like manner by reference to the various tables given. + </p> + <p> + It is very doubtful if a beginner could succeed with this + system. He should tune by an easier system until he can + hear the beats very distinctly and judge quite accurately + the rapidity of them. Having acquired this ability, he may + try this system and follow it in preference to others. + </p> + <p> + <span class='pagenum'><a name="Page_170" + id="Page_170"></a>[Pg 170]</span> + </p> + <p> + In any system used it is well to test your work in the + following manner: + </p> + <p> + Begin with your lowest major third and strike each third in + succession, ascending chromatically. Of course, each third + should beat slightly faster than the one below it. For + instance, in our system of two octaves, take 1C-E; this + third should beat about 5 per second. Next, take + 1C♯-F, which should beat about 5-1/2 per second. The + beats should increase each test nearly a half beat, or the + amount of 5 beats in this octave; hence, 2C-E will beat + about 10 per second; or, using the exact figures, 10.16. + After arriving at the last-named test, 2C-E, you may test + the remainder of the two octaves by tenths, beginning with + 1C-2E. The tenth is similar to the third mathematically, + and its beats are even more distinct. + </p> + <p> + We may remark here that our system may be reduced to the + compass of an octave and a half by simply not tuning the + octaves upward which reach beyond 2F♯; and if + anything were to be gained and nothing lost by shortening + the compass of the temperament, we would advise using only + the octave and a half. But in many years of experience in + tuning <span class='pagenum'><a name="Page_171" + id="Page_171"></a>[Pg 171]</span>all imaginable types, + styles and kinds of pianos, and by all systems, we have + found good reasons for adopting the two-octave temperament + as laid down in Lesson VIII, for universal application. Its + advantages may be summed up as follows: + </p> + <p> + <b>Simplicity.</b> But two kinds of intervals are employed: + the fifth and the octave. The fifth is always tuned to a + fundamental below and hence always flattened, which + relieves the tuner of any mental operation to determine + which way he is to temper. Being a regular succession of + fifths and octaves, without a break, the system is easily + learned, and can be followed with little mental strain. + </p> + <p> + <b>Uniformity.</b> After the tuner has become well trained + in tempering his fifths, there is little danger of an + uneven temperament, as the various intervals used in trials + will prove a false member in some chord in time to correct + it before he has gotten so far from it as to make the + correction difficult. When a correction is necessary, the + offending point is most easily found. + </p> + <p> + <b>Precision.</b> In our experience, we have never known + another system by which we could attain the absolute + precision gained by this. + </p> + <p> + <span class='pagenum'><a name="Page_172" + id="Page_172"></a>[Pg 172]</span> + </p> + <p> + <b>Stability.</b> Stability is the feature wherein rests + the paramount reason for employing two octaves. From what + has been said in previous lessons concerning the liability + of some strings to flatten or sharpen by reason of altering + the tension of other strings, the student will readily see + that the temperament should cover a sufficient portion of + the instrument, if possible, to insure that it will stand + while the remaining portion is being tuned. Our two octaves + cover nearly all the strings between the over-strung bass + and the brace in the metal plate. This being the case, any + reasonable alteration of the strings beyond, or outside, + the braces from the temperament, will rarely, if ever, + affect it noticeably. + </p> + <p> + <b>Final Inspection.</b> Always test every key on the + piano, or especially those of the middle five octaves, for + bad unisons. Upon finding one, search for the string that + has stood in tune, by testing each string of the unison + with its octave. This being done, simply bring the other to + it. Go over the whole key-board, striking octaves, and + correct any that might offend. One extremely bad tone or + octave may disparage your reputation, when in reality your + work merits commendation. + </p> + <p> + <span class='pagenum'><a name="Page_173" + id="Page_173"></a>[Pg 173]</span> + </p> + <p> + <b>Loose Pins.</b> You will occasionally find pianos in + which the tuning pins have become so loose that they will + not resist the pull of the strings. If many of them are in + this condition it is better, before you begin to tune, to + take a hammer of considerable weight and drive them a + little. Commence at one end of the row of pins and aim to + strike all the pins with the same force. Those which are + tight enough will not yield to the blow, while those which + are loose may require two or three blows to tighten them + sufficiently. This defect is generally found in very old + squares or cheap uprights wherein the pin-block is of poor + material or defective in manufacture or in pianos which + have been abused. + </p> + <p> + <b>Split Bridges.</b> Even in pianos of the highest grade, + we sometimes find a string sounding as if there was a pin + or some metallic substance bearing against it. In such + cases, find the string and examine the place where it + crosses the bridge. You will often find the bridge split at + that point or the bridge-pin, having yielded to the + pressure of the string, vibrates against the next pin, + giving rise to the singing effect. You can do little if + anything toward repairing a split bridge. You may, however, + <span class='pagenum'><a name="Page_174" + id="Page_174"></a>[Pg 174]</span>stop the singing by + inserting the point of your screw-driver between the close + pins and pressing them apart. This will generally stop the + difficulty for the time being at least. + </p> + <p> + Strings crossing the bridge near a split will not stand in + tune well, and will, perhaps, have to be gone over two or + three times. The same may be said of a broken metal plate. + Many old squares have broken plates; generally found near + the overstrung bass, or within the first octave of the + treble. All the tuner can do is to apprise the owner of the + defect and inform her that it will not stand well at this + point, as the intense strain is thrown largely upon the + wooden frame, which will have a tendency to yield gradually + to it. + </p> + <p> + <b>Stringing.</b> Strings break while the tuner is drawing + them up, sometimes because he does not pull them gradually, + gives them an abrupt turn or draws them too far above the + pitch at which they are intended to stand. More often, + however, they break from being rusty at the point where + they pass over the bridge or around the tuning pin. The + best instruction concerning putting on new strings is, + follow appearances. Make the string you put on look <span + class='pagenum'><a name="Page_175" id="Page_175"></a>[Pg + 175]</span>just like those on the instrument. In most + modern pianos the string is wound with three coils around + the pin. + </p> + <p> + You will, of course, have to take out the action; not the + key-board, however, unless it be one of those rare cases + where the key-board and upper action are built to come out + together. In the square it is only necessary to remove the + shade over the dampers, and the dampers, which are all + removed easily by taking out the screw at the left. This + allows the whole set of dampers with their support to come + out together. + </p> + <p> + Treble strings are nearly always passed around the + hitch-pin, one wire thus forming two strings. Take out the + old string, noticing how it passes over and under the felt + at the dead end. After removing the string always give the + pin about three turns backward to draw it out sufficiently + so that when a new string is put on, the pin will turn into + the block as far as it did originally. Run one end of the + string barely through the hole in the tuning pin and turn + it about twice around, taking pains that the coils lie + closely; then unwind enough wire (of the same size of + course) from your supply to reach down to the hitch pin and + back. Place the string on the bridge <span + class='pagenum'><a name="Page_176" id="Page_176"></a>[Pg + 176]</span>pins properly, draw it as tight as you can by + hand and cut it off about three fingers' width beyond the + pin upon which it is to be wound. This will make about + three coils around the pin. Place the end in the hole and + turn up gradually, watching that the string is clear down + on hitch pin and properly laid on the bridge. New strings + will require drawing up two or three times before they will + stand in tune, and even then they will run down in a short + time. It is well on this account to leave them slightly + sharp, calling the owner's attention to the fact. + </p> + <div class="center"> + <div class="figcenter" style="width: 400px;"> + <img src="images/image176.png" width="400" height="144" + alt="Knot for Splicing Wire." + title="Knot for Splicing Wire." /> <span + class="caption smcap">Knot for Splicing Wire.</span> + </div> + </div> + <p> + When a bass string breaks at the point where it starts + around the tuning pin, it can nearly always be spliced and + the trouble of sending it away to have a new one made be + avoided. Take a piece of new wire as large or larger than + the old string and splice <span class='pagenum'><a + name="Page_177" id="Page_177"></a>[Pg 177]</span>it to the + broken end by a good secure knot. A knot called the square + or ruft knot is the best for this purpose. When a bass + string breaks too far from the pin to permit of a splice, + the only resort will be to send the broken string to some + factory and have a new one made from it. + </p> + <p class="center"> + QUESTIONS ON LESSON XV. + </p> + <ol> + <li> + Name the advantages and disadvantages of system A. + </li> + <li> + Name the advantages and disadvantages of system B. + </li> + <li> + What are the important points to be desired in any system + of setting temperament? + </li> + <li> + State three or four items of importance in the operation + of putting on a new string. + </li> + <li> + Why do pianos get out of tune? + </li> + </ol> + <hr style="width: 65%;" /> + <p><span class='pagenum'><a name="Page_178" + id="Page_178"></a>[Pg 178]</span></p> + <h2> + <a name="LESSON_XVI" id="LESSON_XVI"></a>LESSON XVI. + </h2> + <hr /> + <h3> + TUNING AND REPAIRING THE REED ORGAN. + </h3> + <p> + An impression seems to be prevalent among some musicians of + the more advanced class, that the reed organ has gone or is + going out of use; in certain communities there appears to + be sufficient ground for such an impression; in other + communities, however, we find the number of organs largely + in excess of the number of pianos. Not only is this the + case, but statistics of the various organ factories + throughout the United States show that the output is + enormous, which is a sufficient assurance that the reed + organ is not an obsolete instrument by any means. To be + sure, the organ has been superseded in numerous cases by + the piano, which is, in many respects, a greatly superior + instrument, and, generally speaking, is more popular; yet, + the reed organ has its special features of tone quality and + adaptation, which render it even more desirable to many + than the piano, aside from the fact of its being less + expensive. + </p> + <p> + <span class='pagenum'><a name="Page_179" + id="Page_179"></a>[Pg 179]</span> + </p> + <p> + The musical effects possible on the organ and not on the + piano may be few; but they are of no small value, when + certain kinds of musical compositions are to be rendered. + </p> + <p> + One great point in favor of the organ is, that it is + capable of continuing any tone or chord for any length of + time, without diminution, while in the piano, the bass + tones may be continued for considerable time, the middle + tones a shorter length of time, and the extreme high tones + of the treble have but the slightest duration; every tone + in the piano gradually grows weaker from the instant of its + sounding until it fades into silence. Another feature of + the organ, not possible in the piano, is its ability of + making the "crescendo" (a gradual increase of strength or + volume) in single tones or chords. Still another point in + favor of the organ (not in the tuner's favor, however) is + that it rarely gets out of tune and does not require being + gone over by the tuner at short intervals in order to keep + it in fit condition to be used. + </p> + <p> + The idea with which we desire to impress the student by the + foregoing remarks is, that while the piano is a superior + instrument, and the art of tuning the piano is a much + deeper study from the general tuner's <span + class='pagenum'><a name="Page_180" id="Page_180"></a>[Pg + 180]</span>standpoint than that of doing the various things + the tuner is called to do on the organ, he should not + consider the reed organ of minor importance, or slight the + organ when called upon to put it in order. The fact is, + persons having organs in their homes cherish them as much + as others do their pianos, and there is no reason why they + should not have as good service. + </p> + <p> + It will be impossible to give anything more than general + instruction in organ work, as the difference in + construction is so pronounced. Pianos are built practically + on the same plan, and when the construction of one is + learned, the tuner will find little difficulty in others of + the same type; but it seems that every organ manufacturer + has his own hobbies as to the best means of securing + results; however, the general principles are the same, and, + like many operations coming under the hand of the tuner, + all that is necessary is to examine, reason, and use good + mechanical judgment. + </p> + <p class="center smcap"> + Cleaning. + </p> + <p> + Organs need cleaning about once a year, or oftener if they + are kept and used in dusty places. The bellows are suction + or exhaustion bellows, and they draw the air in at the top + of the organ through <span class='pagenum'><a + name="Page_181" id="Page_181"></a>[Pg 181]</span>the reeds + and discharge it below. The effect of this is that if any + dust is floating in the air it is drawn in about the action + and reeds, where it settles and clogs the working parts, + stopping the vibration of the reeds entirely. + </p> + <p> + The front board or key strip is usually held in place by a + screw at each end, but sometimes by slides entering the + holes in the side of the case, which may be disconnected by + wooden buttons at each end, which are pulled toward the + center. The back of all organs may be entered by removing + the board at the back of the case, held in place by screws + or buttons. Close all the stops, then take your dust + blower, if you have one, or a cloth, and remove all the + dirt possible in this way. Lift the muffler boards worked + by the right knee-swell, take a brush and clean thoroughly + next to the reeds which will be exposed when the muffler + boards are raised. + </p> + <p> + If any dirt is left here it will be drawn into the reeds + the instant the organ is played. In bad cases, in fact it + is better in every case, to draw every reed, letting them + lie in a row on the reed board and going over each one + separately, brush the dust from it. This will improve the + tone, or, rather, the tune of the <span class='pagenum'><a + name="Page_182" id="Page_182"></a>[Pg + 182]</span>instrument. Dirt on the tongue of a reed adds + sufficient weight to alter the pitch, and if it is removed, + the instrument will generally be in as good tune as when it + left the factory. Simply cleaning an organ in this way is + often called tuning, by inexperienced persons. If it + happens that there are only a few reeds that do not speak, + and the owner does not care to pay for a thorough cleaning, + you will find the silent reeds by the method given under + the head "Examination," and, drawing them, clean and + replace. + </p> + <p class="center smcap"> + Stops. + </p> + <p> + Each stop on the organ (if there be no dummies) affects + either the tone quality or the power of the instrument. The + Vox Humana stop affects the quality of the tone by + operating a fan in the rear of the instrument or a + contrivance contained in a small box, which produces a + tremolo effect. All other stops may be said to affect the + power. Stops having such names as Diapason, Melodia, + Dulcet, Celeste, Cremona, Echo, Principal, Bourdon, Sub + Bass, Piccolo, Flute, Dulciana, etc., etc., open certain + sets of reeds supposed to give forth a tone quality similar + to the instrument whose name it bears, or the tone of the + <span class='pagenum'><a name="Page_183" + id="Page_183"></a>[Pg 183]</span>pipes of the pipe organ + bearing such names. These stops operate on the sets of + reeds by raising the mutes which, when closed, stop the + passage of air through the reeds. + </p> + <p> + The octave coupler stop, sometimes called Harmonique, + controls an arrangement whereby, when a key is depressed, + its octave is made to sound also. "Forte" stops lift the + mufflers or swells, and as these are controlled by the + right knee-swell, the Forte stop may be considered of + little value. The left knee-swell, called the Full Organ + swell, as its name implies, opens up the full power of all + sets of reeds and throws on the couplers. + </p> + <p> + A mere peep into any organ will disclose the mechanical + working of stops, which is in such great variety that we + will not attempt to detail it here. + </p> + <p class="center smcap"> + Examination. + </p> + <p> + After a little experience you will be able to make an + examination of an organ and tell just what it needs without + so much as drawing a screw. The reeds are usually divided + into treble sets and bass sets; two octaves of bass reeds, + and three octaves of treble reeds constitute a set. The + Diapason stop is <span class='pagenum'><a name="Page_184" + id="Page_184"></a>[Pg 184]</span>nearly always present, and + controls the heaviest reeds in the bass except the Bourdon + or Sub Bass, if the organ should have either of these. In + examining an organ, close all stops but the Diapason, for + instance, then successively press every key in the two bass + octaves. + </p> + <p> + Now if, for instance, a key is found silent, that is, just + an octave from the lowest tone, by counting the keys from + the lowest tone, you will find the silent key is number + thirteen. Look into the organ, find the mute that is up by + reason of this Diapason stop's being pulled, and count the + reeds from the lowest to the thirteenth; pull the reed and + you will find it obstructed or perhaps broken. Most organs + have a Dulciana stop in the treble which corresponds with + the Diapason in the bass. Test the reeds of this set just + as you did those of the Diapason. Go over each set of reeds + in like manner. Broken reeds should be sent to the factory + where the organ was built. The manufacturers will send a + new one, often without cost. + </p> + <p> + Stops are sometimes found disconnected from the mutes, + which deprives the player of the use of certain sets of + reeds, and while it is a small matter <span + class='pagenum'><a name="Page_185" id="Page_185"></a>[Pg + 185]</span>to connect them, it adds much to the improvement + imparted to the instrument by the tuner. After + disconnecting the stops for any purpose, always be sure you + connect them properly before leaving your work. + </p> + <p class="center smcap"> + Sticking Keys. + </p> + <p> + The key itself is subject to many of the same faults as is + that of the piano. It may bind in the guide pin or warp so + as to cause it to stick, or it may stick from some + substance between the keys. Sometimes the front board is so + near the front of the keys that when the latter are + depressed they stick against it. A screw is generally found + in the center, the head of which comes against the front + board and holds it out. If the board is too near give the + screw a turn or two back. If there is no screw, place a + piece of card against the board and the case at the ends. + The end keys sometimes stick against the blocks at the ends + of the key-board. Scrape the block or key where it sticks. + A key may stay down because of the cedar pin, sometimes + called the tracker pin or pitman, sticking in the hole. + Take out the key-board which is held by a screw at each + end, sometimes by another in the middle; in which case a + <span class='pagenum'><a name="Page_186" + id="Page_186"></a>[Pg 186]</span>key or two must be removed + to get at it. To remove a key, take off the strip at the + back of the keys, held in place by small screws, and the + key may be lifted up. Now, finding the sticking pin, pull + it out and sandpaper or rub it with black lead until it is + found to work quite freely in the guide hole of the guide + board and the hole in the reed board. + </p> + <p> + Just under the reed board is a wooden slip covered with + soft leather, called the valve or pallet, which covers the + openings in the reed board which admit air to pass down + through the reeds. The tracker pin, pushed down by the key, + opens the pallet which is held against the reed board by a + spring and kept in place by a guide pin at each end. It + sometimes happens that a pallet will be pushed down so far + as to catch on the guide pins and cause the tone to sound + continually. In other cases a piece of dirt will get in the + way of the pallet and prevent it from closing the opening. + If this be the case, draw the reeds that sound when this + key is depressed and also a reed at each side of it, and + pump the bellows briskly, at the same time pressing the + three keys. This will generally create enough air to remove + the obstacle. If the key still sounds and cannot be made to + <span class='pagenum'><a name="Page_187" + id="Page_187"></a>[Pg 187]</span>"hush up" in this way, you + may be compelled to take out the entire action so that you + can get to the pallets, which can be done by removing all + the screws that hold the reed board in place. At the back, + these screws are on top of the board and sometimes they are + on top in front; but often they are under the air chamber + in front. Be sure the screws are all out before trying to + pull the board loose, as you might crack the board and + thereby cause a leak. A moment's notice will reveal the + cause of the trouble in the pallet. + </p> + <p> + New pallet springs may be made of piano wire, using old + springs for a pattern. + </p> + <p class="center smcap"> + Leaks. + </p> + <p> + If a leak is found in the air boards, such as a crack or + split, it can be stopped permanently by gluing a piece of + bellows cloth or any good rubber cloth over the split. A + leak in the bellows can be repaired in the same way, but if + it happens to be a hole at or near a part of the cloth + which is compelled to bend in the working of the bellows, + you will have to use some kind of rubber or leather cement, + preferably the latter. This can be made by dissolving <span + class='pagenum'><a name="Page_188" id="Page_188"></a>[Pg + 188]</span>gutta-percha in bisulphide of carbon, but a good + leather cement may be had at almost any shoe store. If the + bellows are porous, it may be well to give them a coat of + cement, but never paint them; the paint cracks and the + leaks are made worse. + </p> + <p class="center smcap"> + Pedal Detects. + </p> + <p> + Broken pedal straps are the most frequent annoyance. In all + modern organs there is a panel above the pedals which will + come out and admit the mechanic to the bellows, straps, + springs, etc.; but in some old instruments the case is made + solid, in which case the workman must do his work from the + bottom, turning the organ down so as to get at it. Pedal + straps are easily put on; generally with screws at either + end. If the pedal squeaks examine the springs or oil and + change their position slightly. Examine the pulleys over + which the straps work and oil or rub them on the outside + with soap. Broken pedal hinges may be duplicated by any + blacksmith; the ordinary hinges, such as can be bought at + hardware stores, are sometimes substituted, but they rarely + answer the purpose as well as the regular pedal hinge. The + leather flaps over the holes in the <span + class='pagenum'><a name="Page_189" id="Page_189"></a>[Pg + 189]</span>exhausters sometimes get too tight by shrinkage + so that they will not let the air escape readily, and + consequently the pedals come up slowly, often making it + difficult to keep the instrument sufficiently supplied with + power. Simply stretch the leather flaps, being careful not + to pull the tacks loose or tear the leather. + </p> + <p class="center smcap"> + Sympathetic Vibrations. + </p> + <p> + Organs, like pianos, are subject to sympathetic vibrations. + A reed fitting loosely in the reed chamber will sometimes + buzz when sounded. A bit of paper under the back end of the + reed will stop it. Any loose material about the instrument + may cause trouble of this kind. Trace up the cause and the + remedy will suggest itself. + </p> + <p> + A buzzing sound may be caused by a reed's being too tight + in the reed chamber, causing the tongue to vibrate against + the sides of the brass body. In some rare cases, not being + firmly riveted, the tongue will move to one side, causing + the same trouble. Care and pains must be taken in working + with reeds, but when in this condition they must be + repaired. Tap the rivet lightly with a hammer and <span + class='pagenum'><a name="Page_190" id="Page_190"></a>[Pg + 190]</span>try it; if it still does not sound clear, catch + the butt of the reed (riveted end) with a pair of parallel + pliers, and turn it toward the center until, when + vibrating, it clears the jaws. + </p> + <p class="center smcap"> + Tuning. + </p> + <p> + The method of tuning the organ is very simple. To flatten + the tone of a reed, scrape the tongue near the butt or + rivet, making it thinner at that point, which will cause it + to vibrate at a slower rate. To sharpen the tone, scrape it + at the point, thereby lightening the vibrating end, which + will cause a more rapid rate of vibration. When a reed has + been scraped or filed so thin at the point that it will + bear no more scraping, it can sometimes be sharpened by + bending it up and down a few times, which has a tendency to + put temper in the metal. Some reeds are curved at the point + purposely to secure a certain voice. Do not interfere with + the proper curvature when tuning. In tuning organs, the + same system and general instruction given for piano tuning + will apply; however, it is rarely, if ever, necessary to + give an organ as thorough tuning as you would a piano. It + is a very tedious job where you have to draw each <span + class='pagenum'><a name="Page_191" id="Page_191"></a>[Pg + 191]</span>reed, apply the proper method, insert it and try + the result, thus cutting and trying each one perhaps + several times before getting the desired result. In + factories devices are used which render the operation very + much easier. + </p> + <p> + One thing you should know is, that organs are not tempered + as finely as pianos, nor is there the pains taken to secure + perfect unisons. In fact, you can hardly find a perfect + unison in an organ of modern make, much less, a correct + temperament. Finding a tone that is so far out as to be + very disagreeable, adjust it between the octave below and + the octave above, try it in the proper chords and equalize + it in the best possible way; but it is not often you will + be able to tune it to absolute precision with its octaves. + It is thought by many that a slight deviation from correct + unisons, sufficient to give a series of waves, gives the + organ a more mellow voice and consequently a more musical + (?) tone; and while we do not agree with any such + proposition, it makes the tuner's work less exacting. + </p> + <p> + We feel that an apology is in order for not giving + illustrations of the action of the organ, but if the + student will study this lesson in connection with the <span + class='pagenum'><a name="Page_192" id="Page_192"></a>[Pg + 192]</span>instrument itself, we believe he will have no + trouble in learning all about its mechanical action and its + demands upon the tuner. + </p> + <p class="center"> + QUESTIONS ON LESSON XVI. + </p> + <ol> + <li> + Name the musical advantages possessed by the organ which + are absent in the piano. + </li> + <li> + Name the musical advantages possessed by the piano which + are absent in the organ. + </li> + <li> + Describe the mechanical operations taking place in the + organ when a key is being sounded. + </li> + <li> + State what you would do to flatten the tone of a reed and + give reasons. + </li> + <li> + State what you would do to sharpen the tone of a reed and + give reasons. + </li> + </ol> + <hr style="width: 65%;" /> + <p><span class='pagenum'><a name="Page_193" + id="Page_193"></a>[Pg 193]</span></p> + <h2> + <a name="LESSON_XVII" id="LESSON_XVII"></a>LESSON XVII. + </h2> + <hr /> + <h3> + CONCLUDING PROFESSIONAL HINTS. + </h3> + <p> + Peculiar incidents occur in the experience of the piano + tuner, some of which have come under the observation of the + author so frequently that he deems it advisable to mention + them here; there are incidents also that happen once in a + life-time which must be treated in their time with tact and + good judgment, and which it is impossible to describe here, + as each tuner, in his special field, will elicit new + developments. Occasion often requires the tuner to summon + all his wits and tact in order to dispose of questions put + to him, both by pianos and owners. + </p> + <p> + Among the perplexing things that come to the tuner are the + terms used by musicians and piano owners to express certain + qualities of tone and certain discrepancies of the + instrument. We will define a number of these. + </p> + <p> + <b>Brilliant.</b> The sense in which this term is used is + astonishing to one who is accustomed to <span + class='pagenum'><a name="Page_194" id="Page_194"></a>[Pg + 194]</span>using words according to their dictionary + meanings. We have heard persons say their piano was too + <i>brilliant</i>; or, that it was not <i>brilliant</i> + enough. They mean this term to apply to what we are pleased + to call the voice of the instrument. When the hammers are + hard, producing a sharp, penetrating tone, they call it + <i>brilliant</i>; when the hammers are soft and produce + what a trained ear would accept as a soft, sweet, musical + tone, some persons will say that the instrument lacks + brilliancy. Persons of a different taste, and, we would + say, a more cultured ear, call the tone <i>harsh</i> when + the hammers are hard, and they usually desire the tuner to + <i>soften</i> the tone, which he does by softening the + hammer ends as has been described in Lesson VII. This + operation, which we call voicing, is a very delicate piece + of work, and the tuner should exercise care and pains in + doing it; so we will deviate from the trend of the + discourse and offer a few directions here, as the previous + instructions are hardly complete. + </p> + <p> + Insert the felt pick (which should contain only one point, + and not three or four, as they usually do) in the point of + the hammer and give it a rotary motion, so to speak, + loosening up the felt and giving it its <span + class='pagenum'><a name="Page_195" id="Page_195"></a>[Pg + 195]</span>original elasticity. Do not pick up the felt at + the point. This method, which is resorted to by many + tuners, is injurious to the hammers and really does no + permanent good. Another method which is very good, and a + very easy one, is to take your parallel pliers and squeeze + the felt slightly at the point. Apply the pliers at right + angles with the hammer (if the action of the upright, your + pliers will be in an upright position) and catch the hammer + at a depth of about three-quarters of the thickness of the + felt. If the hammers are very hard it may be well to use + both the pliers and the pick; but care must always be taken + not to get the hammers too soft, and extreme care must be + taken not to get some softer than others. Some hammers are + always used more than others and, of course, these will + need more softening. Usually those at the extreme ends of + the instrument will need no softening at all, but sometimes + the bass will bear considerable softening. After going over + them in the above way, try them by playing the chromatic + scale and you will invariably find some that need + additional attention. Be sure that no hard tone is left, as + such a condition is a great annoyance to a delicate ear. + </p> + <p> + <span class='pagenum'><a name="Page_196" + id="Page_196"></a>[Pg 196]</span> + </p> + <p> + <b>Singing.</b> When a damper is out of order and does not + do its work properly, they often say the tone <i>sings</i>. + They say the same thing about the reed organ when a pallet + sticks or a key stays down. Sometimes this term is used to + express the grating vibration which has been treated under + the head of <i>sympathetic rattle</i>. + </p> + <p> + <b>Tin-panny.</b> This term is often used and generally + means that the instrument is out of tune, and especially + that the unisons are out. Sometimes it is used to express a + <i>hollow</i> quality of tone; but you will rarely, if + ever, hear a piano spoken of in this way if it is in + correct tune. Any piano out of tune badly may be said to + sound tin-panny. + </p> + <p> + <b>Bass-ey.</b> This term expresses a very harsh bass. + Imperfect octaves or unisons in the bass of a piano give + rise to the use of this term. If the bass of the instrument + is decidedly flat, the same term is sometimes used to + express the condition. + </p> + <p> + <b>Harsh.</b> This term, when it does not apply to the + voice of the piano, generally reflects upon the work of the + tuner (?). Chords are <i>harsh</i> when they contain + over-sharp thirds, bad fifths, octaves, etc. Take care that + your temperament contains no bad <span class='pagenum'><a + name="Page_197" id="Page_197"></a>[Pg 197]</span>chords, + and after you are all through, see that all tones have + stood, and that you have left no bad unisons or octaves. + One or two carelessly tuned <ins class="corr" title="tonse appears in the original">tones</ins> may disparage your + otherwise creditable work. + </p> + <p> + <b>Questions.</b> Questions are often asked the tuner + concerning the care of the piano. Be prepared to answer any + reasonable question that may come up, which your knowledge + of the instrument should enable you to do. In regard to + temperature, moisture, etc., an extreme either way is the + thing to avoid. A very dry or hot atmosphere will crack the + varnish, warp the wooden parts, crack the sound-board, + cause parts to come unglued, etc. On the other hand, too + much moisture will rust the steel parts, strings, etc.; so + the "happy medium" is the condition to be desired. As to + keeping pianos closed, a question you will often be asked, + we think it is better to keep them open at all times than + to keep them closed at all times; because, if they are kept + open they are subjected to the changes of the atmosphere, + which will rarely permit the piano to become either very + damp or too dry. In a word, a room that is healthy for + human beings is all right for the piano. + </p> + <p> + <span class='pagenum'><a name="Page_198" + id="Page_198"></a>[Pg 198]</span> + </p> + <p> + <b>Seasons for Tuning.</b> The prevalent idea in regard to + this matter is that pianos should be tuned either at the + beginning of cold or of warm weather. In our experience, we + have found that it makes no difference when the piano is + tuned if it is kept in the living room. If, however, a + piano were tuned upon a warm day in the fall and then + allowed to remain in a room in which the temperature + suddenly fell to zero, we could not expect it to stand in + tune; and much less, if the room is heated up occasionally + and then left for an interval at the mercy of the weather. + Persons who treat their pianos in this way should have them + tuned about four times a year. + </p> + <hr style="width: 65%;" /> + <div class="footnotes"> + <h3> + FOOTNOTES + </h3> + <div class="footnote"> + <p> + <a id="fn_A" name="fn_A"></a><a + href="#fnanchor_A"><span class="label">[A]</span></a> + Published by Theodore Presser, Philadelphia, Pa. + </p> + <p> + <a id="fn_B" name="fn_B"></a><a + href="#fnanchor_B"><span class="label">[B]</span></a> + There are two sections of the lower bridge, one for the + treble and one for the overstrung bass. + </p> + <p> + <a id="fn_C" name="fn_C"></a><a + href="#fnanchor_C"><span class="label">[C]</span></a> + The three strings composing the trio or unison are + numbered 1st, 2d or middle, and 3d, from left to right. + </p> + <p> + <a id="fn_D" name="fn_D"></a><a + href="#fnanchor_D"><span class="label">[D]</span></a> + The chromatic scale is a succession of all the half + steps in the compass of one octave. Counting the octave + tone, it contains thirteen tones, but we speak of + twelve, as there are only twelve which differ in name. + </p> + <p> + <a id="fn_E" name="fn_E"></a><a + href="#fnanchor_E"><span class="label">[E]</span></a> + In making these suggestions, no calculation is made for + the liability of the tones tuned to fall. This often + happens, in which case your first test will display a + sharp third. In cases like this it is best to go on + through, taking pains to temper carefully, and go all + over the temperament again, giving all the strings an + equal chance to fall. If the piano is very bad, you may + have to bring up the unisons roughly, inuring this + portion of the instrument to the increased tension, + when you may again place your continuous mute and set + your temperament with more certainty. + </p> + <p> + <a id="fn_F" name="fn_F"></a><a + href="#fnanchor_F"><span class="label">[F]</span></a> + Bear in mind, the foregoing and following instructions + are written with reference to the upright piano. The + square does not permit the observance of these + suggestions so favorably as the upright. + </p> + <p> + <a id="fn_G" name="fn_G"></a><a + href="#fnanchor_G"><span class="label">[G]</span></a> + When the bushing of the center-pin of the hammer butt + becomes badly worn or the hammer-flange becomes loose, + or the condition of the hammer or flange becomes so + impaired that the hammer has too much play, it may so + strike the strings as to tend to produce the phenomenon + described in the above paragraph. When in such a + condition, one side of the hammer may strike in advance + of the other just enough to throw the vibrations in + opposition. Once you may get a strong tone, and again + you strike with the same force and hear but a faint, + almost inaudible sound. For this reason, as well as + that of preventing excessive wear, the hammer joint + should be kept firm and rigid. + </p> + </div> + </div> + <hr style="width: 65%;" /> + <p><span class='pagenum'><a name="Page_199" + id="Page_199"></a>[Pg 199]</span></p> + <h2> + <a name="INDEX" id="INDEX"></a>INDEX. + </h2> + <hr /> + <ul> + <li> + Action, <a href="#Page_017">17</a> + <ul> + <li> + brackets, <a href="#Page_024">24</a> + </li> + <li> + of grand piano, <a href="#Page_037">37</a>, <a + href="#Page_038">38</a>, <a href="#Page_062">62</a> + </li> + <li> + of square piano, <a href="#Page_032">32</a>, <a + href="#Page_034">34</a> + </li> + <li> + removing, square and grand, <a + href="#Page_038">38</a> + </li> + <li> + replacing, square and grand, <a + href="#Page_039">39</a> + </li> + <li> + requisites of, <a href="#Page_017">17</a>, <a + href="#Page_018">18</a> + </li> + <li> + top, of square piano, <a href="#Page_034">34</a> + </li> + <li> + trap, of square piano, <a href="#Page_019">19</a>, <a + href="#Page_034">34</a> + </li> + </ul> + </li> + <li> + Advantages of two-octave temperament, <a + href="#Page_171">171</a> + </li> + <li> + Ancient instruments, <a href="#Page_013">13</a> + </li> + <li class="break"> + Back check, adjustment of, <a href="#Page_049">49</a> + <ul> + <li> + and back catch, <a href="#Page_018">18</a>, <a + href="#Page_027">27</a>, <a href="#Page_028">28</a>, + <a href="#Page_033">33</a>, <a + href="#Page_037">37</a> + </li> + <li> + wire, <a href="#Page_027">27</a> + </li> + </ul> + </li> + <li> + Balance pin, <a href="#Page_021">21</a> + <ul> + <li> + rail, <a href="#Page_021">21</a> + </li> + </ul> + </li> + <li> + Bearing bar, <a href="#Page_017">17</a> + </li> + <li> + Beats, waves, and pulsations, <a href="#Page_073">73</a>, + <a href="#Page_150">150</a> + <ul> + <li> + of unison, octave, and major third, <a + href="#Page_154">154</a> + </li> + <li> + cause of, <a href="#Page_077">77</a>, <a + href="#Page_150">150</a> + </li> + </ul> + </li> + <li> + Black lead, use of, <a href="#Page_064">64</a> + </li> + <li> + Block rail, <a href="#Page_027">27</a>, <a + href="#Page_051">51</a> + </li> + <li> + Bottom or capstan, adjustment of, <a + href="#Page_048">48</a>, <a href="#Page_099">99</a> + <ul> + <li> + or key rocker, <a href="#Page_023">23</a>, <a + href="#Page_033">33</a>, <a href="#Page_048">48</a>, + <a href="#Page_056">56</a>, <a + href="#Page_057">57</a> + </li> + </ul> + </li> + <li> + Bracket bolts, <a href="#Page_025">25</a> + </li> + <li> + Bridle, <a href="#Page_028">28</a> + <ul> + <li> + putting in new, <a href="#Page_050">50</a> + </li> + <li> + wire, <a href="#Page_028">28</a>, <a + href="#Page_050">50</a> + </li> + </ul> + </li> + <li> + Bridges, <a href="#Page_016">16</a>, <a + href="#Page_017">17</a> + <ul> + <li> + split, <a href="#Page_173">173</a> + </li> + </ul> + </li> + <li> + Building of upright piano, <a href="#Page_016">16</a> + </li> + <li> + Butts, <a href="#Page_028">28</a> + <ul> + <li> + and flanges, repairing of, <a href="#Page_059">59</a> + </li> + </ul> + </li> + <li class="break"> + Capstan, <a href="#Page_024">24</a>, <a + href="#Page_048">48</a> + </li> + <li> + Cause of beats <a href="#Page_027">27</a>, <a + href="#Page_150">150</a> + </li> + <li> + Center-pins, <a href="#Page_025">25</a> + <ul> + <li> + putting in new <a href="#Page_052">52</a> + </li> + </ul> + </li> + <li> + Clicks at release of key, <a href="#Page_051">51</a>, <a + href="#Page_052">52</a> + </li> + <li> + Compromises, the, <a href="#Page_099">99</a>, <a + href="#Page_100">100</a> + </li> + <li> + Continuous mute, <a href="#Page_089">89</a> + </li> + <li class="break"> + Damper lever, <a href="#Page_029">29</a> + <ul> + <li> + felt, softening, <a href="#Page_054">54</a> + </li> + </ul> + </li> + <li> + Damper, of grand piano, <a href="#Page_037">37</a> + <ul> + <li> + of square piano, <a href="#Page_036">36</a>, <a + href="#Page_060">60</a> + </li> + <li> + rod, <a href="#Page_030">30</a> + </li> + <li> + rod, squeaking of, <a href="#Page_055">55</a> + </li> + <li> + spoon, <a href="#Page_029">29</a> + </li> + <li> + springs broken, <a href="#Page_054">54</a> + </li> + </ul> + </li> + <li> + Dampers, <a href="#Page_018">18</a>, <a + href="#Page_029">29</a> + </li> + <li> + Damping, defective, <a href="#Page_054">54</a>, <a + href="#Page_060">60</a>, <a href="#Page_061">61</a> + </li> + <li> + Ditonic comma <a href="#Page_144">144</a> + </li> + <li class="break"> + Evolution of the piano, <a href="#Page_012">12</a> + </li> + <li> + Extension, <a href="#Page_023">23</a> + </li> + <li class="break"> + False waves, <a href="#Page_160">160</a>, <a + href="#Page_161">161</a> + </li> + <li> + Fifths, beats of, <a href="#Page_079">79</a> + <ul> + <li> + not all tempered alike, <a href="#Page_105">105</a>, + <a href="#Page_106">106</a> + </li> + <li> + tempering of, <a href="#Page_079">79</a>, <a + href="#Page_104">104</a> + </li> + </ul> + </li> + <li> + Final inspection, <a href="#Page_172">172</a> + </li> + <li> + Fischer System of temperament, diagram of, <a + href="#Page_082">82</a> + </li> + <li> + Flanges, <a href="#Page_025">25</a> + <ul> + <li> + repairing of, <a href="#Page_059">59</a> + </li> + </ul> + </li> + <li class="break"> + Guide pins, <a href="#Page_023">23</a> + </li> + <li class="break"> + Hammer, butt, refelting, <a href="#Page_051">51</a> + <ul> + <li> + capping with buckskin, <a href="#Page_059">59</a> + </li> + <li> + felts, cleaning, <a href="#Page_034">34</a> + <ul> + <li> + gluing, <a href="#Page_054">54</a> + </li> + <li> + hardening, <a href="#Page_054">54</a> + </li> + <li> + softening, <a href="#Page_054">54</a> + </li> + <li> + trimming, <a href="#Page_060">60</a> + </li> + <li> + voicing, <a href="#Page_054">54</a>, <a + href="#Page_104">104</a> + </li> + </ul> + </li> + <li> + head <a href="#Page_029">29</a> + </li> + <li> + rail, <a href="#Page_029">29</a>, <a + href="#Page_033">33</a> + </li> + <li> + shank or stem, <a href="#Page_029">29</a>, <a + href="#Page_053">53</a> + <ul> + <li> + broken, <a href="#Page_063">63</a> + </li> + <li> + renewing, <a href="#Page_053">53</a> + </li> + </ul> + </li> + <li> + spring, <a href="#Page_052">52</a> + </li> + <li> + sticking, <a href="#Page_052">52</a> + </li> + </ul> + </li> + <li> + Hitch-pins, <a href="#Page_016">16</a>, <a + href="#Page_017">17</a> + </li> + <li class="break"> + Instrumental attachments, removal of, <a + href="#Page_118">118</a> + </li> + <li> + Intervals flattened, <a href="#Page_157">157</a> + <ul> + <li> + sharpened, <a href="#Page_157">157</a> + </li> + </ul> + </li> + <li> + Ivories, regluing, <a href="#Page_064">64</a> <span + class='pagenum'><a name="Page_200" id="Page_200"></a>[Pg + 200]</span> + </li> + <li class="break"> + Jack, <a href="#Page_026">26</a> + <ul> + <li> + repairing of, <a href="#Page_050">50</a>, <a + href="#Page_058">58</a> + </li> + <li> + sluggish, <a href="#Page_057">57</a> + </li> + <li> + -spring broken, <a href="#Page_058">58</a> + </li> + </ul> + </li> + <li class="break"> + Key, defects in, <a href="#Page_047">47</a>, <a + href="#Page_048">48</a> + <ul> + <li> + leads, <a href="#Page_022">22</a> + </li> + <li> + organ, sticking, <a href="#Page_185">185</a>, <a + href="#Page_186">186</a> + </li> + <li> + removing, square piano, <a href="#Page_056">56</a> + </li> + <li> + squeaking, <a href="#Page_064">64</a> + </li> + <li> + sticking, <a href="#Page_046">46</a> + </li> + </ul> + </li> + <li class="break"> + Lead, in keys, <a href="#Page_022">22</a> + <ul> + <li> + black, use of, <a href="#Page_064">64</a> + </li> + <li> + loose in key, <a href="#Page_064">64</a> + </li> + </ul> + </li> + <li> + Length, tension, and weight of strings, <a + href="#Page_075">75</a> + </li> + <li> + Loud pedal, <a href="#Page_019">19</a>, <a + href="#Page_030">30</a> + </li> + <li class="break"> + Main rail, <a href="#Page_025">25</a> + </li> + <li> + Mathematics of tempered scale, <a + href="#Page_126">126</a> + </li> + <li> + Metal plates, <a href="#Page_015">15</a> + </li> + <li> + Mute, continuous, <a href="#Page_089">89</a>, <a + href="#Page_090">90</a> + </li> + <li> + Mutes, setting in upright piano, <a + href="#Page_117">117</a>-<a href="#Page_120">120</a> + <ul> + <li> + in bass, <a href="#Page_121">121</a> + </li> + <li> + beyond temperament, <a href="#Page_120">120</a> + </li> + <li> + in square piano, <a href="#Page_122">122</a> + </li> + <li> + on nodal points, <a href="#Page_161">161</a> + </li> + </ul> + </li> + <li class="break"> + Octave, dividing into major thirds, <a + href="#Page_134">134</a> + <ul> + <li> + into minor thirds, <a href="#Page_140">140</a> + <ul> + <li> + perfect fifths, <a href="#Page_142">142</a> + </li> + </ul> + </li> + </ul> + </li> + <li> + Octaves, relative vibration of, <a + href="#Page_078">78</a> + </li> + <li> + Organ, reed, tuning and repairing the, <a + href="#Page_178">178</a> + <ul> + <li> + bellows, leaks in, <a href="#Page_187">187</a> + </li> + <li> + capabilities of, <a href="#Page_179">179</a> + </li> + <li> + cleaning, <a href="#Page_180">180</a> + </li> + <li> + examination, <a href="#Page_183">183</a> + </li> + <li> + keys sticking, <a href="#Page_185">185</a>, <a + href="#Page_186">186</a> + </li> + <li> + pallets, <a href="#Page_186">186</a> + </li> + <li> + pedal defects, <a href="#Page_188">188</a> + </li> + <li> + reeds, to find, <a href="#Page_184">184</a> + <ul> + <li> + tuning, <a href="#Page_190">190</a> + </li> + </ul> + </li> + <li> + stops, <a href="#Page_182">182</a> + <ul> + <li> + disconnected, <a href="#Page_184">184</a> + </li> + </ul> + </li> + <li> + sympathetic vibration, <a href="#Page_189">189</a> + </li> + </ul> + </li> + <li> + Over-tension, <a href="#Page_114">114</a> + </li> + <li class="break"> + Panel, removing of, <a href="#Page_075">75</a> + </li> + <li> + Parts of grand action, <a href="#Page_038">38</a> + <ul> + <li> + of square action, <a href="#Page_034">34</a> + </li> + </ul> + </li> + <li> + Pendulum to aid in judgment of a second of time, <a + href="#Page_104">104</a> + </li> + <li> + Piano frame, <a href="#Page_015">15</a> + <ul> + <li> + tuner, requisites of, <a href="#Page_007">7</a>, <a + href="#Page_070">70</a> + </li> + </ul> + </li> + <li> + Pianos, special use of, <a href="#Page_085">85</a>, <a + href="#Page_086">86</a> + </li> + <li> + Pitch, concert, <a href="#Page_127">127</a> + <ul> + <li> + international, <a href="#Page_081">81</a>, <a + href="#Page_127">127</a> + </li> + </ul> + </li> + <li> + Pitch, left to tuner's judgment, <a + href="#Page_086">86</a>, <a href="#Page_087">87</a>, <a + href="#Page_089">89</a> + <ul> + <li> + to determine most favorable, <a + href="#Page_085">85</a> + </li> + </ul> + </li> + <li> + Professional hints, <a href="#Page_193">193</a> + </li> + <li class="break"> + Questions asked by owners, <a href="#Page_197">197</a> + </li> + <li class="break"> + Ratio of intervals, <a href="#Page_132">132</a> + </li> + <li> + Reed organ. See <i>Organ</i>. + </li> + <li> + Regulating button, <a href="#Page_026">26</a>, <a + href="#Page_051">51</a> + <ul> + <li> + rail, <a href="#Page_026">26</a>, <a + href="#Page_036">36</a> + </li> + </ul> + </li> + <li> + Repairing small wooden parts, <a href="#Page_063">63</a> + </li> + <li> + Repetition of stroke, <a href="#Page_018">18</a>, <a + href="#Page_027">27</a> + </li> + <li class="break"> + Searching for articles on sound board, <a + href="#Page_044">44</a> + </li> + <li> + Seasons for tuning, <a href="#Page_198">198</a> + </li> + <li> + Soft pedal, <a href="#Page_029">29</a>, <a + href="#Page_036">36</a>, <a href="#Page_038">38</a> + </li> + <li> + Sound board, <a href="#Page_016">16</a> + <ul> + <li style="display: none;"> + <ul> + <li> + split, <a href="#Page_044">44</a> + </li> + <li> + unglued, <a href="#Page_045">45</a> + </li> + </ul> + </li> + <li> + waves, interference of, <a href="#Page_078">78</a>, + <a href="#Page_150">150</a> + </li> + </ul> + </li> + <li> + Splicing piano wire, <a href="#Page_176">176</a> + </li> + <li> + Spring rail, <a href="#Page_029">29</a> + </li> + <li> + Stringing of upright, <a href="#Page_016">16</a>, <a + href="#Page_017">17</a> + </li> + <li> + Strings growing sharper, <a href="#Page_088">88</a> + <ul> + <li> + putting in new, <a href="#Page_174">174</a>, <a + href="#Page_175">175</a> + </li> + <li> + rendering through bridges, <a + href="#Page_112">112</a>, <a href="#Page_114">114</a> + </li> + <li> + splicing, <a href="#Page_176">176</a> + </li> + </ul> + </li> + <li> + Study and practice of tuning, <a href="#Page_066">66</a> + </li> + <li> + Sustaining pedal, <a href="#Page_030">30</a> + <ul> + <li> + squeaking of, <a href="#Page_055">55</a> + </li> + </ul> + </li> + <li> + Sympathetic rattle, <a href="#Page_043">43</a> + </li> + <li> + Syntonic comma, <a href="#Page_132">132</a> + </li> + <li> + Systems of temperament, various, <a + href="#Page_163">163</a> + </li> + <li> + System A, <a href="#Page_165">165</a> + <ul> + <li> + B, <a href="#Page_166">166</a> + </li> + <li> + C, <a href="#Page_167">167</a>, <a + href="#Page_168">168</a> + </li> + </ul> + </li> + <li class="break"> + Tables of relative string length, <a + href="#Page_131">131</a>, <a href="#Page_136">136</a>, <a + href="#Page_140">140</a>, <a href="#Page_143">143</a> + </li> + <li> + Temperament, advantages of the two-octave, <a + href="#Page_171">171</a> + <ul> + <li> + equal, <a href="#Page_097">97</a>, <a + href="#Page_144">144</a> + </li> + <li> + Fischer system, <a href="#Page_074">74</a> + </li> + <li> + finishing up, <a href="#Page_156">156</a> + </li> + <li> + introductory remarks on, <a href="#Page_068">68</a>, + <a href="#Page_072">72</a> + </li> + <li> + rationale of, <a href="#Page_128">128</a>, <a + href="#Page_139">139</a> + </li> + <li> + requisites of, <a href="#Page_133">133</a> + </li> + <li> + setting, specific instructions, <a + href="#Page_085">85</a> + </li> + <li> + theory of, <a href="#Page_097">97</a> + </li> + <li> + unequal, <a href="#Page_098">98</a> + </li> + <li> + various systems, <a href="#Page_163">163</a>-<a + href="#Page_168">168</a> + </li> + </ul> + </li> + <li> + Tension, equalization of, <a href="#Page_111">111</a>, <a + href="#Page_112">112</a> + </li> + <li> + Terms to express tone qualities, <a + href="#Page_193">193</a>-<a href="#Page_196">196</a> + </li> + <li> + Testing by thirds and tenths, <a href="#Page_170">170</a> + </li> + <li> + Tests, chords, <a href="#Page_094">94</a>, <a + href="#Page_099">99</a>, <a href="#Page_103">103</a> + </li> + <li> + Third, excessive sharpness of, <a + href="#Page_095">95</a>, <a href="#Page_103">103</a> + </li> + <li> + Thirds, major, <a href="#Page_135">135</a> + <ul> + <li> + major, sharper than perfect, <a + href="#Page_135">135</a> + </li> + <li> + minor, flatter than perfect, <a + href="#Page_141">141</a> + </li> + </ul> + <span class='pagenum'><a name="Page_201" + id="Page_201"></a>[Pg 201]</span> + </li> + <li> + Tones, harmonic, <a href="#Page_120">120</a>, <a + href="#Page_130">130</a> + </li> + <li> + Touch, altering the, <a href="#Page_048">48</a> + </li> + <li> + Treble, extreme, sharper than perfect, <a + href="#Page_159">159</a> + </li> + <li> + Tuning, instructions for first experiments in, <a + href="#Page_092">92</a>-<a href="#Page_095">95</a> + <ul> + <li> + hammer, manipulation of, <a href="#Page_110">110</a>, + <a href="#Page_115">115</a>, <a + href="#Page_116">116</a> + </li> + <li> + pins, marking of in square, <a + href="#Page_122">122</a> + <ul> + <li> + loose, <a href="#Page_173">173</a> + </li> + <li> + setting of, <a href="#Page_112">112</a>-<a + href="#Page_114">114</a> + </li> + </ul> + </li> + <li> + the bass, <a href="#Page_160">160</a> + </li> + <li> + the treble, <a href="#Page_157">157</a>, <a + href="#Page_159">159</a> + </li> + </ul> + </li> + <li class="break"> + Vibration numbers, comparison of, <a + href="#Page_137">137</a>, <a href="#Page_146">146</a>, <a + href="#Page_147">147</a>, <a href="#Page_148">148</a> + </li> + <li class="break"> + Watchmaker's screwdriver, use of in piano repairing, <a + href="#Page_063">63</a> + </li> + <li> + Wippen, <a href="#Page_025">25</a> + </li> + <li> + Wire splicing, <a href="#Page_176">176</a> + </li> + <li> + Wooden parts, shrinking, rattling, <a + href="#Page_059">59</a> + <ul> + <li> + repairing of small, <a href="#Page_063">63</a> + </li> + </ul> + </li> + </ul> + <div class="footnotes"> + <h3> + Transcriber's Note + </h3> + <div class="footnote"> + <p> + On page 197, 'tones' has been misspelt in the original text as 'tonse'. + </p> + </div> + </div> + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of Piano Tuning, by J. 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