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+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: ASCII
+
+*** 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
+
+
+
+
+
+
+
+
+
+J. CREE FISCHER
+
+PIANO TUNING
+
+A SIMPLE AND ACCURATE METHOD
+FOR AMATEURS
+
+
+
+DOVER PUBLICATIONS, INC.
+NEW YORK
+
+
+
+
+Copyright (c) 1907 by Theo. Presser.
+
+All rights reserved under Pan American and International Copyright
+Conventions.
+
+Published in Canada by General Publishing Company, Ltd., 30 Lesmill
+Road, Don Mills, Toronto, Ontario.
+
+Published in the United Kingdom by Constable and Company, Ltd., 10
+Orange Street, London WC 2.
+
+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+out-of-date: Practical Application of Piano Tuning as a Profession,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.
+
+_International Standard Book Number: 0-486-23267-0_
+
+_Library of Congress Catalog Card Number: 75-14759_
+
+Manufactured in the United States of America
+
+Dover Publications, Inc.
+
+180 Varick Street
+
+New York, N.Y. 10014
+
+
+
+
+PREFACE.
+
+
+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 variously
+estimated at from four to five millions. This means _more work for
+tuners_.
+
+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 occupation--persons 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
+many who are incompetent are following this profession, and that
+there is an increasing demand for tuners of skill.
+
+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.
+
+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.
+
+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.
+
+While the book is designed for self-instruction, the systematic
+arrangement of the text, and the 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.
+
+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.
+
+THE AUTHOR.
+
+
+
+
+CONTENTS.
+
+                                                             page
+
+LESSON I.                                                       7
+    Introduction.
+
+LESSON II.                                                     11
+    General construction of the piano and something of its
+    evolution and history,
+
+LESSON III.                                                    20
+    Technical Names and Uses of the Parts of the Upright
+    Action,
+
+LESSON IV.                                                     32
+    Action of the Square Piano. Action of the Grand Piano.
+    Instructions for Removing the Square and Grand Piano
+    Actions,
+
+LESSON V.                                                      43
+    Regulating and Repairing. Faults in Pianos aside from
+    the Action and their Remedies. Regulating and Repairing
+    the Upright Action,
+
+LESSON VI.                                                     56
+    Regulating and Repairing the Square Action.
+    Miscellaneous Repairs,
+
+LESSON VII.                                                    66
+    The Study and Practice of Piano Tuning,
+
+LESSON VIII.                                                   72
+    The Temperament. Beats, Waves, Pulsations. The New
+    System of Temperament. The Octave. The Fifth. Pitch.
+    Diagram of the Fischer System of Temperament,
+
+LESSON IX.                                                     85
+    Specific Instructions in Setting Temperament. The
+    Continuous Mute,
+
+LESSON X.                                                      97
+    Theory of the Temperament. Equal Temperament. Unequal
+    Temperament,
+
+LESSON XI.                                                    109
+    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,
+
+LESSON XII.                                                   126
+    Mathematics of the Tempered Scale. Rationale of the
+    Temperament. Proposition I,
+
+LESSON XIII.                                                  139
+    Rationale of the Temperament, Concluded. Proposition
+    II. Proposition III. Numerical Comparison of the
+    Diatonic with the Tempered Scale. Various Mathematical
+    Tables and Examples,
+
+LESSON XIV.                                                   150
+    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,
+
+LESSON XV.                                                    163
+    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,
+
+LESSON XVI.                                                   178
+    Tuning and Repairing the Reed Organ. Cleaning. Stops.
+    Examination. Sticking Keys. Leaks. Pedal Defects.
+    Sympathetic Vibrations. Tuning,
+
+LESSON XVII.                                                  193
+    Concluding Professional Hints. Peculiar Expressions
+    Used in Designating Qualities of Tone. Questions often
+    Asked the Piano Tuner. Seasons for Tuning,
+
+INDEX,                                                        199
+
+
+
+
+LESSON I.
+
+~INTRODUCTION.~
+
+
+Undoubtedly every human being is fitted for some sphere of
+usefulness--some 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."
+
+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
+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.
+
+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] and the student is required to master
+the first two chapters and prepare manuscripts upon each of the
+lessons. Below is a number of the most important questions selected
+from those lessons upon which manuscripts have been written:
+
+     1. Every white key on the piano represents an "absolute pitch."
+     By what names are these pitches known? How are the black keys
+     named?
+
+     2. How many tones constitute the diatonic scale? Give numerical
+     names.
+
+     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?
+
+     4. Why is there no black key between E and F, and between B and
+     C?
+
+     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?
+
+     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?
+
+     7. What do we mean by the term, Fundamental of a chord? What is
+     added to it to complete the common chord?
+
+     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?
+
+     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?
+
+     10. How many keys (white and black) are there between 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?
+
+     11. How many keys (white and black) are there between two keys
+     comprising a perfect fourth?
+
+     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[b]? Upon D[b]? Upon E[b]? Upon D?
+     Upon E? Upon A? Upon B?
+
+If one is able to answer these questions correctly he is qualified to
+begin the study of Piano Tuning.
+
+    [A] Published by Theodore Presser, Philadelphia, Pa.
+
+
+
+
+LESSON II.
+
+~GENERAL CONSTRUCTION OF THE PIANO; SOMETHING OF ITS EVOLUTION AND
+HISTORY.~
+
+
+The piano of today is, unquestionably, the most perfect, and
+consequently the most popular and beloved of all musical instruments.
+
+    That enchanting Queen of the home,
+      Whose place in the hearts of the family
+    Is as dear as though it could speak
+      In words of joy and sorrow,
+    Sadness or consolation;
+      Soothing, animating, enrapturing,
+    Charming away the soul
+      From its worldly weight of cares,
+    And wafting it softly
+      Into the realm of celestial dreams.
+
+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."
+
+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.
+
+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.
+
+History gives credit to Italy for the first productions of this kind,
+about 1600 A.D., when the faculty 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. (_Piano e forte_: soft and loud.)
+
+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.
+
+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 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.
+
+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.
+
+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.
+
+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 are "made to
+sell" are often much too light to fulfil this requirement.
+
+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.
+
+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.
+
+At the lower end of the plate, and just below the bridges,[B] 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 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.
+
+    [B] There are two sections of the lower bridge, one for the treble
+    and one for the overstrung bass.
+
+[Illustration]
+
+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.)
+
+After that portion of the case is completed which forms the key-bed or
+action frame, we are ready to set in the
+
+
+ACTION.
+
+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.
+
+The requisites of the action are as follows:
+
+The keys must descend quickly and easily at the touch of the
+performer, giving quick response.
+
+The weight of the hammer must be properly proportioned to the strings
+it causes to vibrate.
+
+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.)
+
+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.
+
+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.
+
+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.
+
+A means must be provided for releasing all the dampers from the
+strings at the will of the performer. The loud pedal, as it is
+called, but more properly, the damper pedal, accomplishes this end by
+raising the dampers from the strings.
+
+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.
+
+The "trap-action" consists of the pedals and the parts which convey
+motion to the action proper.
+
+
+QUESTIONS ON LESSON II.
+
+    1. What have been some of the salient obstacles necessary to
+    overcome in producing the perfected piano?
+
+    2. Of what use are the dampers? Explain their mechanical action.
+
+    3. Mention several of the qualities necessary to a good action.
+
+    4. Describe the building of an upright piano.
+
+    5. Contrast the musical capacity and peculiar characteristics of
+    the piano with those of the organ, which has the same keyboard.
+
+
+
+
+LESSON III.
+
+~TECHNICAL NAMES AND USES OF THE PARTS OF THE UPRIGHT PIANO ACTION.~
+
+
+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.
+
+The illustration accompanying this lesson is from a Wessell, Nickel
+and Gross Upright action. This 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.
+
+[Illustration]
+
+_Ky_, is the Key in its resting position.
+
+_c_, 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.
+
+_Bnc R_, shows the end of the balance rail, extending the entire
+length of the keyboard.
+
+_B P_, 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 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.
+
+_L_, 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, while in the upright, the hammer rests in a
+vertical position, only requiring to be thrown forward.
+
+_G P_, 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.
+
+_Bm_, 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.
+
+_E_, 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 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:
+
+_Cpn_, 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.
+
+_B_, is the metal action bracket. The bracket is one solid piece of
+metal. There are generally four brackets in the upright action. The
+brackets rest on supports in and at the sides of the keybed, and are
+secured at the top by large bolts,
+
+_BB_, 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.
+
+_M R_, 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.)
+
+_W_, is the wippen. Those pieces upon which or by which the small
+letter _g_ 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 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.
+
+_j_, 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.
+
+_js_, jack spring. Its purpose is to hold the jack inward against the
+"nose" or "heel" of the hammer butt. (See _Bt_, hammer butt.)
+
+_Rr_, regulating rail. The _regulating button_ is shown attached to
+the rail by the regulating screw which is turned by means of its ring
+on top of _Rr_. 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 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.
+
+_BR_, 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.")
+
+_BC_, 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.
+
+_BCW_, 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.
+
+_Bl_, 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.
+
+_Bl W_, bridle wire, screwed into wippen, bent in the shape of a
+buckle at top to hold bridle.
+
+_Bt_, butt; or, more specifically, hammer butt. In some cheap actions
+the butt is joined to its flange _g_, 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 explained elsewhere,
+all center-pins turn in the flange and not in the middle part.
+
+_HS_, hammer shank in rest position.
+
+_H_, hammer showing wood body or head, and covering of two layers of
+felt.
+
+_H R_, hammer rail, resting on felt cushion, _c_, 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.
+
+_sr_, spring rail screwed to the brackets. This rail supports the
+light wire springs which assist the hammers in returning to rest
+position.
+
+_S_, string.
+
+_D_, is the damper head secured to the damper wire by a set screw.
+
+_DL_, damper lever, working in damper flange _g_, which is screwed to
+main rail.
+
+_s_, spoon; so called from its shape. It is screwed into 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.
+
+_DR_, 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 _sustains_ any number of tones struck successively, giving the
+effect of more volume.
+
+The student should familiarize himself with all technical terms used
+in this lesson, as they will be referred to frequently in the
+succeeding lessons on repairing and regulating.
+
+
+QUESTIONS ON LESSON III.
+
+Without reference to anything but the cut, give technical names for
+parts of action represented by the following letters or abbreviations:
+
+    1. Bnc R, c, G P, BP, Ky, L.
+
+    2. Bm, Cpn, E, W, j, js, g, and M R.
+
+    3. Rr, B C, B R, B C W, Bl, and Bl W.
+
+    4. Bt, H, H S, H R, and sr.
+
+    5. S, D, D L, D R, s, B, and B B.
+
+    6. Explain the purpose and movements of the jack.
+
+    7. Describe a flange and the joint of same.
+
+    8. Give names of the four flanges shown in cut.
+
+    9. What is the purpose of the back catch and back check?
+
+    10. Explain the mechanical action of the damper pedal, and its
+    effect when used; also, that of the soft pedal.
+
+
+
+
+LESSON IV.
+
+~ACTION OF SQUARE AND GRAND PIANOS.~
+
+
+ACTION OF THE SQUARE PIANO.
+
+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.
+
+Compare the three cuts of actions in the study of this lesson.
+
+The main constituent parts of the square action are similar in
+appearance to those of the upright; in 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.
+
+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.
+
+Beginning with the key, it has its balance pin, guide pin, cushions,
+etc., practically the same as in the other types.
+
+The bottom, or key rocker, is reversed in the square; the end
+transmitting the motion being nearest the performer.
+
+The extension and wippen are absent in the square, as the jack is
+attached directly to the bottom or key-rocker.
+
+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.
+
+[Illustration: ACTION OF THE SQUARE PIANO.]
+
+     ACTION OF THE SQUARE PIANO.
+
+    A. Action Frame.
+
+    B's Indicate the Cushions, or Bushing, of felt, cloth or leather.
+
+    C. Balance Rail.
+
+    D. Balance Pin. Round.
+
+    E. Mortised Cap for Balance Pin. Bushed.
+
+    F. Key.
+
+    G. Lead.
+
+    H. Back Check.
+
+    I. Bottom or Key Rocker.
+
+    J. Bottom Screws; used to regulate height of Jack.
+
+    K. Jack.
+
+    L. Jack Spring; concealed under Bottom.
+
+    M. Center Pin to Jack.
+
+    N. Hammer Rail.
+
+    O. Regulating Screw.
+
+    P. Regulating Button.
+
+    Q. Flange Rail.
+
+    R. Flange. Split.
+
+    S. Flange Rail Screw.
+
+    T. Flange Screw, to regulate jaws of flange.
+
+    U. Hammer Butt.
+
+    V. Center Pin.
+
+    W. Hammer Stem or Shank.
+
+    X. Hammer Head.
+
+    Y. Hammer Felt. Treble hammers sometimes capped with buckskin in
+    old instruments.
+
+
+     TOP ACTION OF SQUARE PIANO.
+
+    1. Damper Lifter Wire.
+
+    2. Damper Lifter Buttons.
+
+    3. Damper Felt.
+
+    4. Damper Head.
+
+    5. Damper Lever.
+
+    6. Damper Leads.
+
+    7. Shade, supported by wire stanchions, on top of which are
+    screwed shade buttons.
+
+    8. Damper Rail. Tilted by Loud Pedal Rod which raises all the
+    dampers simultaneously.
+
+    9. Damper Flange.
+
+    10. Flange Screw.
+
+    11. Damper Lever Center Pin.
+
+     THE TRAP ACTION
+
+     consists of Pedals, Pedal Braces, Pedal Feet, Pedal Rods, Roller
+     Boards or Elbows, Studs, Plugs, Trap Springs, Wires and Lifter
+     Rods.
+
+     The cut is from the French action. Nearly all square pianos in
+     use at the present time are of this type.
+
+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.
+
+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.
+
+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 there until the
+key is released, when all movable parts fall to rest position.
+
+The action of the jack is the same in all types.
+
+
+ACTION OF THE GRAND PIANO.
+
+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.
+
+The grand action partakes of the characteristics of both the upright
+and the square, and is somewhat more complicated than either.
+
+The bottom and extension are almost identical with those of the
+upright; the extension, however, is necessarily very short.
+
+The wippen is of different construction, and somewhat more complicated
+in the grand.
+
+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.
+
+The back check is identical with that of the square.
+
+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.
+
+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.
+
+The student should study the three types of actions from the actions
+themselves, if possible.
+
+[Illustration: ACTION OF THE GRAND PIANO.]
+
+     ACTION OF THE GRAND PIANO.
+
+    1. Indicates the felt, cloth or leather, upon which the various
+    parts of the action rest, or fall noiselessly.
+
+    2. Key.
+
+    3. Bottom; sometimes called Key Rocker.
+
+    4. Extension; split at lower end to receive center pin in Bottom.
+
+    5. Wippen Support.
+
+    6. Jack.
+
+    7. Jack Spring.
+
+    8. Flange and Regulating Rail.
+
+    9. Regulating Screw, Button and Cushion.
+
+    10. Escapement Lever.
+
+    11. Regulating Screw in Hammer Flange, for Escapement Lever.
+
+    12. Check Wire, for Escapement Lever.
+
+    13. Screw to regulate fall of Escapement Lever.
+
+    14. Lever Flange, screwed to Flange Rail.
+
+    15. Hammer Shank.
+
+    16. Hammer.
+
+    17. Back Check.
+
+    18. Damper Lever, leaded.
+
+    19. Damper Wire, screwed into upright.
+
+    20. Damper Wire Guide, fastened to Sound-Board.
+
+    21. Damper Head and Felt.
+
+    0. Center Pins. Holes lined with Bushing Cloth.
+
+
+
+INSTRUCTIONS FOR REMOVING THE SQUARE AND GRAND ACTIONS.
+
+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.
+
+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.
+
+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 of the hammers to
+strike the props for which the openings are left in the back
+extremities of action.
+
+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.
+
+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
+summoned to assist in surmounting obstacles which are sure to arise
+unexpectedly.
+
+
+QUESTIONS ON LESSON IV.
+
+    1. From a philosophical point of view, which do you consider the
+    easiest and most perfect of the three types of actions? Also give
+    reasons.
+
+    2. 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?
+
+    3. Name the parts found in the upright action that are absent in
+    the square.
+
+    4. Describe the three methods by which soft tone is obtained from
+    use of soft pedal in the three types of actions.
+
+    5. 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?
+
+
+
+
+LESSON V.
+
+~REGULATING AND REPAIRING.~
+
+FAULTS IN PIANOS, ASIDE FROM THE ACTION, AND THEIR REMEDIES.
+
+
+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.
+
+The article may generally be found near the front of the sound board
+under the top piece of the 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.
+
+A split in the sound board, in any style of piano, sometimes causes
+trouble due to the vibrating edges 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.
+
+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 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.
+
+
+REGULATING AND REPAIRING THE UPRIGHT ACTION.
+
+(Use cut of upright action for reference in following study.)
+
+We will begin with the key and take up each part of the action in the
+succession in which motion is transmitted.
+
+1. _Key_.--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 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.
+
+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.
+
+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.
+
+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.
+
+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.
+
+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.
+
+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.
+
+2. _The Bottom or Capstan_.--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 hammer. Depress the key slowly, watching the hammer,
+and the fault will be discovered.
+
+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.
+
+3. _Back Check_.--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 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.
+
+4. _Bridle and Bridle Wire_.--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.
+
+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.
+
+5. _Jack_.--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.
+
+6. _Regulating Button_.--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.
+
+The block rail is properly adjusted at the factory and requires no
+attention.
+
+7. _Hammer Butt_.--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 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.
+
+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.
+
+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 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.
+
+Before leaving the hammer butt, see that the hammer spring is in its
+place.
+
+8. _Hammer Stem_.--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.
+
+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.
+
+9. _Hammers_.--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.
+
+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.
+
+10. _Dampers_.--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.
+
+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.
+
+Damper springs sometimes break. It is necessary to take out the damper
+lever to put in a new one.
+
+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.
+
+11. _Damper Rod_.--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.
+
+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.
+
+
+QUESTIONS ON LESSON V.
+
+    1. If you should find a key sticking, how would you determine the
+    cause?
+
+    2. Name all the defects to which the key is subject.
+
+    3. Describe the proper adjustment of bottom or capstan.
+
+    4. Give two causes of blocking.
+
+    5. Give the purpose of the regulating button, and its proper
+    adjustment.
+
+
+
+
+LESSON VI.
+
+~REGULATING AND REPAIRING.--(Continued.)~
+
+THE SQUARE ACTION.
+
+
+1. _The key_ 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.
+
+2. _Bottom or Key Rocker_.--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 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.
+
+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.
+
+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 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.
+
+3. _Jack_.--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.
+
+4. _The back check, hammer stem and regulating button_ 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.
+
+5. _Hammers_, 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.
+
+6. _Butts and Flanges_.--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.
+
+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.
+
+The flange, shown in the cut, is what is called a split flange. By the
+set screw T, 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.
+
+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.
+
+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 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.
+
+7. _Dampers_.--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 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.
+
+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.
+
+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.
+
+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 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.
+
+8. _The grand action_ 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.
+
+
+MISCELLANEOUS REPAIRS.
+
+A few miscellaneous difficulties, common to all styles of actions, are
+occasionally met with and need to be rectified.
+
+1. _Broken Hammer Shank_.--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.
+
+2. _Flanges, damper heads_, 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 wrapping is not permissible, and
+you are compelled to drill. Keep the screwdriver well sharpened and
+the drilling is easy.
+
+3. _Ivories_.--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.
+
+4. _Leads_ 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.
+
+5. _Friction_.--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.
+
+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.
+
+
+QUESTIONS ON LESSON VI.
+
+    1. When a key snaps or clicks at the instant it is let up, give
+    two or more conditions that might cause it.
+
+    2. When a key simply rattles, what parts of the action would you
+    examine for the trouble?
+
+    3. When a key is struck and there is no response, what may be the
+    cause?
+
+    4. Give two causes for defective damping in a square piano.
+
+    5. Give cause of and remedy for a squeaking key.
+
+
+
+
+LESSON VII.
+
+~THE STUDY AND PRACTICE OF PIANO TUNING.~
+
+
+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.
+
+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 tuning--one, 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.
+
+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.
+
+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 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.
+
+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 plan--a 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.
+
+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.
+
+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. 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.
+
+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.
+
+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 intervals in tuning and the easiest
+ones--those 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.
+
+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 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.
+
+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.
+
+
+
+
+LESSON VIII.
+
+~THE TEMPERAMENT.~
+
+
+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:
+
+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 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.
+
+~Beats, Waves, Pulsations.~--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.
+
+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 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.
+
+_The Fischer System_ 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.
+
+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, zither, or any stringed instrument. An instrument with metal
+strings, however, is better, as the vibrations are more perfect.
+
+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.
+
+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.
+
+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 being the
+easiest way in which to detect the beats, we advise that the student
+practice on it first.
+
+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 tone--a 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 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.
+
+_The cause_ 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."
+
+~The Octave.~--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.
+
+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.
+
+~The Fifth.~--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.
+
+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.
+
+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 to determine
+this by his own judgment. The tempering of the fifth will be treated
+exhaustively in subsequent lessons.
+
+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.
+
+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.
+
+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 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.
+
+The diagram illustrates the two octaves of the key-board, and shows
+how each key is designated in giving the system of temperament.
+
+~Pitch.~--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.
+
+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 octave, always tuning the
+octave whichever way is necessary to keep within the two octaves.
+
+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.
+
+DIAGRAM OF THE TWO OCTAVES USED IN "TEMPERAMENT," AND OF THE
+SUCCESSION IN WHICH THEY ARE TUNED.
+
+ C[#] D[#]    F[#] G[#] A[#]      C[#] D[#]    F[#] G[#] A[#]
+C    D    E  F    G    A    B    C    D    E  F    G    A    B   C
+                                 *
+1C,  1D,  1E, etc.               2C,  2D,  2E, etc.              3C
+-------------------------------  --------------------------------
+
+Middle C begins second octave; known by the asterisk (*) under it.
+
+~THE FISCHER SYSTEM OF SETTING TEMPERAMENT.~
+
+First, tune 3C by tuning pipe, or as directed.
+
+By this, tune 2C, and by 2C tune 1C; then tune as follows:
+
+    By  1C         tune 1G    fifth above,
+     "  1G          "   2G     octave above,
+     "  1G          "   2D    fifth above,
+     "  2D          "   1D     octave below,
+    By  1D         tune 1A    fifth above,
+    "   1A          "   2A     octave above,
+    "   1A          "   2E    fifth above,
+    "   2E          "   1E     octave below,
+    "   1E          "   1B    fifth above,
+    "   1B          "   2B     octave above,
+    "   1B          "   2F[#] fifth above,
+    "   2F[#]       "   1F[#]  octave below,
+    "   1F[#]       "   2C[#] fifth above,
+    "   2C[#]       "   1C[#]  octave below,
+    "   1C[#]       "   1G[#] fifth above,
+    "   1G[#]       "   2G[#]  octave above,
+    "   1G[#]       "   2D[#] fifth above,
+    "   2D[#]       "   1D[#]  octave below,
+    "   1D[#]       "   1A[#] fifth above,
+    "   1A[#]       "   2A[#]  octave above,
+    "   1A[#](B[b]) "   2F    fifth above,
+    "   2F          "   1F     octave below,
+    "   1F        try   2C    fifth above.
+
+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.
+
+
+QUESTIONS ON LESSON VIII.
+
+    1. What is the cause of the beats or pulsations?
+
+    2. Have you practiced tuning the unison?
+
+    3. Can you distinguish the beats clearly?
+
+    4. Have you practiced tuning the octave?
+
+    5. Do you thoroughly understand the system of setting the
+    temperament as set forth in this lesson?
+
+
+
+
+LESSON IX.
+
+~SPECIFIC INSTRUCTIONS IN TEMPERAMENT SETTING.~
+
+
+~Pitch.~--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:
+
+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 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.
+
+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.
+
+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 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:
+
+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.
+
+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 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.
+
+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:
+
+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
+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.
+
+~The Continuous Mute.~--Do not try to set a temperament without a
+continuous mute. Its purpose is to mute all outside (1st and 3d[C])
+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 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.
+
+    [C] The three strings composing the trio or unison are numbered 1st,
+    2d or middle, and 3d, from left to right.
+
+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 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.
+
+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
+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.
+
+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.
+
+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; 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.
+
+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 impossible to make
+them so, and get a correct scale, as we shall see later on.
+
+Now tune 2G by the 1G just tuned, to a perfect octave. Remember that
+all octaves should be left perfect--all 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.
+
+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
+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 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.
+
+
+QUESTIONS ON LESSON IX.
+
+    1. Define the terms, "International Pitch," and "Concert Pitch."
+
+    2. How would you arrive at the most favorable pitch at which to
+    tune a piano, if the owner did not suggest any certain pitch?
+
+    3. What is the advantage in using the continuous mute?
+
+    4. Tell what is necessary in the tuning of a string to insure it
+    to stand well?
+
+    5. What would result in the major third C-E, if all the fifths, up
+    to E, were tuned perfect?
+
+
+
+
+LESSON X.
+
+~THEORY OF THE TEMPERAMENT.~
+
+
+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.
+
+~Equal Temperament.~--Equal temperament is one in which the twelve
+fixed tones of the chromatic scale[D] are equidistant. Any chord will
+be as harmonious in one key as in another.
+
+    [D] 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.
+
+~Unequal Temperament.~--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.
+
+Upon the system table you will notice that the first five tones tuned
+(not counting the octaves) are 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.
+
+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.
+
+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.
+
+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.
+
+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 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-steps--twelve perfectly similar intervals--it seems very simple.
+
+Bear in mind that the two cardinal points of the system of tuning are:
+
+    1. All octaves shall be tuned perfect.
+
+    2. All fifths shall be tuned a little flatter than perfect.
+
+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.
+
+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.
+
+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.
+
+The following suggestions will serve you greatly in testing: When a
+third sounds disagreeably sharp, one or more fifths have not been
+sufficiently flattened.[E] 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.
+
+    [E] 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.
+
+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.
+
+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 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.
+
+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
+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.
+
+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.
+
+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 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.
+
+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.
+
+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.
+
+
+QUESTIONS ON LESSON X.
+
+    1. What is meant by the term "equal temperament"?
+
+    2. What is meant by the term "unequal temperament"?
+
+    3. Webster defines the term "temperament" thus: "A system of
+    compromises in the tuning of pianofortes, organs, etc." Explain
+    fully what these compromises are.
+
+    4. In testing chords to ascertain if temperament is correct, what
+    is the main thing to listen for as a guide?
+
+    5. In what three chords would you try the tone A, in testing your
+    temperament?
+
+    6. With what results have you demonstrated the experiments in this
+    and the previous lesson?
+
+
+
+
+LESSON XI.
+
+~THE TECHNIQUE OR MODUS OPERANDI OF PIANO TUNING.~
+
+
+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.
+
+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 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.
+
+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.
+
+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.
+
+
+MANIPULATION OF THE TUNING HAMMER.
+
+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 _vibrating
+section_ of the string 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.
+
+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).
+
+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 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.
+
+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.
+
+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 draw it tighter. Coming now to the exact
+manipulation of the tuning hammer, there are some important items to
+consider.[F] 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.
+
+    [F] 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.
+
+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 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.
+
+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
+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."
+
+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.
+
+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 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.
+
+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.
+
+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.
+
+
+SETTING THE MUTES OR WEDGES IN THE UPRIGHT.
+
+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 above, and assures the reader that a
+great deal of time can be saved by following it.
+
+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.
+
+The following diagram will, we think, demonstrate clearly the method
+employed:
+
+Upper row----  o   o   o   o   o   o   o   o   o   o    Tim-
+
+Middle row---   o   o   o   o   o   o   o   o   o   o   ing
+
+Lower row----    o   o   o   o   o   o   o   o   o   o  Pins.
+             ------------------------------------------ Bridge.
+
+             * 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * &c
+           /// /// /// /// /// /// /// /// /// ///    Treble stringing.
+           B   C  C[#] D  D[#] E   F  F[#] G  G[#] &c
+
+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.
+
+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[#], then
+third string of D and so on. By this method, you tune two strings
+every time you reset your mute.
+
+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.
+
+(T e m p e r a m e n t )   1   2   3   4   5   6   7    &c.
+ *** *** *** *** *** ***   A   B
+/// /// /// /// /// /// /// /// /// /// /// /// /// ///
+                           C[#] D  D[#] E   F  [F#] G   &c.
+
+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 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.
+
+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.
+
+                          9    8    7    6    5    4    3    2    1
+I   I   I   I   I   I   I   II   II   II   II   II   II   II   II   II
+                    C  C[#] D   D[#]  E    F   F[#]  G   G[#]  A   A[#]  B  C
+ Contra-Bass.                              Bass.                        Treble.
+
+
+SETTING THE MUTES IN THE SQUARE PIANO.
+
+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.
+
+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:
+
+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, 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.
+
+
+QUESTIONS ON LESSON XI.
+
+    1. By what means is the tuner enabled to make the strings draw
+    through the bridges and equalize the tension throughout their
+    entire length?
+
+    2. State conditions that may result from a tuning pin's not being
+    properly set.
+
+    3. In this system of muting, state definitely which string is
+    tuned first after the continuous mute is removed. Which second?
+    Which third?
+
+    4. 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?
+
+    5. Upon beginning to tune the treble beyond the temperament, which
+    string is tuned first? Which second? Which third?
+
+    6. (a) How many mutes are used in tuning outside the strings of
+       the temperament?
+
+       (b) In what proportion is the number of times the mute is
+       changed to the number of strings tuned?
+
+    7. (a) How many mutes are used in tuning the treble beyond the
+       temperament?
+
+       (b) In what proportion is the number of times the mute is
+       changed to the number of strings tuned?
+
+    8. Which pairs of pins are marked in the square piano to guide the
+    tuner in placing his hammer? Also, how are they marked?
+
+    9. 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[#]?
+
+    10. Tell what you can of the requirements necessary to insure that
+    a piano will stand in tune.
+
+
+
+
+LESSON XII.
+
+=MATHEMATICS OF THE TEMPERED SCALE.~
+
+
+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.
+
+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.
+
+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 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.
+
+International--3C--517.3. Concert--3C--540.
+
+(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.)
+
+Temperament denotes the arrangement of a system of musical sounds in
+which _each one_ will form a serviceable interval with _any one_ 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:
+
+    C must serve as 1, in the key of C major or C minor.
+       "      "     2,   "       "   B[b] "     B[b] "
+       "      "     3,   "       "   A[b] "     A    "
+       "      "     4,   "       "   G    "     G    "
+       "      "     5,   "       "   F    "     F    "
+       "      "     6,   "       "   E[b] "     E    "
+       "      "     7,   "       "   D[b] "     C[#] "
+
+Likewise, all other tones of the instrument must be so stationed that
+they can serve as _any member_ of _any scale_, major or minor.
+
+This is rendered necessary on account of the various modulations
+employed in modern music, in which every possible harmony in every key
+is used.
+
+
+RATIONALE OF THE TEMPERAMENT.
+
+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
+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.
+
+We must, therefore, flatten each fifth of the complete circle,
+C-G-D-A-E-B-F[#]-C[#]-G[#] or A[b]-E[b]-B[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.
+
+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.
+
+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 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.
+
+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.
+
+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.
+
+Funda- | Major | Major | Perfect | Perfect | Major |  Major  |  Oc- |
+mental |Second | Third | Fourth  |  Fifth  | Sixth | Seventh | tave |
+       |       |       |         |         |       |         |      |
+   C   |   D   |   E   |    F    |    G    |   A   |    B    |  C   |
+   1   |  8/9  |  4/5  |   3/4   |   2/3   |  3/5  |   8/15  | 1/2  |
+
+
+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:
+
+ C  |  D  |  E  |  F  |  G  |  A  |  B  |  C  |
+360 | 320 | 288 | 270 | 240 | 216 | 192 | 180 |
+
+
+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
+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 54--multiplying 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.
+
+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 _syntonic comma_.
+
+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.
+
+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.
+
+The chief requisites of any system of musical temperament adapted to
+the purposes of modern music are:--
+
+    1. That all octaves must remain perfect, each being divided into
+    twelve semitones.
+
+    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.
+
+    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.
+
+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.
+
+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.
+
+
+PROPOSITION I.
+
+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[b]),
+A[b]-C, then the C obtained from the last third, A[b]-C, will be too
+flat to form a perfect octave by a small quantity, called in the
+theory of harmonics a _diesis_, which is expressed by the ratio 128 to
+125.
+
+EXPLANATION.--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 4/5 of its length.
+
+In like manner, G[#], the major third to E, will be produced by 4/5 of
+that segment of the string which sounds the tone E; that is, G[#] will
+be produced by 4/5 of 4/5 (4/5 multiplied by 4/5) which equals 16/25
+of the entire length of the string sounding the tone C.
+
+We come, now, to the last third, G[#] (A[b]) to C, which completes the
+interval of the octave, middle C to 3C. This last C, being the major
+third from the A[b], will be produced as before, by 4/5 of that
+segment of the string which sounds A[b]; that is, by 4/5 of 16/25,
+which equals 64/125 of the entire length of the string. Keep this last
+fraction, 64/125, 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.
+
+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 64/125 an
+exact half? No; using the same numerator, an exact half would be
+64/128.
+
+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, 64/125, representing a longer segment of the
+string than 64/128 (1/2), it would produce a flatter tone than the
+exact half.
+
+It is evident, therefore, that _all major thirds must be tuned
+somewhat sharper than perfect_ in a system of equal temperament.
+
+The ratio which expresses the value of the _diesis_ is that of 128 to
+125. If, therefore, the octaves are to remain perfect, which they must
+do, _each major third must be tuned sharper than perfect by one-third
+part of the diesis_.
+
+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.)
+
+                             Middle C (2C) 60 inches.
+    --------------------------------------------------
+    O                                                O
+
+                             E (4/5 of 60) 48 inches.
+          --------------------------------------------
+          O                                          O
+
+               G[#] (A[b]) (4/5 of 48) 38-2/5 inches.
+                --------------------------------------
+                O                                    O
+
+                  3C (4/5 of 38-2/5) 30-18/25 inches.
+                      --------------------------------
+                      O                              O
+
+This diagram clearly demonstrates that the last C obtained by the
+succession of thirds covers a segment of the string which is 18/25
+longer than an exact half; nearly three-fourths of an inch too long,
+30 inches being the exact half.
+
+To make this proposition still better understood, we give the
+comparison of the actual vibration numbers as follows:--
+
+Perfect thirds in ratio
+4/5 have these vibration
+numbers: =
+
+            1st third            2d third                3d third
+         (C 256 - E 320)     (E 320 - G[#] 400)     (G[#] 400 - C 500)
+         ---------------     ------------------     ------------------
+             no beats            no beats                no beats
+
+Tempered thirds qualified
+to produce true
+octave: =
+
+  (C 256 - E 322 5/10) (E 322 5/10 - G[#] 406 4/10) (G[#] 406 4/10 - C 512)
+  -------------------- ---------------------------- -----------------------
+         10 beats            13-1/10 beats                 16 beats
+
+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.
+
+
+QUESTIONS ON LESSON XII.
+
+    1. Why is the pitch, C-256, adopted for scientific discussion, and
+    what is this pitch called?
+
+    2. 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?
+
+    3. What tone is produced by a 2/3 segment of a string? What by a
+    1/2 segment? What by a 4/5 segment?
+
+    4. (a) What intervals must be tuned absolutely perfect?
+
+       (b) In the two intervals that must be tempered, the third and
+       the fifth, which will bear the greater deviation?
+
+    5. What would be the result if we should tune from 2C to 3C by a
+    succession of perfect thirds?
+
+    6. Do you understand the facts set forth in Proposition I, in this
+    lesson?
+
+
+
+
+LESSON XIII.
+
+~RATIONALE OF THE TEMPERAMENT.~ (Concluded from Lesson XII.)
+
+PROPOSITION II.
+
+
+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.
+
+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
+words, 5/6 of any string sounds a tone which is an exact minor third
+above that of the whole string.
+
+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:
+
+Middle C-E[b]; E[b]-F[#]; F[#]-A; A-3C.
+
+Demonstrate by figures as follows:--Let the whole length of string
+sounding middle C be represented by unity or 1.
+
+    E[b] will be sounded by 5/6 of the string                5/6
+    F[#], by 5/6 of the E[b] segment; that is, by 5/6 of
+      5/6 of the entire string, which equals                25/36
+    A, by 5/6 of 25/36 of entire string, which equals      125/216
+    3C, by 5/6 of 125/216 of entire string, which equals   625/1296
+
+Now bear in mind, this last fraction, 625/1296, 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 this gives 648/1296, which is an exact half. Notice the
+comparison.
+
+    3C obtained from a succession of exact minor thirds,      625/1296
+    3C obtained from an exact half of the string              648/1296
+
+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 23/1296 of the length of the whole string.
+
+If, therefore, all octaves are to remain perfect, it is evident that
+_all minor thirds must be tuned flatter than perfect_ in the system of
+equal temperament.
+
+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 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.)
+
+
+PROPOSITION III.
+
+Proposition III deals with the perfect fifth, showing the result from
+a series of twelve perfect fifths employed within the space of an
+octave.
+
+METHOD.--Taking 1C as the fundamental, representing it by unity or 1,
+the G, fifth above, is sounded by a 2/3 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 4/9 (2/3 of 2/3 equals 4/9) 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: 4/9 times 2 equals 8/9, the segment sounding
+the D within the octave.
+
+We may shorten the operation as follows: Instead of multiplying 2/3 by
+2/3, giving us 4/9, and then multiplying this answer by 2, let us
+double the fraction, 2/3, which equals 4/3, and use it as a multiplier
+when it becomes necessary to double the segment to keep within the
+octave.
+
+We may proceed now with the twelve steps as follows:--
+
+Steps--
+
+1.  1C   to 1G                                  segment  2/3    for 1G
+2.  1G    " 1D Multiply  2/3      by 4/3, gives segment  8/9      " 1D
+3.  1D    " 1A    "      8/9      "  2/3   "     "      16/27     " 1A
+4.  1A    " 1E    "     16/27     "  4/3   "     "      64/81     " 1E
+5.  1E    " 1B    "     64/81     "  2/3   "     "     128/243    " 1B
+6.  1B    " 1F[#] "    128/243    "  4/3   "     "     512/729    " 1F[#]
+7.  1F[#] " 1C[#] "    512/729    "  4/3   "     "    2048/2187   " 1C[#]
+8.  1C[#] " 1G[#] "   2048/2187   "  2/3   "     "    4096/6561   " 1G[#]
+9.  1G[#] " 1D[#] "   4096/6561   "  4/3   "     "   16384/19683  " 1D[#]
+10. 1D[#] " 1A[#] "  16384/19683  "  2/3   "     "   32768/59049  " 1A[#]
+11. 1A[#] " 1F    "  32768/59049  "  4/3   "     "  131072/177147 " 1F
+12. 1F    " 2C    " 131072/177147 "  2/3   "     "  262144/531441 " 2C
+
+Now, this last fraction should be equivalent to 1/2, 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
+262144/524288, the segment producing the true octave; so the fraction
+262144/531441, which represents the segment for 2C, obtained by the
+circle of fifths, being evidently less than 1/2, 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 fifths is sharper than the
+true octave in the ratio expressed by 531441 to 524288, which ratio is
+called the _ditonic comma_. This comma is equal to one-fifth of a
+half-step.
+
+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.
+
+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:--
+
+"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, 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."
+
+
+NUMERICAL COMPARISON OF THE DIATONIC SCALE WITH THE TEMPERED SCALE.
+
+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.
+
+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.
+
+     |DIATONIC.|TEMPERED.| |DIATONIC.|TEMPERED.|
+    C|32.      |32.      |C|512.     |512.     |
+    D|36.      |35.92    |D|576.     |574.70   |
+    E|40.      |40.32    |E|640.     |645.08   |
+    F|42.66    |42.71    |F|682.66   |683.44   |
+    G|48.      |47.95    |G|768.     |767.13   |
+    A|53.33    |53.82    |A|853.33   |861.08   |
+    B|60.      |60.41    |B|960.     |966.53   |
+    C|64.      |64.      |C|1024.    |1024.    |
+
+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.
+
+TABLE OF VIBRATIONS PER SECOND.
+
+    C    |128.   |256.   |512.   |1024.   |
+    C[#] |135.61 |271.22 |542.44 |1084.89 |
+    D    |143.68 |287.35 |574.70 |1149.40 |
+    D[#] |152.22 |304.44 |608.87 |1217.75 |
+    E    |161.27 |322.54 |645.08 |1290.16 |
+    F    |170.86 |341.72 |683.44 |1366.87 |
+    F[#] |181.02 |362.04 |724.08 |1448.15 |
+    G    |191.78 |383.57 |767.13 |1534.27 |
+    G[#] |203.19 |406.37 |812.75 |1625.50 |
+    A    |215.27 |430.54 |861.08 |1722.16 |
+    A[#] |228.07 |456.14 |912.28 |1824.56 |
+    B    |241.63 |483.26 |966.53 |1933.06 |
+    C    |256.   |512.   |1024.  |2048.   |
+
+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.
+
+EXAMPLE.--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. 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.
+
+TABLE SHOWING RELATIVE VIBRATION OF INTERVALS BY IMPROPER FRACTIONS.
+
+    The relation of the Octave to a Fundamental is expressed by  2/1
+     "     "         "  Fifth to a         "          "          3/2
+     "     "         "  Fourth to a        "          "          4/3
+     "     "         "  Major Third to a   "          "          5/4
+     "     "         "  Minor Third to a   "          "          6/5
+     "     "         "  Major Second to a  "          "          9/8
+     "     "         "  Major Sixth to a   "          "          5/3
+     "     "         "  Minor Sixth to a   "          "          8/5
+     "     "         "  Major Seventh to a "          "         15/8
+     "     "         "  Minor Second to a  "          "         16/15
+
+
+QUESTIONS ON LESSON XIII.
+
+    1. State what principle is demonstrated in Proposition II.
+
+    2. State what principle is demonstrated in Proposition III.
+
+    3. What would be the vibration per second of an exact (not
+    tempered) fifth, from C-512?
+
+    4. Give the figures and the process used in finding the vibration
+    number of the _exact_ major third to C-256.
+
+    5. 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?
+
+
+
+
+LESSON XIV.
+
+~MISCELLANEOUS TOPICS PERTAINING TO THE PRACTICAL WORK OF TUNING.~
+
+
+~Beats.~--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.
+
+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 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.
+
+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.
+
+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. 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.
+
+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.[G]
+
+    [G] 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.
+
+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.
+
+Two strings struck at the same time, one tuned an octave higher than
+the other, will vibrate in the ratio of 2 to 1. If these two strings
+vary from this ratio to the amount of _one_ vibration, they will
+produce _two_ 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 _one_ vibration, there will occur _three_ beats per second.
+In the case of the major third, there will occur _four_ beats per
+second to a variation of _one_ 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.
+
+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.
+
+By referring to the table in Lesson XIII, above referred to, the exact
+beating of any fifth may be ascertained as follows:--
+
+Ascertain what the vibration number of the _exact_ fifth would be,
+according to the instructions given beneath the table; find the
+difference between this and the _tempered_ 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.
+
+_Example._--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 (22/100). Multiply
+.22 by 3 and the result is .66, or about two-thirds of a beat per
+second.
+
+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 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.
+
+~Finishing up the Temperament.~--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:
+
+    1. Fifths too flat.
+
+    2. Fifths not flat enough.
+
+    3. Some fifths correctly tempered and others not.
+
+    4. Some fifths sharper instead of flatter than perfect; a
+    condition that must be watched with vigilance.
+
+    5. Some or all of the strings tuned fall from the pitch at which
+    they were left.
+
+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 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.
+
+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.
+
+The mistuned or tempered intervals are as follows:--
+
+    INTERVALS FLATTENED.     INTERVALS SHARPENED.
+    The Fifth, slightly.     The Fourth, slightly.
+    The Minor Third,         The Major Third,
+      considerably.             greatly.
+    The Minor Sixth,         The Major Sixth,
+      considerably.             greatly.
+
+~Tuning the Treble.~--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 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 _octaves_ higher
+in the treble than the point at which the beats of the _fifth_ become
+unavailable; and in tuning _unisons_, the beats are discernible almost
+to the last tone.
+
+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.
+
+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.
+
+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[b] but one, in the standard 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.
+
+~Tuning the Bass.~--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.
+
+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.
+
+~False Waves.~--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 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.
+
+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.
+
+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, 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.
+
+
+QUESTIONS ON LESSON XIV.
+
+    1. Explain the cause of the beats.
+
+    2. How many _beats_ per second in a unison of two strings, one
+    tuned to 100, the other to 101 vibrations per second?
+
+    3. How many beats per second in an octave, the lower tone of which
+    is tuned to 100, the upper to 201 vibrations per second?
+
+    4. How many beats per second in a fifth, the fundamental of which
+    is tuned to 100, the fifth to 151?
+
+    5. The fifth, 2F-3C, when properly tempered, should beat 1-3/4
+    times per second. How often should a fifth, an octave higher,
+    beat?
+
+
+
+
+LESSON XV.
+
+~MISCELLANEOUS TOPICS PERTAINING TO THE PRACTICAL WORK OF TUNING,
+REGULATING, AND REPAIRING.~
+
+
+~Comparison of the Different Systems.~--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.
+
+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. 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.
+
+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.
+
+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.
+
+
+                               SYSTEM A.
+
+    By middle C  tune F             fifth below.      Temper sharp.
+           By F    "  B[b] (A[#]) fourth above.         "     "
+            " C    "  G             fourth below.       "    flat
+            " G    "  D           fifth above.          "     "
+            " D    "  A             fourth below.       "     "
+            " A    "  E           fifth above.          "     "
+            " E    "  B             fourth below.       "     "
+            " B    "  F[#]          fourth below.       "     "
+            " F[#] "  C[#]        fifth above.          "     "
+            " C[#] "  G[#]          fourth below.       "     "
+            " G[#] "  D[#]        fifth above.          "     "
+    Then try D[#] with A[#] previously tuned for "wolves."
+
+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.
+
+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[#] 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.
+
+
+                       SYSTEM B.
+
+    By 3C   tune 2C       octave below.
+    "  2C    "   2G    fifth above.
+    "  2G    "   1G       octave below.
+    "  1G    "   2D    fifth above.
+    "  2D    "   2A    fifth above.
+    "  2A    "   1A       octave below.
+    "  1A    "   2E    fifth above.
+    "  2E    "   2B    fifth above.
+    "  2B    "   1B       octave below.
+    "  1B    "   2F[#] fifth above.
+    "  2F[#] "   1F[#]    octave below.
+    "  1F[#] "   2C[#] fifth above.
+    "  2C[#] "   2G[#] fifth above.
+    "  2G[#] "   1G[#]    octave below.
+
+
+    By 2C   tune 1F    fifth below. Temper sharp.
+    "  1F    "   2F       octave above.
+    "  2F    "   1B[b] fifth below. Temper sharp.
+    "  1B[b] "   2B[b]    octave above.
+    "  2B[b] "   2E[b] fifth below. Temper sharp.
+
+    Now by 2E[b] try 1A[b] (G[#]) fifth below for the "wolf."
+
+    Note that this last trial brings you back to the last tone tuned
+    before the break.
+
+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.
+
+
+                             SYSTEM C.
+
+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.
+
+Take 1F as a standard.
+
+By 1F, tune 2C, fifth above.
+By 1F, tune 1B[b], fourth above.
+By 1F, tune 1A, major third above.
+By 1F, tune 2D, sixth above.
+By 1F, tune 1A[b], minor third above.
+By 1F, tune 2F, octave above.
+By 2C or 2D, tune 1G, fourth or fifth below.
+By 1G, 1A or 2C, tune 2E, sixth, fifth or third above.
+By 1G or 2E, tune 1B, third above or fourth below.
+By 1A or A[#], tune 2C[#], major or minor third above.
+By 1A[b], 1B[b] or 1B, tune 2E[b], fifth, fourth or major third above.
+By 1B[b], 1B, 2C[#] or 2E[b], tune 1F[#], major third, fourth, fifth
+   or sixth below.
+
+As each step is taken in this system, the tone tuned is tested with
+any or all of the tones previously tuned.
+
+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.
+
+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.
+
+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.
+
+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.
+
+In any system used it is well to test your work in the following
+manner:
+
+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.
+
+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 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:
+
+~Simplicity.~--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.
+
+~Uniformity.~--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.
+
+~Precision.~--In our experience, we have never known another system by
+which we could attain the absolute precision gained by this.
+
+~Stability.~--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.
+
+~Final Inspection.~--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.
+
+~Loose Pins.~--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.
+
+~Split Bridges.~--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, 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.
+
+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.
+
+~Stringing.~--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 just like those on the
+instrument. In most modern pianos the string is wound with three coils
+around the pin.
+
+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.
+
+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 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.
+
+[Illustration: KNOT FOR SPLICING WIRE.]
+
+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 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.
+
+
+QUESTIONS ON LESSON XV.
+
+    1. Name the advantages and disadvantages of system A.
+
+    2. Name the advantages and disadvantages of system B.
+
+    3. What are the important points to be desired in any system of
+    setting temperament?
+
+    4. State three or four items of importance in the operation of
+    putting on a new string.
+
+    5. Why do pianos get out of tune?
+
+
+
+
+LESSON XVI.
+
+~TUNING AND REPAIRING THE REED ORGAN.~
+
+
+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.
+
+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.
+
+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.
+
+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
+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.
+
+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.
+
+
+CLEANING.
+
+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 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.
+
+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.
+
+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 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.
+
+
+STOPS.
+
+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
+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.
+
+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.
+
+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.
+
+
+EXAMINATION.
+
+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 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.
+
+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.
+
+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 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.
+
+
+STICKING KEYS.
+
+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 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.
+
+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 "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.
+
+New pallet springs may be made of piano wire, using old springs for a
+pattern.
+
+
+LEAKS.
+
+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 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.
+
+
+PEDAL DETECTS.
+
+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 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.
+
+
+SYMPATHETIC VIBRATIONS.
+
+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.
+
+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 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.
+
+
+TUNING.
+
+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 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.
+
+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.
+
+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 instrument itself, we believe he will have no
+trouble in learning all about its mechanical action and its demands
+upon the tuner.
+
+
+QUESTIONS ON LESSON XVI.
+
+    1. Name the musical advantages possessed by the organ which are
+    absent in the piano.
+
+    2. Name the musical advantages possessed by the piano which are
+    absent in the organ.
+
+    3. Describe the mechanical operations taking place in the organ
+    when a key is being sounded.
+
+    4. State what you would do to flatten the tone of a reed and give
+    reasons.
+
+    5. State what you would do to sharpen the tone of a reed and give
+    reasons.
+
+
+
+
+LESSON XVII.
+
+~CONCLUDING PROFESSIONAL HINTS.~
+
+
+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.
+
+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.
+
+~Brilliant.~--The sense in which this term is used is astonishing to
+one who is accustomed to using words according to their dictionary
+meanings. We have heard persons say their piano was too _brilliant_;
+or, that it was not _brilliant_ 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
+_brilliant_; 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 _harsh_ when the
+hammers are hard, and they usually desire the tuner to _soften_ 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.
+
+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 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.
+
+~Singing.~--When a damper is out of order and does not do its work
+properly, they often say the tone _sings_. 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 _sympathetic rattle_.
+
+~Tin-panny.~--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 _hollow_ 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.
+
+~Bass-ey.~--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.
+
+~Harsh.~--This term, when it does not apply to the voice of the piano,
+generally reflects upon the work of the tuner (?). Chords are _harsh_
+when they contain over-sharp thirds, bad fifths, octaves, etc. Take
+care that your temperament contains no bad 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 tones may
+disparage your otherwise creditable work.
+
+~Questions.~--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.
+
+~Seasons for Tuning.~--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.
+
+
+
+
+INDEX.
+
+
+
+Action, 17
+  brackets, 24
+  of grand piano, 37, 38, 62
+  of square piano, 32, 34
+  removing, square and grand, 38
+  replacing, square and grand, 39
+  requisites of, 17, 18
+  top, of square piano, 34
+  trap, of square piano, 19, 34
+
+Advantages of two-octave temperament, 171
+
+Ancient instruments, 13
+
+
+Back check, adjustment of, 49
+  and back catch, 18, 27, 28, 33, 37
+  wire, 27
+
+Balance pin, 21
+  rail, 21
+
+Bearing bar, 17
+
+Beats, waves, and pulsations, 73, 150
+  of unison, octave, and major third, 154
+  cause of, 77, 150
+
+Black lead, use of, 64
+
+Block rail, 27, 51
+
+Bottom or capstan, adjustment of, 48, 99
+  or key rocker, 23, 33, 48, 56, 57
+
+Bracket bolts, 25
+
+Bridle, 28
+  putting in new, 50
+  wire, 28, 50
+
+Bridges, 16, 17
+  split, 173
+
+Building of upright piano, 16
+
+Butts, 28
+  and flanges, repairing of, 59
+
+
+Capstan, 24, 48
+
+Cause of beats 27, 150
+
+Center-pins, 25
+  putting in new 52
+
+Clicks at release of key, 51, 52
+
+Compromises, the, 99, 100
+
+Continuous mute, 89
+
+
+Damper lever, 29
+  felt, softening, 54
+
+Damper, of grand piano, 37
+  of square piano, 36, 60
+  rod, 30
+  rod, squeaking of, 55
+  spoon, 29
+  springs broken, 54
+
+Dampers, 18, 29
+
+Damping, defective, 54, 60, 61
+
+Ditonic comma 144
+
+
+Evolution of the piano, 12
+
+Extension, 23
+
+
+False waves, 160, 161
+
+Fifths, beats of, 79
+  not all tempered alike, 105, 106
+  tempering of, 79, 104
+
+Final inspection, 172
+
+Fischer System of temperament, diagram of, 82
+
+Flanges, 25
+  repairing of, 59
+
+
+Guide pins, 23
+
+
+Hammer, butt, refelting, 51
+  capping with buckskin, 59
+  felts, cleaning, 34
+    gluing, 54
+    hardening, 54
+    softening, 54
+    trimming, 60
+    voicing, 54, 104
+  head 29
+  rail, 29, 33
+  shank or stem, 29, 53
+    broken, 63
+    renewing, 53
+  spring, 52
+  sticking, 52
+
+Hitch-pins, 16, 17
+
+
+Instrumental attachments, removal of, 118
+
+Intervals flattened, 157
+  sharpened, 157
+
+Ivories, regluing, 64
+
+
+Jack, 26
+  repairing of, 50, 58
+  sluggish, 57
+  -spring broken, 58
+
+
+Key, defects in, 47, 48
+  leads, 22
+  organ, sticking, 185, 186
+  removing, square piano, 56
+  squeaking, 64
+  sticking, 46
+
+
+Lead, in keys, 22
+  black, use of, 64
+  loose in key, 64
+
+Length, tension, and weight of strings, 75
+
+Loud pedal, 19, 30
+
+
+Main rail, 25
+
+Mathematics of tempered scale, 126
+
+Metal plates, 15
+
+Mute, continuous, 89, 90
+
+Mutes, setting in upright piano, 117-120
+  in bass, 121
+  beyond temperament, 120
+  in square piano, 122
+  on nodal points, 161
+
+
+Octave, dividing into major thirds, 134
+  into minor thirds, 140
+    perfect fifths, 142
+
+Octaves, relative vibration of, 78
+
+Organ, reed, tuning and repairing the, 178
+  bellows, leaks in, 187
+  capabilities of, 179
+  cleaning, 180
+  examination, 183
+  keys sticking, 185, 186
+  pallets, 186
+  pedal defects, 188
+  reeds, to find, 184
+    tuning, 190
+  stops, 182
+    disconnected, 184
+  sympathetic vibration, 189
+
+Over-tension, 114
+
+
+Panel, removing of, 75
+
+Parts of grand action, 38
+  of square action, 34
+
+Pendulum to aid in judgment of a second of time, 104
+
+Piano frame, 15
+  tuner, requisites of, 7, 70
+
+Pianos, special use of, 85, 86
+
+Pitch, concert, 127
+  international, 81, 127
+
+Pitch, left to tuner's judgment, 86, 87, 89
+  to determine most favorable, 85
+
+Professional hints, 193
+
+
+Questions asked by owners, 211
+
+
+Ratio of intervals, 132
+
+Reed organ. See _Organ_.
+
+Regulating button, 26, 51
+  rail, 26, 36
+
+Repairing small wooden parts, 63
+
+Repetition of stroke, 18, 27
+
+
+Searching for articles on sound board, 44
+
+Seasons for tuning, 198
+
+Soft pedal, 29, 36, 38
+
+Sound board, 16
+    split, 44
+    unglued, 45
+  waves, interference of, 78, 150
+
+Splicing piano wire, 176
+
+Spring rail, 29
+
+Stringing of upright, 16, 17
+
+Strings growing sharper, 88
+  putting in new, 174, 175
+  rendering through bridges, 112, 114
+  splicing, 176
+
+Study and practice of tuning, 66
+
+Sustaining pedal, 30
+  squeaking of, 55
+
+Sympathetic rattle, 43
+
+Syntonic comma, 132
+
+Systems of temperament, various, 163
+
+System A, 165
+  B, 166
+  C, 167, 168
+
+
+Tables of relative string length, 131, 136, 140, 143
+
+Temperament, advantages of the two-octave, 171
+  equal, 97, 144
+  Fischer system, 74
+  finishing up, 156
+  introductory remarks on, 68, 72
+  rationale of, 128, 139
+  requisites of, 133
+  setting, specific instructions, 85
+  theory of, 97
+  unequal, 98
+  various systems, 163-168
+
+Tension, equalization of, 111, 112
+
+Terms to express tone qualities, 193-196
+
+Testing by thirds and tenths, 170
+
+Tests, chords, 94, 99, 103
+
+Third, excessive sharpness of, 95, 103
+
+Thirds, major, 135
+  major, sharper than perfect, 135
+  minor, flatter than perfect, 141
+
+Tones, harmonic, 120, 130
+
+Touch, altering the, 48
+
+Treble, extreme, sharper than perfect, 159
+
+Tuning, instructions for first experiments in, 92-95
+  hammer, manipulation of, 110, 115, 116
+  pins, marking of in square, 122
+    loose, 173
+    setting of, 112-114
+  the bass, 160
+  the treble, 157, 159
+
+
+Vibration numbers, comparison of, 137, 146, 147, 148
+
+
+Watchmaker's screwdriver, use of in piano repairing, 63
+
+Wippen, 25
+
+Wire splicing, 176
+
+Wooden parts, shrinking, rattling, 59
+  repairing of small, 63
+
+
+    [Transcriber's note:
+
+    1. Bold text is enclosed in tilde (~) characters.
+
+    2. On page 197, 'tones' has been misspelt in the original text as
+    'tonse'.]
+
+
+
+
+
+End of the Project Gutenberg EBook of Piano Tuning, by J. Cree Fischer
+
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