p I t^ »i « ■ so -< CO so > so ^ 7^1 (-3 O ^., < % THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES fi<> A«" so ^v C3 CI r-ry *1 ^/ c^Of 4^: ANCElfj> CO so > -< ^i!/0JllV3JO'^ ^OJIIVJ-JO"^ #" o > so ^ ,0FCAllF0/?4j, ^OFCAIIFO/?^ ^ en .^M[DNIVER% 1^1 ■ ^-tfOJIlVOJO"^ '^OJnVJJO'^ ;lOSANCElfj> '^/ya3AiNa-3WV^ ^^lllBRARYQ^ ^tllBRARYQc '^.f/OJIWDJO^ ^^mmy\^ ^\WEllNlVERS/4 vvlOSANCElfj> a ^^-^ — ^^ ^^OFCAllFOff^ ^OFCAIIFO%, ■^/sa3AiNn3WV^ "^^JAbvyaii^s^ ^^Awaani^ ^^HIBRARYQr ^^tllBRARYQ^^ '^.vo-invi-io -^.vn-iiivT-io^" AWEUNIVERJ/a. NCElfj> 5 ^f oCi ,^4,0FCALIF0/?/(^ ,S;OFCAIIFO% ^ '^ \\\t UNlVERi//i MODERN PIANO TUNING AND ALLIED ARTS INCLUDING Principles and Practice of Piano Tuning, Regulation of Piano Action, Repair of the Piano, Elementary Princi- ples of Player-Piano Pneumatics, General Construction of Player Mechanism, and Repair of Player Mechanism BY WILLIAM BRAID WHITE Technical Editor of the Music Trade Review. New York. Author of "Theory and Practice of Pianoforte Build- ing." "The Player-Piano Up-to-date," and other works WITH DRAWINGS. DIAGRAMS. TA^ES. NOTES AND AN INDEX NEW YORK EDWARD LYMAN BILL, Incorporated 1917 Copyright, 1917, by EDWARD LYMAN BILL, Incorporated Entered at Stationers' Hall Murta LfbrBxy TO THE CONFERENCE OF AMERICAN PIANO TECHNICIANS MEETING IN CHICAGO, U. S. A. Whose valuable and exhaustive discussions mark an epoch in the development of American musical technology. This Book is, by one who has the honor of membership in that Conference, RESPECTFULLY AND AFFECTIONATELY DEDICATED 'f^. PREFATORY NOTE In writing this book, I have tried to do two things which are always thought to be admirable but seldom thought to be conjunctible. I have tried to set forth the theory of Equal Tempera- ment in a manner at once correct and simple. Simultaneously I have tried to construct and ex- pound a method for the practical application of that theory in practical tuning, equally correct, equally simple and yet thoroughly practical. The construction of the piano has not in this volume been treated with minuteness of detail, for this task I have already been able to perform in a former treatise ; but in respect of the sound- board, the strings, the hammers and the action, the subject-matter has been set forth quite elaborately, and some novel hypotheses have been advanced, based on mature study, research and experience. Here also, however, the theoretical has been justified by the practical, and in no sense have I yielded to the temptation to square facts to theories, 111 iv Prefatory Note In the practical matters of piano and player repairing, I have presented in these pages the results of nineteen years' practical and theoreti- cal work, undertaken under a variety of condi- tions and circumstances. In writing this part of the volume I have had the inestimable advan- tage of the suggestions and experiences of many of the best American tuners, as these have been gathered from past numbers of the Music Trade Review, the Technical Department of which pa- per I have had the honor to edit and conduct, without intermission, for fourteen years. The preliminary treatment of the Acoustical basis of piano tuning may seem elaborate; but I have tried to handle the subject-matter not only accurately but also simply; and as briefly as its nature permits. The need for really accurate in- formation here justifies whatever elaboration of treatment has been given. I desire here to express my thanks to Mr. J. C. Miller for permission to utilize some of his valuable calculations, to Mr. Arthur Lund, E. E., for drawings of acoustical curves, and to my brother, Mr. H. Sidney White, M. E., for dia- grams of mechanical details. Most books intended for the instruction and Prefatory Note v guidance of piano tuners have been either so theoretical that their interest is academic purely; or so superficial that accuracy in them is through- out sacrificed. I have tried to avoid both er- rors, and to provide both a scientifically correct text-book for teaching and a pocket guide for the daily study and use of the working tuner. The program has been ambitious ; and I am con- scious, now that the task is finished, how far short of perfection it falls. But I think it fills a want ; and I ask of all practitioners and students of the noble art of tuning their indulgence to- wards its faults and their approval of any vir- tues it may appear to them to possess. The writing of the volume began in the winter of 1914 and was completed during the spring of 1915. Various causes have operated, how- ever, to retard its publication; notably the sud- den passing of the honored man whose en- couragement and kindness made possible the publication of the other books which have ap- peared over my name. It is however fortunate that the successor of Colonel Bill, the corporation which now bears his name and is carrying on so successfully his fine work, has been equally de- sirous with me, of pushing the book to publica- vi Prefatory 'Note tion. A thorough rereading of the manuscript, however, during the interim, has suggested many slight changes and a number of explanatory notes, which have been incorporated with, or appended to, the text. A new, and I hope valuable, feature is the In- dex, which I have tried to make copious and use- ful, to the student and to the tuner alike. William Braid White. Chicago, 1917. ERRATUM Pade 300. For ^Sectional View of Doutle-valve Action ' read ^Sectional View oi Smgle-valve Action. OMIT tke following words: 5a Secondary Poucli. r\ V 7a Secondary Reduced Pressure Chamber. 8a Secondary Valve. 11 Primary-Secondary Channel. Contents PAGE Prefatory Note iii Chapter I. Mechanics of the Musical Scale ....'.. 1 On the Vibration of a Piano String 36 Temperament .... 72 Chapter II. Chapter Chapter III. IV. Chapter V. Practical Tuning in Equal Temperament .... 95 Mechanical Technique of Tuning 114 Chapter VI. The Modern Piano . 130 Chapter VII. Sound-Board and Strings 152 Chapter VIII. The Action and Its Regula- tion 184 Chapter IX. The Hammer and Its Rela- tion to Tone .... 223 Chapter X. Repair of the Piano . 244 Chapter XI. Elementary Pneumatics 261 Contents PAGE Chapter XII. General Construction of Player Mechanisms . . 284 Chapter XIII. Eepair of Player Mech- anism 310 Bibliographical Note 329 Index 331 Chapter I. MECHANICS OF THE MUSICAL. SCALE. He who undertakes to master the art of piano tuning must have some acquaintance, exact rather than comprehensive, with that general body of knowledge known as Acoustics. This term is used to designate the Science of the phenomena known as Sound. In other words, by the term Acoustics we mean the body of facts, laws and rules which has been brought together by those who have sys- tematically observed Sound and have collected their observations in some intelligible form. Piano Tuning itself, as an Art, is merely one of the branches of Practical Acoustics ; and in order that the Branch should be understood it is neces- sary to understand also the Trunk, and even the Root. But I might as well begin by saying that no- body need be frightened by the above paragraph. I am not proposing to make any excursions into realms of thought too rarefied for the capacity of the man who is likely to read this book. I sim- 1 2 Modern Piano Tuning. ply ask that man to take my word for it that I am going to be perfectly practical and intelligible, and in fact shall probably make him conclude that he has all along been a theorist without knowing it; just as Moliere's M. Jourdain discovered that he had been speaking prose all his life without knowing it. The only difference has been that my reader has not called it "theory." He has called it ''knowing the business." Anyhow, we are going to begin by discovering something about Sound. We are in fact to make a little excursion into the delectable kingdom of Acoustics. What is Sound? When a street-car runs over a crossing where another line intersects, we are conscious of a series of grinding crashes exceed- ingly unpleasant to hear, which we attribute per- haps to flat tires on the wheels or to uneven lay- ing of the intersecting trackage. The most prominent feature of such a series of noises is their peculiarly grating and peculiarly spasmodic character. They are on the one hand discontinu- ous, choppy and fragmentary, and on the other hand, grating, unpleasant to the hearing, and to- tally lacking in any but an irritant effect. These are the sort of sounds we speak of as ''noise." Mechanics of the Musical Scale. 3 In fact, lack of continuity, grating effect and gen- eral fragmentariness are the distinguishing fea- tures of noises, as distinguished from other sounds. If now we listen to a orchestra tuning up roughly off-stage, the extraordinary medley of sounds which results, may — and frequently does — have the effect of one great noise; although we know that each of the single sounds in the up- roar is, by itself, musical. So it appears that noises may be the result of the chance mixture of many sounds not in themselves noises, but which may happen to be thrown together without system or order. Lack of order, in fact, marks the first great distinction between noises and other sounds. If now we listen to the deep tone of a steamer's siren, or of a locomotive whistle, we are conscious of a different kind of sound. Here is the im- mediate impression of something definite and con- tinuous, something that has a form and shape of its own, as it were, and that holds the same form so long as its manifestation persists. If, in fact, we continue to seek such sounds, we shall find that what are called Musical Sounds are simply more perfect examples of the continuity, the order and 4 Modern Piano Tuning. the definite character which we noticed in the lo- comotive whistle's sound. The more highly per- fected the musical instrument, the more perfectly will the sounds evoked by it possess the qualities of continuity, order and definite form. Continuity, persistence and definiteness, then, are the features which distinguish Musical Sounds^ from Noises. And there are therefore only two kinds of sounds: musical sounds and noises. Now, what is Sound? The one way in which we can know it, plainly, is by becoming conscious of what we call the Sensation of Sound; that is, by hearing it. If one considers the matter it be- comes plain that without the ability to hear there would be no Sound in the world. Sound cannot exist except in so far as there previously exist capacities for hearing it. The conditions that produce Sound are obviously possible, as we shall soon see, to an interminable extent in all direc- tions ; yet what we may call the range of audible Sound is very small indeed. We can hear so very little of the conceivably bearable material; if I may use so rough an expression. So it becomes quite plain that Sound cannot be considered as something in itself, existing in the sounding body apart from us, but must rather be Mechanics of the Musical Scale. 5 thought of as the form in which we perceive some- thing ; the form, in fact, in which we perceive the behavior of certain bodies, which behavior could not be perceived in any other way. Soun(i then can be considered only from the view-point pf the physical laws which govern the behavior of the bodies in question. The laws which govern that sort of behavior which we perceive as Sound, alone form the subject of Acoustics. Why we should experience these perceptio||^ as Sound rather than as Light or Heat is m>t a, question to be decided by/ Acoustics ; is nof a j^oblem of the natural sciences, but of Metaphysics. Limited th^efore to a strictly mechanical in- vestigation, let us consider the production of Sound from this view-gpf6int. Suppose that I strike a tuning-fork aga*nst the knee and hold it to the ear. I am conscious of a sound only mod- erate in intensity but of persistent and quite defi- nite character, agreeable, and what we call ** musi- cal." No one has any hesitation in calling this a "musical sound." But what produces it, physi- cally speaking? We can discover this for our- selves by making a simple experiment. By lightly touching the prongs of the fork while it is sounding I discover them to be in a state of 6 Modern Piano Tuning. vibration. If I examine them under a micro- scope I shall perhaps be able to detect an exceed- ingly rapid vibratory motion. In order however to make sure of the existence of these unseen vi- brations, it is only necessary to obtain a sheet of glass and smoke one surface of it by passing it over the flame of a candle. Then let a tuning fork be fitted with a very light needle point stuck on the end of one prong with a bit of wax, in such Figure 1. a position that if the sheet of glass be placed parallel with the length of the fork, the needle point will be at right angles to both. Now set the fork to sounding, and hold it so that the needle point lightly touches the smoked surface. Have a second person then move the sheet of glass lengthwise while the fork is held still. At once the needle-point will trace out a continuous wavy line, each wave being of that pe- culiar symmetrical form known technically as a Mechanics of the Musical Scale. 7 curve of sines or sinusoidal curve. By adjusting the experimental apparatus with sufficient exact- ness it would be possible to find out how many of these little waves are being traced out in any given time. Each of these waves corresponds to one vibration or pendulum-like back and forth mo- tion of the fork. By examining the wavy line with close attention, we shall see that if the motion of the glass sheet has been uniform, each sinusoid is identical in size with all the others, which in- dicates that the vibrations are periodic, that is to say, recur at regular intervals and are of similar width or amplitude. We may therefore conclude from this one ex- periment that the physical producer of musical sound is the excitation of the sounding body into periodic vibrations. Listen to the noise of the macliinery in a saw mill. When the circular saw starts to bite at a piece of wood you hear a series of grating cracks, which almost instantly assume the character of a complete definite musical sound, though rough in character. As the saw bites deeper into the wood the sound becomes first lower, then higher, until it mounts into a regular song. As the saw comes out through the wood the sounds mount quite high 8 Modern Piano Tuning. and then instantly die away. What is the cause of this phenomenon? The circular saw is a steel wheel with a large number of teeth cut in its circumference. Sup- pose there are fifty such teeth. At each revolu- tion of the wheel, then, each tooth will bite the wood once. If the wheel revolves at the rate of say four revolutions per second, it follows that there will be four times fifty or two hundred bites at the wood in this time. That means that the wood will receive two hundred separate scrapes per second. Hence, the rotation of the wheel will be slightly interrupted that number of times in one second. Hence, again, the surface of the air around the wheel will be vibrated back and forth just as many times, because the entry and emer- gence of each tooth will cause an alternate com- pression and suction on the air around it. Try another experiment. Stand five boys up in a row one behind the other, so that each boy has his out- stretched hands upon the shoulders of the boy in front of him. Push the last boy. He falls for- ward, pushes the next and regains his position. Next falls forward, pushes Third and regains his position. Third falls forward, pushes Fourth and regains his position. Fourth falls forward, Mechanics of the Musical Scale. 9 pushes Fifth and regains his position. Fifth has no one in front of him and so falls forward with- out being able to regain his position. In this way we illustrate the compression and rarefaction of the air by the alternate fallings forward and re- gainings of position undertaken by the boys. The air is even more elastic than the boys and so forms these waves of motion which we saw traced out by the stylus on the tuning fork. Now, it is plain that as the rotation of the cir- cular saw increases in speed the pulses become suf- ficiently rapid to fuse into one continuous musical sound. If the saw were rotated at irregular, con- stantly shifting speed, the separate shocks would not coalesce and we should have merely the sen- sation of a discontinuous, fragmentary, grating series of shocks which we should call a noise. Thus again we see that regularly recurring mo- tions of the sounding body are requisite to pro- duce musical sounds. Transmission of Sound. But the illustration of the five boys (which is due to the late Professor Tyndall, by the way) shows something further. It shows first how the excitation of a body into vibration at regular intervals produces an effect upon the immediately surrounding air, causing it 10 Modern Piano Timing. in turn to oscillate back and forth in pulses of alternate compression and rarefaction. But it shows more. It shows that the sound-motion, as we may call it, is transmitted any distance through the air just as the shock started at one end of the row of boys is felt at the other end, although each boy moves only a little and at once recovers Figure 2. his position. So also each particle of air merely receives its little push or compres- sion from the one motion of the tuning-fork or string, and transmits this to the next one. At the backward swing of the tuning-fork or string the air particle drops back to fill up the partial vacuum it left in its forward motion, whilst the motion transmitted to the second particle goes on to the third and to the fourth and so on to the ear of the hearer. Yet each particle has merely os- cillated slightly back and forth. Now, this mode of transmission evidently de- Mechanics of the Musical Scale. 11 pends upon the existence of an atmosphere. In fact, we can soon show that, apart from all ques- tion of ears, Sound could not exist for us, as we are in this state of existence, without an atmos- phere. Let an alarm-clock be set to ringing and then placed under the glass bell of an air-pump. We now begin to displace the air therefrom by working the handle of the pump. As the quantity of air inside the bell thus becomes smaller and smaller, the sound of the alarm-clock's ringing becomes fainter and fainter, until, where the air is at a certain point of rarefaction, it entirely disappears; although the clapper of the alarm will still be seen working. In other words, there must be an atmosphere or other similar medium, like water, for transmission of the sound-motion from the excited body to the ear. Properties of Musical Sounds. Having arrived at this point, we are now in a position to discuss musical sounds in general and to discover the laws that govern their behavior. The first prin- ciple we shall lay down is that musical Sounds are distinguished from noises by the continuity of their sensation ; or in other words, musical sounds are evoked by periodic vibrations. It is thus pos- sible to measure the frequency of vibration that 12 Modern Piano Tuning. evokes a sound of some given Leight; in other words to determine its pitch. It is also possible, as we shall see, to determine a second quality of musical sounds ; namely, their relative loudness or softness, or, as we shall call it, their intensity. Lastly, we can discover differences in character or quality between musical sounds, and we shall see also that it is possible to measure these dif- ferences accurately. Loudness. Let us begin with the second qual- ity mentioned; that of loudness or intensity. If a tuning-fork be excited by means of a violin bow and then examined through a microscope while its motion persists, it will be observed that as the sound dies away, the amplitude or width of swing of the prongs is becoming less and less, until the cessation of motion and of the sound occur to- gether. If, whilst the sound is thus dying away, the fork is again bowed, the amplitude of the prong's motion again is seen to increase just as the sound increases. In fact, it has been found by authoritative experiments that not only does the loudness of a sound vary with the amplitude of the vibrations of the sounding body; but ex- actly as the square of the amplitude. For in- Mechanics of the Musical Scale. 13 stance, if a piano string can be made to vibrate so that the width of swing in its motion is one-fif- tieth of an inch, and if another piano string giv- ing the same pitch can be made to vibrate with an amplitude of one twenty-fifth of an inch, then the second will have an amplitude twice that of the first and its sound will be four times as loud. However, let it be remarked that the mechanical operations thus described do not necessarily cor- respond with what we actually seem to hear. In other words, the sensation of loudness and the mechanical cause thereof do not always agree, for the reason that we do not hear some musical sounds as well as others. For instance, it is well known that low sounds never seem as loud as high sounds, even though the amplitude of vibration in each case be the same. A low sound always sounds softer than it really should be, to use a rough expression, and a high sound louder than it really should be. There is only one more important point about sound-intensity, namely, that the loudness of a sound varies inversely as the square of the dis- tance of the sounding body from the hearer. Thus, other things being equal, a sound heard at a distance of fifty feet should be four times as 14 Modern Piano Tuning. loud as one heard at a distance of twice fifty, or one hundred feet. However, it must also be re- membered that the situation of the sounding body and of the hearer in proximity to other objects, has a modifying effect upon the loudness of sound as perceived. In fact, we shall see that this is only part of the truth expressed in the term "res- onance," about which we shall have something to say later on. Pitch. Without making any special attempt at producing an ideal definition of "pitch," it will be enough to call it the relative acuteness or gravity of a musical sound. Everybody knows what is meant by saying that a musical sound is liigh or low. The province of Acoustics lies in finding some measuring-rule, some standard, whereby we can measure this lowness or highness of a sound and place it accurately in relation to all others. The whole system of music is built upon simply a measure of pitch, as we shall see. Now, first of all, let us find out what it is that makes a sound high or low. In other words, what is the mechanical reason for a sound producing a sensation of highness or lowness? Musical sounds are produced through the pe- riodic continuous vibration of some body. In the Mechanics of the Musical Scale. 15 experiment of the circular saw, to which I di- rected attention some pages back, it was pointed out that as the speed of the saw increases, so the musical sound produced through its contact with the wood rises in height. This may be veri- fied by any number of experiments that one chooses to make, and the net result is the fact that the pitch of musical sounds depends upon the number of vibrations in a given unit of time per- formed by the sounding body. Let us put it in a formula, thus: The pitch of a musical sound varies directly as the number of vibrations per unit of time per- formed by the sounding body: the greater the number of vibrations, the higher the pitch. Unit of Time. It is customary to assign the second as the unit of time in measuring frequency of vibrations, and in future we shall use this al- ways. If, therefore, we speak of a certain pitch as, say, 500, we shall mean 500 vibrations per second. Double Vibrations. In counting vibrations, we understand that a motion to and fro constitutes one complete vibration. A motion to or fro would be merely a semi-vibration or oscillation. In the United States and England it is customary to im- 16 Modern Piano Tuning. ply a double vibration (to and fro) when speak- ing of a ''vibration." In France the single or semi-vibration is the unit of measurement, so that the figures of pitch are always just double what they are as reckoned in the English or American style. Range of Audibility. It is found as the result of experiment that the human sense of hearing is distinctly limited. The lowest tone that can be distinctly heard as a musical sound is probably the lowest A (A-i) of the piano which, at the stand- ard international pitch, has a frequency of 27.1875 vibrations per second. Sounds of still lower fre- quency may perhaps be audible, but this is doubt- ful, except in the cases of persons specially trained and with special facilities. In fact, any spe- cific musical sounds lower than this probably do not exist for human beings, and when supposed to be heard, are in reality not such sounds at all, but upper partials thereof.^ The 64-foot organ pipe, which has occasionally been used, nominally real- izes tones lower than 27 vibrations per second, but these are certainly not audible as specific separate sounds. They can and do serve perhaps as a bass to reinforce the upper partials of the pipe or the 1 See Chapter II, Mechanics of the Musical Scale. 17 upper tones of a chord; but they do not appear as separate sounds, simply because the ear does not realize their pulses as a continuous sensation, but separates them. In fact, we may feel safe in concluding that the lowest A of the piano is the lowest of musical sounds generally audible. This statement is made in face of the fact that the sound evoked by the piano string of this note is usually powerful and full. This only means, how- ever, that the sound we hear on the piano is not the pure fundamental vibration of 27.1875 vibra- tions per second, but a mixture of upper partials re-inforced by the fundamental. Of these par- tials we shall have to speak later, for they are of vital importance to the due consideration of our subject-matter.^ A similar limitation confronts us when we come to the highest tones audible by the human ear. Plere again there is considerable diversity of opinion as well as of experience. The highest note of the piano, C7, has a frequency of 4,138.44 vibrations per second at the international pitch. -.J^ However, there is no special difficulty in hear- 1 For a very interesting discussion of the whole question of deepest tones, I refer the reader to Helmholtz, "Sensations of Tone," third English edition. Chapter IX. 18 Modern Piano Tuning. ing sounds as much as two octaves higher, or up to 16,554 vibrations per second. Above this limit, comparatively few people can hear anything, al- though musicians and acousticians have been able to go much higher.^ The Musical Range. The limits of audibiUty therefore embrace eleven octaves of sounds, but the musical range is considerably smaller. The modern piano embraces virtually the complete compass of sounds used in music, and, as we all know, that range is seven octaves and a minor third, from A-i to C7. Let it be noted that if the range of bearable sounds lies between, say 27 and 32,000 vibrations per second, the number of possible distinct musi- cal sounds is enormous. We know that it is quite possible for the trained ear to discriminate be- tween sounds which, at the lower end of the gamut anyhow, are no more than 4 vibrations per second apart. For many years the late Dr. Rudolph Koenig of Paris, one of the most gifted acousti- 1 Many years ago, before I had become practically interested in Acoustics, and when my ear therefore was in every sense untrained, I was tested by the Galton whistle up to 24,000 vibrations per second, which is near G^, two and one-half octaves above the piano's hif^hest note. This is well up to the higher limit of most trained ears, although some acousticians have tuned forks run- ning up to Cjo, with 33,108 vibrations per second. Mechanics of the Musical Scale. 19 cians the world has ever known, was engaged in the construction of a so-called Universal Tono- meter, consisting of a superb set of one hundred and fifty tuning forks, ranging in frequency from 16 to 21,845.3 vibrations per second. In this re- markable instrument of precision, the lowest sounds differ from each other by one-half a vi- bration per second, while within the musical com- pass the difference never exceeds four vibrations. It can readily be seen therefore that the number of possible musical sounds is very much greater than the eighty-eight which comprise the musical gamut of the piano. Just how the musical scale, as we know it, came to be what it is, I cannot discuss here; for the simple reason that the whole question is really to one side of our purpose.^ Whatever may be the origin of musical scales, however, we know that the diatonic scale has existed since the twelfth cen- tury, although the foundation of what we call mod- ern music, employing the chromatic tempered 1 The claims made for the eleventh century monk, Guide d'Arezzo, have been disputed, and the reader who is interested in the historical aspect of the subject is referred to Grove's "Dic- tionary of Music and Musicians," to Helraholtz' "Sensations of Tone," and to A. J. Ellis' "History of Musical Pitch," quoted in Appendix 20 of his translation of Helmholtz (3rd edition). 20 Modern Piano Tuning. scale, was rightly laid only by Sebastian Bach, who died 1750. Music is a young, an infantile, art, as time goes. The Diatonic Scale. We have already seen that the musical tone is a fixed quantity, as it were, being the sensation that is produced or evoked by a definite number of vibrations in a given time. This being the case, it becomes evi- dent that all possible tones must bear mathemati- cal relations to each other. As long ago as the sixth century b. c. the Greek philosopher and scientific investigator Pythagoras propounded the notion that the agreeableness of tones when used with each other is in proportion to the simplicity of their mathematical relations. Now, if we look at the scale we use to-day we find that although the relations of the successive members of it to each other appear to be complex, yet in fact these are really most simple. Let us see how this is : Unison. We all know that we can recognize one single tone and remember it when we hear it a second time. If now we draw the same tone from two sources and sound the two tones together, we find that they blend perfectly and that we have what we call a Unison. If we were to designate Mechanics of the Musical Scale. 21 the first tone by the mathematical symbol 1, we should say that the Unison is equivalent to the proportion 1 : 1. This is the simplest of rela- tions ; but it is so because it is a relation between two of the same tone, not between two different tones. Octave. We all recognize also the interval which we call the octave and we know that in reality two sounds an octave apart are identical, except that they exist on different planes or levels. So, if we play the sound C and then evoke the C which lies an octave above, we find that we have two sounds that actually blend into one and are virtually one. When we come to discover the re- lations between two sounds at the octave inter- val, we find that the higher sound is produced by just twice as many vibrations in a given time as suffice to produce the lower sound, and so we can express this octave relation mathematically by the symbol 1 : 2. This is a relation really as simple as that of the Unison, for in reality the Octave to a given tone is simply a Unison with one member thereof on a higher or lower plane. Perfect Fifth. The relation next in simplicity should naturally give us the next closest tone-re- lation. And we find that the ear at once accepts 22 Modern Piano Tuning. as the next closest relation what is called the Fifth. If one strikes simultaneously the keys C — G upwards on the piano one observes that they blend together almost as perfectly as the tones C — C or G — G, or any other octave or unison. The Interval or relation thus sounded is called a Perfect Fifth. When we come to trace up its acoustical relations we find that a tone a Fifth above any other tone is produced by just one and a half times as many vibrations in a given time as suffice to produce the lower tone. Thus we can place the mathematical relation of the interval of a Perfect Fifth as 1 : IH, or better still, for the sake of simplicity, as 2 : 3, which is the same thing. So we now have the simplest relation that can ex- ist between different tones; the relation of the Per- fect Fifth or 2:3. This important fact will lead to essential results, as we shall see. The Natural Scale. This interval, the Fifth, will be found competent to furnish us with the en- tire scale which the musical feeling and intuition of men have caused them, throughout the entire Western World at least, to accept as the basis of music and of musical instruments ; that is to say, the diatonic scale. If we begin with the tone C at Mechanics of the Musical Scale. 23 any part of the compass and take a series of Fifths upwards we shall arrive at the following scale : C G D E B F sharp. JSl m ot "ST D A Figure 3, B F SHARP These tones of course are spread over a compass of five octaves, but if they are drawn together into the compass of one octave, as they may rightly be drawn (see supra ''The Octave") then we shall have a scale like this : C D E F sharp GAB Now the F sharp in the present case is not ac- tually used, but instead we have F natural, which in fact is drawn from the interval of a Perfect Fifth below the key-tone C. The reason for this preference of F natural over F sharp lies in the 24 Modern Piano Tuning. fact that the diatonic scale is thereby given a cer- tain symmetry of sound which otherwise it would lack and because the work of practical musical composition is advantaged by the substitution/ The Diatonic Scale. We have arrived now at the Diatonic Major Scale and although we need not here be concerned with the origin thereof, we may be satisfied to know that it appears to sat- isfy the musical needs of civilized mankind. Let us again examine the series of tones, this time including the octave to C, whereby we in reality complete the circle of Fifths, as it may be called, and return to the key-tone, for the octave is the same for musical purposes as the Unison. We have then, counting upwards, CDEFGABC which we can readily identify as the series of seven white keys on the piano ; with the eighth fol- lowing and beginning a new series or scale. The complete diatonic scale, when founded on the tone C, may thus be seen, merely by looking at the piano, to consist of a series of such scales, seven 1 For a general discussion of these reasons consult Goetschius' "Theory and Practice of Tone-Relations." Mechanics of the Musical Scale. 25 in all, following one another from one end of the piano to the other.^ Relations. Now, if we go a step further and discover the relations which these tones hold to each other mathematically, when brought together into one octave, we find them to be as follows, ex- pressing the lower C as 1 and the upper C as 2, and counting upwards always: CDEFGABC 1 9/8 5/4 4/3 3/2 5/3 ,15/8 2 Or in other words, the relation C to D is the same as the ratio 8 to 9. The relation C to E is like- wise 4 to 5. The relation C to F is 3 to 4, C to G is 2 to 3, C to A is 3 to 5, C to B is 8 to 15 and C to its octave is 1 to 2. Tones and Semitones. Now if we glance at the C scale as shown on the white keys of the piano we shall see that it exhibits some interesting pe- culiarities. Between each pair of white keys, such as C — D or D — E, is a black key, which most people know is called a sharp or a flat. But between E — F and B — C is no space whatever, these pairs of white keys being immediately adjacent to each 1 Note, however, that the modern piano contains three tones lower than tlie lowest C, making a minor third more of compass. 26 Modern Piano Tuning. other. If we run over the keys to sound them we shall find that the sound-interval between E — F or B — C can at once be heard as being closer or narrower, as it were, than the sound-interval be- tween A— B or C— D or D— E, or F— G or G— A or A — B. The longer intervals, between which we find the black keys, are called Diatonic Whole Tones, and the shorter intervals E — F and B — C are called Diatonic Semitones. Diatonic Relationships. The exact relations subsisting between the steps or degrees of the Diatonic Scale can be ascertained by dividing the ratios previously had, by each other, pair to pair. Consulting the table previously given {page 25) showing the relations of the steps to their key- tone, we find that when the ratios are divided pair by pair we get the following relations between each pair of notes : C D....E..F G....A B..C, 8:9 9:10 15:16 8:9 9:10 8:9 15:16 Now the first thing that will be observed is that there are three intei'vals here, not two. There are in fact, evidently two kinds of whole-step or whole-tone. For it is evident that the sound-dis- tance between C and D is more than the sound- ■i.4 5 Mechanics of the Musical Scale. 27 distance between D and E. In actual fact, these two whole-steps must be recognized as distinct. This, however, brings about an entirely new con- dition and one quite unsuspected. For inasmuch as the Diatonic Scale must of course always re- tain the same relationships among its successive steps, it is evident that this idea of two ditferent kinds of whole-step must land us in difficulties. The trouble is that we cannot always play in the key of C, by which I mean that sometimes, in fact very often, we desire to build our music upon Dia- tonic Scales which are founded upon other tones than C. From the point of view towards which I am leading — namely, that of tuning — we see here a serious difficulty, for it is at once evident that if we undertake to tune a Diatonic Scale, as sug- gested some time back, by considering it as a series of Perfect Fifths, we shall find ourselves in deep water as soon as we quit the key of C. Let me make this plainer. Understand first of all that we have as yet talked only of a scale founded on C and therefore including what are known simply as the white keys or natural notes. Suppose we begin by tuning a series of fifths quite perfect from some given C, say for the sake of convenience a C of which the 28 Modern Piano Tuning. pitcli is 64 vibrations per second. This is a little less than the pitch of C would be at the Interna- tional standard but is more convenient for pur- poses of calculation. Then we should get a result like this: m -o- F42.66 C64- G96 DI44 AEI6 Figure 4. E324 B486 Now, let us reduce this down to one octave, by transferring the higher tones down, through the simple process of dividing by 2 for each octave of transference down and multiplying by 2 for each octave of transference up. This will give us the folloAving result: F42.66 C 64. G96 DI44 A 216 Figure 5. E324 ^^ ^ n O < c 9- 64 -2> ^^. -^ .-'"''-''' n73^ ro,-'^' ''85.31'- ^.G96 AI08 / BI2I.5 w\* .- ^ ^- '-' ~ y /• ■jf / / (m ^ -• r,^ M-' iT) . jr- - tf ^^^ B486 Mechanics of the Musical Scale. 29 Gathering this together, we have the following scale founded on C = 128, or in acoustical nota- tion Co = 128.1 Co D, Eo F, G, A, B, Ca 128 144 162 170.66 192 216 243 256 Now, suppose we want to play a tune based on another key-tone than C. Suppose, for instance, that we want to use D 144 as the basis of a scale ; that is to say, we want to play in the key of D, as we say. The first thing to do is to find out whether we have notes tuned already which will give us such a scale. Going on the same plan as the pattern Diatonic Scale of C, and applying it to D, we find that we need the following notes : D E F# G A B C# D. All of these we already have except F# and C#. We can get F# by tuning a perfect Fifth above B 243, which will give us FjJ 364.5. Dropping this an 1 Acoustical notation is as follows: Lowest C on the piano is ca:lled C. The second C is C„ the third is Cj, middle C is C3 and so on up to the highest note on the piano, which is C,. The notes between the various C'a are called by the number of the C below. Thus, all notes in the middle C octave, between C, and C^ are called D3, E3, F3, etc., up to C^, when they begin again D^, E4, etc., up to C5. This is the modern notation and I shall use it exclusively. 30 Modern Piano Tuning. octave we have F# 182.25. C# is a Perfect Fifth above F# and so will be 546.75, or, dropping an octave, 273.375. Now, we can construct a scale of D as follows, beginning with the D 144 that we al- ready have, using all the other notes already pro- vided and the two new ones besides. That gives ust D, Eo F#2 G, A, B, C#3 D3 144 162 182.25 192 216 243 273.375 288 If you will look at it closely you will see that there must be something wrong. The distance be- tween F# and G seems small, and so does the dis- tance between C# and D. To test the thing, let us now construct a diatonic scale on the ratios we know to be correct ^ and see what results we get. It works out as follows : D2 E^ F#2 G2 A, B, C#3 I>3 144 162 180 192 216 240 270 288 Ratios 8:9 9:10 15:16 8:9 9:10 8:9 15:16 Now, just for purposes of comparison, let us put these two scales together, one below the other. They look like this : 1 See pa{2^e 25 et seq. Mechanics of the Musical Scale. 31 SCALE MADE UP FROM C SCALE AND PEBFECT FIFTHS TUNED THERE- FROM D E F# G A B c# D 144 162 182.25 192 216 243 273.375 288 SCALE MADE UP FROM KNOWN DIATONIC RATIOS 144 162 180 192 216 2JfO 210 288 At once it can be seen that the F# and the C# which we manufactured by the perfectly legitimate method of tuning perfect Fifths from the nearest tone available in the scale of C, are both wrong when secured in this way. Also, it can be seen that the B which belongs to the scale of C will not do for the scale of D. Not only is this so, but if the experiment is made with other key-tones, it will be found that they all, except the scale of G, differ somewhere and to a greater or less extent from the scale of C, even with reference to the notes which they have in common with C True Intonation. It is evident, therefore, that no method of building up diatonic scales by tuning pure intervals, will do for us if we are going to use the same keys and the same strings for all the scales we need. It is evident, in fact, that if we tune perfect Fifths or any other intervals from C or any other key- tone and expect thereby to gain a scale that will be suitably in tune for all 32 Modern Piano Tuning. keys in which we may want to play, we shall be disappointed. Not only is this so, but it must be remembered that so far we have not attempted to consider any of the so-called sharps and flats, except in the one case where we found two sharps in the scale of D, properly belonging there. It turns out, however, when we investigate the sub- ject, that the sharp of C, when C is in the scale of C, is quite a different thing, for instance- (as to pitch), from the C# which is the leading tone of the scale of D. Chromatic Semitone. The chromatic semitone, which found its way into the scale during the formative period of musical art — mainly because it filled a want — is found upon investigation to bear to its natural the ratio ^%5 or 2%4, according as it is a flat or a sharp. In the case we have been considering, then, whilst C# as the leading tone in the scale of D has a pitch, in true intona- tion, of 270, the C# which is the chromatic of C 256 (see previous tables) would have a pitch of 256 X ^%4 or 266.66. Similar differences exist in all cases between chromatic and diatonic semi- tones, thus introducing another element of con- fusion and impossibility into any attempt to tune in true intonation. Mechanics of the Musical Scale. 33 Derivation of chromatic ratio. Actually the chromatic semitone is the difference between a ^% ratio whole tone or minor tone as it is often called, and a diatonic semitone ; thus ^% -— The Comma. The difference between the % (major) and the ^% (minor) tones is called a comma = ^%o. This is the smallest musical in- terval and is used of course only in acoustics. (%-^^% = «yso).^ Musical Instruments Imperfect. The above dis- cussion, then, leads us to the truth that all musical instruments which utilize fixed tones are neces- sarily imperfect. As we know, the piano, the organ and all keyed instruments are constructed on a basis of seven white and five black keys to each octave, or as it is generally said, on a 12-to- the-octave basis (13 including the octave note). If now we are to play, as we of course do play, in all keys on this same key-board, it is evident that we cannot tune pure diatonic scales. The imper- fection here uncovered has, of course, existed ever since fixed-tone musical instruments came into be- ing. The difficulty, which has always been recog- 1 The diatonic minor scale is affected equally by this ar,?iimcnt; but has not been mentioned here for reasons set forth in Chap. in. 34 Modern Piano Tuning. nized by instrument builders and musical theorists, can be put succinctly as follows : The piano and all keyed instruments are imper- fect, in that they must not be tuned perfectly in any one scale if they are to be used in more than that one scale. Hence a system of compromise, of some sort, must be the basis of tuning. The violins and violin family, the slide trombone and the human voice can of course sound in pure intonation, because the performer can change the tuning from instant to instant by moving his finger on the string, modifying the length of the tube or contracting the vocal chords. When they are played, however, together with keyed instru- ments, the tuning of these true intonation instru- ments is of course modified (though unconsci- ously), to fit the situation. All tuning imperfect. All tuning, therefore, is necessarily imperfect, and is based upon a system called ' ' Temperament. ' ' This system is described and explained completely in the third and fourth chapters of this book. Temperament. I have taken the reader through a somewhat lengthy explanation of the necessity for Temperament on the notion that thereby he will be able to understand for himself, from the Mechanics of the Musical Scale. 35 beginning, the necessity for doing things that otherwise would seem illogical and inconsistent. The peculiar kind of tuning that the piano tuner must do would seem in the highest degree absurd if the student did not understand the reasons for doing what he is taught to do. Seeing also that this correct knowledge is seldom given by those who teach the practical side of the art, I thought it better to go into some detail. In any case, it is well to realize that no man can possibly be a really artistic piano tuner unless he does know all that is contained in this chapter and all that is contained in the next three. It is worth while therefore to be patient and follow through to the end the course of the argument set forth here.^ 1 A complete discussion of the problem of True or Just Intona- tion is to be found in the classic work of Helmholtz, to which the reader is referred. See especially Chapter XVI, Appendices 17 and 18 and the famous Appendix 20, composed by the English translator, A. J. Ellis. My own "Theory and Practice of Piano- forte Building" contains (Chapter VI) a useful discussion of the Musical Scale and Musical Intonation. Chapter II. ON THE VIBRATION OF A PIANO STRING. Of all sounding bodies known to music, tlie musical string is without doubt the most common, the most easily manipulated for musical and me- chanical purposes, and the most efficient. Ac- quaintance with ascertained facts as to the be- havior of musical strings under practical condi- tions is necessary for the complete equipment of the piano tuner; although this acquaintance need not be exhaustive, so long as it be, to its extent, exact. Avoiding mathematical symbols which, requisite as they are to a comprehensive study of Acoustics, may nevertheless be beyond the famil- iarity of most of those who will read this book, I shall here briefly investigate certain properties of musical strings and especially of the piano string. The discussion, I can promise, need seem neither dry nor uninteresting. The String. To be exact, a string should be defined as a perfectly flexible and perfectly uni- 36 On the Vibration of a Piano String. 37 form filament of solid material stretched between two fixed points. But such a string, it must be ob- served, can exist only as a mathematical abstrac- tion, since neither perfect uniformity nor perfect flexibility can be expected in strings made by human hands. A string of given flexibility be- comes more flexible, as to its whole length, if that length be increased, and, conversely, stiffer as its length is decreased. The property of weight also fluctuates in the same way. Likewise if the force whereby a given string is stretched between two points be measured in a given number of pounds, the effective tension equivalent thereto will of course be decreased if the string be lengthened ; or conversely will be increased if the string be short- ened. A string 12 inches long stretched with a weight of 10 pounds is subjected to a lower tension than is a 6-inch string of similar density and thickness stretched with the same weight. These allowances and corrections, obvious as they are, must constantly be kept in mind if we are to un- derstand the behavior of practical strings, since all the acoustical laws which govern such behavior must be modified in practice according to the facts disclosed above. Simple Vibration. We have learned that mus- 38 Modern Piano Tuning. ical sounds owe their existence to the fact that some solid body is thrown into a state of periodic vibration. The kind of vibration can best be ex- plained by likening it to the swing to and fro of s a pendulum. A pendulum is fixed at one end and tends naturally to swing back and forth on its pivot. The kind of vibration which the pendulum performs is called simple or pendular vibration. The tuning fork, when set in vibration, is also very much the same thing as a pendulum, since one end of each prong is fixed and the other end can there- fore swing freely. The tuning fork furnishes, when excited, an excellent practical example of simple or pendular vibration of sufficient rapidity to produce musical sound. Tones of the Piano String. Go to a piano and strike one of the low bass keys in the octave be- tween A-i and A. These very low keys operate on single strings only and hence are excellently adapted for our purpose.^ Strike on the piano the key (say) F. Hold the 1 Incidentally, let me say that the piano is an almost complete ready-made acoustical instrument for the investigation of the phenomena of musical strings, sympathetic resonance, beats and beat-tones, and partials. With a piano at hand the student can dispense with all experimental means except the tuning-fork. I shall suppose that a piano is at hand during the reading of this and other chapters. On the Vibration of a Piano String. 39 key down, and listen carefully. At first you will hear simply the full sonorous tone F, deep and solemn. But listen closely, repeating the experi- ment till the ear becomes familiar, and you will gradually observe that, mingled with the original sound F, there are a number of other sounds, ap- parently very closely related to the original, color- ing it rather than altering its pitch, but at the same time recognizable as sounds that spring from a different level. By repeating the experiment with various of these low strings (or by going higher and taking care that one string in the two- string unisons is damped off), you will gradually be able to perceive the remarkable fact that every piano string produces a sort of compound tone, consisting primarily of its natural tone or funda- mental, as we may call it, but containing also the octave thereto, the fifth above that and the second octave. It is true that these extra sounds are feeble and can be heard only by means of practice and the exercise of patience; but heard they can be, more and more clearly as one's familiarity with the process grows. Partial Tones. The truth is that the piano string does not evolve a simple but an exceedingly complex musical tone. Not only the three extra 40 Modern Piano Tuning, tones of which I spoke before can be proved to exist, but in fact an immense number of other tones, all bearing given harmonic relations to the fundamental, can be shown to be evoked, and by the use of suitable apparatus can be detected and isolated, one by one, through the sense of hear- ing. Special resonators have been made which enable the hearer to detect these partial tones clearly. Even without such special apparatus, however, we can detect a number of the partial tones if we take advantage of the piano 's property of sympa- thetic resonance; a property imparted by the sound-board. Sympathetic Resonance. Hold down the middle C key, without striking the string. Then, while holding the key down, strike a powerful blow on the C immediately below. When the sound has swelled up, let go the lower key whilst holding on to the upper or silently pressed key. At once the sound of middle C floats out of the silence, pure and ethereal. What is the cause of this sound? How has the middle C string been excited? The answer is found in the fact that the lower string which was struck, not only produces its funda- mental tone but also evokes its octave above. The On the Vibration of a Piano String. 41 peculiar sort of vibration of the C2 string which produced this octave is resonated through the sound-board and reproduced on the middle-C string. In the same way, the twelfth (G3) can be brought out, and so can the next octave C4. In fact, with a very good piano and by choosing a low enough sound for the fundamental, even higher partial tones can thus be brought out by sympa- thetic resonance from the original string to the string corresponding with the true pitch of that partial.^ Complex String Vibration. Thus we learn that the piano string vibrates as a complex of vibra- tions, not as one simple form of vibration; for it is evident that if the string evokes, as we know it does, a complex of sounds, these must arise from a complex of vibrations. Let us see how this is : Turning again to the piano, select a string in such a position that it can be measured accurately as to its speaking length. A grand piano is most convenient for the purpose, and the string may be selected from the overstrung or bass section. Now accurately measure the speaking length of the string between bridges, and mark carefully 1 For a further discussion of sympathetic resonance, see Chap- ter VII. 42 Modern Piano Tuning. with a piece of chalk on the sound-board the exact middle point as near as you can determine it. Then sound the string and whilst holding down the key, touch the string at the middle point very lightly with a feather. If you perform the operation skilfully enough, you will find that in- stantly the fundamental tone of the string ceases and there floats out the octave above, quite alone and distinct. Measure now one-third of the length, mark it, and again sound the string. Placing the feather carefully at the exact division point and damping the shorter segment with a finger, the fifth above the original sound is heard. Automatic string division. What is the mean- ing of all this? Plainly in the first case it meant that the string naturally subdivides itself into two parts of equal length and that the vibration of either half gives the octave above the original. Thus we have two vitally important facts at our disposal, one relating to the form of vibration of the string and the other to the law of string length as proportioned to pitch. Moreover, in the second case, if we allowed the Vs division of the string to vibrate, we should get from it a sound an octave above the sound of the On the Vibration of a Piano String. 43 longer or % division. Since we damped the shorter segment, however, we conclude that the fifth above the original sound was produced by a string length % of the original length. If we now continue our experiments we may find that % of the original length produces a major 3rd above the original sound, and that H of the length produces a sound 2 octaves above the original sound. Plainly then, we have two great laws revealed. The first is : When a string fixed at each end like the piano string, is struck at one end, it vibrates in a com- plex form, most strongly in its full length but also perceptibly in segments of that length such as ^, %, % and H. The second law is equally important. It may be stated as follows: Length and Pitch. The pitch of a string — that is to say, the number of vibrations, per unit of time, it can perform, is proportional inversely to its length. Thus, since an octave above a given sound has twice as many vibrations per second as the original sound, it follows that to obtain a sound an octave above a given sound we must have a string one-half as long. Weight, Thickness and Tension. Similar laws 44 Modern Piano Tuning. exist with regard to the influence upon string vi- brations of weight, thickness and tension. With- out undertaking to prove these completely, we may state them briefly as follows : The frequency of a string's vibration is in- versely proportional to the square root of its weight. In other words, if the weight be di- vided by 4 (the square of 2) the frequency will be multiplied by 2. To produce a tone one octave below its original tone, the weight of the string must be increased in the proportion 4:1. To produce a tone one octave above the original tone, the weight of the string must be only Yi its original weight. The frequency of string vibrations is directly proportional to the square root of their tension. In other words, to get twice as many vibrations, you must multiply the tension by 2 ^ = 4. To get four times as many vibrations you must multiply the tension by 4 ^ = 16. So if a string be stretched with a weight of 10 lbs. and it is desired to make it sound an octave higher, this can be done by mak- ing the stretching weight (4 X 10)= 40 lbs. The frequency of string vibrations is inversely proportional to the thickness of the string. If a string of a given length and weight produces a On the Vibration of a Piano String. 45 tone of a given number of vibrations, a string of the same length and twice the thickness will give a tone one octave lower; that is, of half the num- ber of vibrations. Mechanical Variable Factors. All of these laws, be it remembered, are based on the assump- tion of mathematical strings, in which weight and stiffness remain constant through all changes in length. In the case of the actual piano string, in which the weight and tension do vary with the length, some compensation must be made when calculating. Thus, to illustrate, it is found that whereas the acoustical law for frequency of vi- bration requires a doubling of the string length at each octave downwards or halving at each octave upwards, the practical string, where weight and tension vary with length, requires a proportion of 1 : 1.875 instead of 1 : 2. This difference must be kept in mind.^ Why Strings Subdivide. Before, however, we go on to consider the influence exerted, through the peculiar manner in which strings vibrate, upon the problems of tuning and tone-quality, we must take the trouble to discover why they should, in 1 For discussions of this point, see my "Theory and Practice of Pianoforte Building," Chapter VIII. 46 Modern Piano Tuning. fact, vibrate in this rather than in some other way. It is easy to talk about string subdivision and partial tones, but there is very little use in mouth- ing words that do not carry with them to our minds real meanings, or in talking about processes which we do not really understand. So, let us take the trouble to discover why a string vibrates as we have shown it to vibrate. Here again, the piano shall be our instrument of investigation. The Wash-line Experiment. The first thing to realize when we begin to talk about string vibra- tions is that the vibration itself is merely the transmission of a motion from one end of the string to the other. This motion will continue un- til it is transformed into some other sort of energy or else is thrown out of its direction into another direction. Suppose that you take a long cord, like a wash-line. Obtain one as much as twenty feet long. Fasten one end to a post and stretch the cord out until you hold the other end in your hand with the entire length fairly slack. Now try to jerk the cord up and down so that you can get it to vibrate in one long pulse. That pulse will af- fect the entire length of the cord, which you will observe to rise from its plane of rest, belly out in a sort of wave, descend to the point of rest On the Vibration of a Piano String. 47 again, belly out once more on tlie opposite side and return to the point of rest, making a complete swing to and fro. Compare the illustration fig- ure 6. When you find that you can do this (practice is needed), try a different experiment. Try to jerk the cord with a sort of short sharp jerk so that, instead of vibrating in its whole length, a sort of Figure 6. hump is formed on the cord which travels like a wave through a body of water. This short wave will travel along the whole cord, as you will be able to see by watching it narrowly, until it comes to the end fixed on the post. At once you will see that the wave, instead of disappearing, is reflected back, reversing its direction of travel and also its position, being now on the opposite side of the cord. Thus reflected, the short wave travels back to you. This is an example of what is called the reflec- 48 Modern Piano Tuning. Hon of a sound impulse. But it has a very impor- tant bearing on the general problem of piano string vibration, as we shall see. Suppose that you are able to time your efforts so carefully that you can deliver a series of these short sharp jerks, forming these short waves, at the rate of one per second. If you time your im- pulses carefully, you will find that the second impulse will start away from your hand just as the Figure 7. first impulse starts back from the fixed end of the string. The two impulses, traveling in opposite directions and in opposite phases of motion (in positions on the cord opposite to each other), will meet precisely in the center, for neither one can pass the other. At their meeting place, the exact middle of the string, the forces are equal and opposite, so that a node or point of greatly dimin- ished amplitude of motion is formed. The two pulses therefore have no option but to continue vibrating independently, thus dividing the string into two independently vibrating halves, each of On the Vibration of a Piano String. 49 double the original speed. See the illustration figure 7. Meanwhile a second impulse from the hand be- gins to travel along the cord and upon its meeting the already segmented halves the result is a fur- ther reflection and subdivision. This again con- tinues still further at the next impulse, so that finally, if the impulses can be kept up long enough, the result will be the division of the cord into four, five, six, and up to perhaps ten of these "ventral segments," separated by nodes. Harmonic Motion. This being the mode of vi- bration of slow moving cords, we can see how the rapidly moving piano strings are instantly thrown into the state of complex vibration described above ; for we must remember that not only is the vibration very rapid, ranging from 27 to more than 4100 vibrations per second, but also that there is no limit to the possible number of subdivisions. Moreover, the piano string is very stiff and being fixed at both ends and excited by a stiff blow, its motion is not only rapid but powerful, so that the reflections are unusually strong and numerous. Hence the wave of motion of the piano string is remarkably complex. Besultant Motion. The entire complex motion 50 On the Vibration of a Piano String. 51 of the piano string is of course the result of the operation of many forces, moving from different directions, upon a single resistance; so that the result of the interference of the forces with each other is that their net efficiency works out in some direction which is a resultant of all the directions. Thus, the piano string, if it be examined under mo- tion by any optical method, is seen to vibrate in a wave motion which is the resultant of all the par- tial motions. The general appearance of such a wave is as shown in the illustration, figure 8, which gives (theoretically) the resultant of a wave mo- tion including subdivision into six segments.^ The piano usually has the first eight and often the ninth, in the lower and middle registers, and still higher partials in the high treble, but the latter can hardly be isolated without special apparatus ; and then not easily. Of course, as we shall see later, there are certain causes which affect the form of the wave in the piano string, in practical 1 This illustration is after the original by Prof. A. M. Mayer, of Stevens Institute, one of the most eminent of American acous- ticians. Professor Mayer's drawings of harmonic curves and re- sultants were first published in the Philosophical Magazine for 1875. In order to show clearly the six separate wave motions, their respective amplitudes have been made proportional to wave length. This is of course a scientific fiction, but the eflFect upon the resultant curve is not markedly distorting. 52 Modern Piano Tuning. conditions, and so modify the series of partials. Fourier's Theorem. One of the greatest of French mathematicians, Fourier, investigating an- other subject altogether, discovered the law of this harmonic motion of a string when he showed that every complex vibratory motion can be re- duced to a series of simple pendular motions, of which the terms are as follows : 1 1/ 1/ 1/ IZ 1/. 1/4 1/ 1/. V-ir, ^i<^- «"^ infinitum. 1, 72, 73, A, /5, /G, /7, /S, /9, /lO, In other words, the very subdivision of the piano string into segments is here shown mathematically to be the necessary basis of all compound motion in vibrational form. Thus mathematics, from an- other angle, amply confirms the ideas above set forth.i Partial Tones. The string, then, vibrates in its whole length, its y2, Vs, Vi, M, Yc, Vi, Vs, and smaller segments indefinitely. The whole length vibra- tion produces the fundamental tone of the string. The % gives twice as many vibrations, or the oc- tave above. The Vs gives the twelfth, and the % gives the double octave. Thus, the piano string C 64, when sounded, actually involves not only the fundamental tone but all the following: ij. B. Fourier, 1768-1830, author of "Analysis of Determinate Equations." On the Vibration of a Piano String. 53 First 16 partiala of Ci = 64. Ej 63 Bbj C4 D4 E* Ft»4 G* A* Bb* BK C5 ^ ? \> y ^ r rf^r f 12 3 4 64 128 192 256 5 6 7 8 9 10 II 12 13 14 15 r6 320 384 448 512 576 640 704 766 832 896 960 (024 Figure 9. and many more not shown. All these are called partials. The fundamental is the first partial, the octave is the second, and so on. Above the tenth, although the number of possible subdivisions is unlimited, the pitch becomes less and less definitely referable to any specific note of the scale. The first 6 partials, as can be seen, are simply the common chord of C spread out. The 8th, 10th, 12tli and 16th are octaves to the 4th, 5th, 6th and 8th. The 7th is flatter than the diatonic seventh which we use, although the former is the natural tone and the latter quite artificial.^ The other odd-numbered partials are all more or less out of tune with their nominal equivalents, until, at a short distance above the 16th, all pretence of con- sonance except in the 20th, 24th and 32nd, has van- ished. 1 Cf. Chapter 1, "Natural Scale." 54 Modern Piano Tuning. Influence of Partials. It should be remembered that, although all the odd- and most of the even- numbered partials above the 10th are dissonant and this dissonance progressively increases — if one may use the term — the number of partials that may occur above the 10th in a piano string is quite large. This being the case, it will be under- stood that although these partials are relatively feeble, and their sounds do not affect the general sensation of pitch, they do have another effect; and this is felt in what is called the ** quality" or ''color" of the sound. In fact, as we shall soon see, the harshness or mellowness, thinness or full- ness, of a sound, as evoked from the piano, not to mention the greater characteristic differences which distinguish the tone of one instrument from that of another, are all to be attributed to the manner in which the various partials are mixed with the fundamental. Series of Partials. But why should there be from one piano string a mixture of partial tones different from that which persists in another? For that matter, since the tendency of other sonor- ous bodies, like pipes for instance, is to divide up naturally into ventral segments, like strings, why should not all tone quality be alike? Obviously On the Vibration of a Piano String. 55 the difference must arise because one wave form varies from another ; or in other words because one string or pipe or rod produces one specific mix- ture of partials and another a different mixture. Why this should be so in the case of the piano string, which is our present concern, I shall now comprehensively explain, and the following dis- cussion will be of great assistance in promoting an understanding of some most important prob- lems. Point of Contact. The piano string is excited by a more or less violent blow from a felt-covered hammer. The impulse thus given to the string is relatively powerful, and its effect upon the highly tensioned filament of steel is such as to induce instant reflection of the sound-impulse and sub- division of the string into many ventral segments. But the exact individual segments into which the subdivision takes place are determined by one spe- cial condition ; namely, by the position of the ham- mer 's point of contact. As will be remembered, the segments of the string are separated from each other by points of apparent rest called nodes. Of course, these nodes are not actually at rest, but the amplitude of their motion is greatly restricted by reason of the opposed forces pulling from each 56 Modern Piano Tuning. side upon them. If now the exciting blow is struck exactly on one of the nodes, the vibration of the shorter of the two segments into which that node divides the string, and equally the vibrations of all multiples thereof, are blotted out. Thus, if we wish to eliminate the 7th partial, we must strike on the 7th node, that is to say at exactly Vi of the string's speaking length. It is obvious that since the first six partials are simply components of the common chord of the fundamental or 1st partial, and the 8th is triple octave thereto, the elimination of the 7th will produce a perfectly harmonious flow of partials and in consequence a full round mellow tone. Experience confirms this deduction, although the exigencies of piano build- ing usually compel a striking distance, as it is called, positioned at Vs or even higher for the greater number of the strings, and running pro- gressively higher in the upper treble till it some- times reaches /44 at the extreme C7. The influence of contact point position is thus clearly shown, for if any of the very high strings be purposely struck at lower points than the hammers are fixed to strike them, it will be found that their tone is less bright, more mellow and even feebler. The last quality is due to the fact that the prime On the Vibration of a Piano String. 57 or 1st partial of these short stiff strings is not sufficiently powerful of itself and needs the back- ing, as one may say, of many partials to give it consistency and ^^ring." It might be remem- bered incidentally that in the two highest octaves of the piano the progressively higher contact points of the hammers on the strings introduce series of partials running from the first ten to the first twenty. But the longer and more natu- rally powerful strings are struck at about Vs of their distance and would often be bettor off if struck at Yt. Material. The properties of the material from which the string is made are also of importance in considering the precise nature of the mixture of partials which any given example may show. The stiffer a string is, other things being equal, the more rapid and complex will be the reflections of wave-motion and the consequent formation of ven- tral segments. By stiffness I do not mean thick- ness; for of course the thicker the string the less intense will be the wave-reflections and the fewer the high partials produced. But the piano is peculiar in that the tension of its strings does not vary largely from one end to the other, whilst the thickness does indeed differ very largely in 58 Modern Piano Tuning. proportion, since even in the understrung part of the scale the difference betwen the extreme treble and the first above the overstrung will usually be something like the difference between 5 and 8. So it follows that the upper treble strings are very- much stiffer than those in the lower regions, in proportion to their length. Of course, the length factor enters into the complex here too, for the higher strings are shorter, and so again stiffer, for any given stretching force. / / Wire density. In the circumstances it would seem, after one has tested various pianos of vari- ous grades, that the idea of intensely hard wire is most distinctly a wrong idea; at least if we are trying to get round full tone and not hard glitter. The very hard wire is no longer so generally de- manded, and piano makers are begining to require a string of softer steel which shall tend to produce, under the lowered tension conditions thus made necessary, vibrational mixtures involving fewer ventral segments, the upper of which with their consequent partials shall be less prominent. String Tension. A softer wire cannot with- stand excessive tensions. But we can easily see that high tension means stiffness, and one only has to listen critically to the tone of most pianos On the Vibration of a Piano String. 59 to realize that their strings do not err on the side of resiliency. They are usually too stiff as it is, and although the craze for clang and noise seems to be dying out — for which we should be thank- ful — still, there is much to be done yet. The piano of the future, let us hope, will be a low tension piano, equipped with softer wire and with a ham- mer shaped and positioned to kill the 7th harmonic and all its multiples ; a piano which will have few partials in its tone above the seventh and which in consequence will evoke sounds, full, mellow and sustained in quality.^ Voicing. In Chapter IX of this book, I make use of the material here set forth in order to show the practical application of Acoustical science to the work of tone-regulating or voicing pianos by manipulation of the hammer felt. Simultaneous String Vibrations. We shall now have to face the last and in some ways the most fascinating of all the subjects which we shall con- front in the course of our examination into the vibrations of the piano string. So far we have 1 other piano string characteristics: For some special cases exhibited by piano strings under practical conditions, the reader may consult Chapter VII. Piano Ibass strings: The special cases exhibited by the covered strings for the bass tones, are dis- cussed in Chapter VII. 60 Modern Piano Tuning. confined our thought to individual strings sound- ing alone. We now have to consider the very beautiful and important phenomena arising from the sounding of two tones simultaneously. The inquiry is of the utmost importance in the higher analysis of piano tuning. Beats. The piano serves us again to good pur- pose in examining the behavior of simultaneously sounded tones. Let us damp off one string in a triple unison on the piano. (All strings of the modern piano above the overstrung section are strung with three strings to the note.) This will leave two strings vibrating. If the piano has not been tuned very recently, it is almost certain that when we listen carefully to the sounding of these two strings we shall hear a sort of sound that can only be described as discontinuous and **wavy." In order to make sure, suppose we choose the strings corresponding to Cg = 258.65 (middle C at international pitch). Let us damp one string of the triple and then slightly turn the pin of one of the others so as definitely to put it out of tune with its fellow. A very slight turn, just enough to feel the string give, will be suffi- cient. Now, take a tuning fork sounding exactly the same international pitch Q^= 258.65. Sound On the Vibration of a Piano String. 61 it, and listen carefully. You will hear a clear con- tinuous tone, which persists without deviation or fluctuation. Put aside the tuning fork, strike the piano key, and listen. By contrast you hear a con- fused medley of sound, in which the fundamental pitch is discernible, but is surrounded by, and buried in, a mass of wavy, fluctuating, rising-and- falling sounds of a peculiar character, which are unmistakable when once heard. The peculiar character of these sounds is their rise-and-fall ef- fect. The tone swells out far beyond its normal intensity and then dies away. This wave-like sound rises and falls at definite intervals, and it will be seen that the further apart in pitch the two strings are, the more of these rise-and-fall periods there will be in a given time. If now we begin to turn the tuning-pin backward, so as to bring the disturbed string again to its original equality of pitch with the other, we shall find that the wavy sounds gradually become slower and slower, until at length they disappear, and only the pure continuous tuning-fork tone remains; showing that the two strings have now been brought into perfect accord. Let us see what causes this interesting phenomjenon. Condensation and Rarefaction. We must go Figure 10. 62 On the Vibration of a Piano String. 63 back for a few moments to some earlier considera- tions. A sound-wave is an oscillation to and fro. When a tuning fork prong vibrates, the first half of the vibration is when the prong moves away from its rest position and pushes the air in front of it against the surrounding air. This pai-t of the vibration has the effect of compressing the air on that side, whilst on the other side the air moves forward to fill up the vacuum left by the moving away of the prong and thus is rarefied or thinned. Consider a vibrating pendulum (Fig. 10), and think of it as if it were a slow moving tuning fork. As the pendulum moves in one direction it con- denses or compresses the air in front of it, and then as it moves back that same air is again rare- fied or thinned out to its original density ; for air is elastic and rebounds. Thus each complete vibra- tion of tuning-fork, string, or pendulum, no mat- ter how slow or rapid, produces a condensation followed by a rarefaction of the surrounding air. Wave-length. The space or distance between one condensation and the next, or between one Figure 11. 64 Modern Piano Tuning. rarefaction and the next, is called the wave-length. The more of these pulses there are in a second or other unit of time, the shorter the length of each. Sound travels at the rate of 1100 feet per second, roughly speaking — the wave-length of a tone of 100 vibrations per second therefore is ^^^%oo or 11 feet. Figure 11 illustrates this point. Phase. Thus we see that a sound-wave propa- gated through the air consists of a series of these oscillations of rarefaction and condensation. Figure 12. Now suppose that you start two such wave systems simultaneously from two strings perfectly in tune. Start them exactly at the same time so that the condensations begin together. A good example is the striking of two strings at once on the piano. The two run exactly together, condensation with condensation and rarefaction with rarefaction, as is shown by Figure 12, and are said to be in the same phase. Difference of Phase. Now suppose we can ar- On the Vibration of a Piano String. 65 range to start one string vibrating just half a complete vibration beliind the other. Then con- densation of No. 2 begins with the first rarefac- FlGURE 13. tion of No. 1 and we have the state of affairs pictured in Figure 13. Such a condition is called difference of phase. Difference of one vibration. Suppose two piano strings, one of which gives just one vibration less per second than the other. Now, when these two strings are sounded simultaneously, it follows that at the end of a whole second one will be exactly one vibration behind the other. Likewise at the end of half a second one will be half a vibration behind the other ; or in other words at the end of half a second, or right in the middle of one sec- ond's complete series of vibrations, the two will be in different phases, while at the end of a whole second they will have regained identity of phase ; will be in the same phase together again. Sup- pose now we lay out on paper two wave systems, whose frequencies shall be in the ratio 8 : 9, for the Modern Piano Tuning. ^< C sake of simplicity. Let us also show, by a third wave-curve, the result of the simultaneous activi- ties of the two waves. In order to avoid a complex drawing I show just eight vibrations of the one and nine of the other. These will con- sequently begin and end together. Resonance and Interference. Now as soon as we examine these superimposed curves, we see that at the second complete vibration they are distinctly out of step with each other and by the time one has made four complete vibrations they are in definitely opposite phase. From this point onwards the difference subsides until at the eighth vibration of the one and the ninth of the other, the phase is again the same for both. Now, it will at once be seen that when the two waves start, two condensations come together and so we have one condensation on top of the other, which of course 66 On the Vibration of a Piano String. 67 means an increase in amplitude of the combined sound. Hence at the beginning of the waves the sound of the combined tones will be increased over the sound of either of them alone. We have a condition of resonance, as it is called. On the other hand, when the middle of the curve has been reached we see that the condensation of one meets the rarefaction of the other exactly, so that at this point the one wave blots out the other and produces a perfect interference as it is called, cancelling the sound altogether. Hence we have the rise and fall of sound which we heard so clearly in the two piano strings men- tioned above.^ This rise and fall is very distinct and in the present case would occur at each 8-to-9 period; in other words, if the two waves were vibrating at 80 and 90 vibrations per second re- spectively, there would be heard 10 beats per sec- ,ond between them when sounded together. Frequency of Beats. Beats therefore arise be- tween sounds nominally in unison but actually slightly out of tune with each other. The number of beats in a given time is equal to the difference between the frequencies of the generating tones. Coincident Partials. Beats arise only between 1 See pages 60 and 61. 68 Modern Piano Tuning. unisons. When heard in such intervals as the Octave, Fifth, Fourth, Third or others, this is because partial tones which may be common to both are thrown out of tune slightly ; and the beats arise between them. For instance, the beats in an octave which is somewhat out of tune arise between the prime of the upper tone and the second of the lower; which are the same. Ex- ample: C, = CA and C2 = 128. Prime of the higher is 128. Second of the lower is 128.^ These are therefore coincident, and if the strings which produce the primes are not in accord, the coinci- dent partials will generate beats as above. The same is true in the interval of a perfect Fifth where the coincident partials are the 2nd of the higher and the 3rd of the lower. Please observe that the coincident partials always bear the same num- bers as express the ratio of the fundamentals. Thus octave ratio = 1:2 and coincident partials are 2 and 1. Fifth ratio ==2:3 and coincident partials are 3 and 2. Fourth ratio = 3:4, and co- incident partials are 4 and 3; and so on for all other intervals. For instance: Suppose one tone = 200 and another = 301. The interval is a Fifth, slightly out of tune, as the higher should be 1 See supra, p. 53. On the Vibration of a Piano String. 69 300. Coincident partials are 3d lower and 2d higher. 200 X 3 = 600 ; 301 X 2 = 602. 602 — 600 ^ 2 ^ number of beats per second in this out-of-tune Fifth. Use of Beats. From what I have said, it be- comes plain that the tuner will find beats very use- ful and must devote himself to practicing the art of hearing them and counting them. For it is evi- dent that if the number of beats between any two coincident partials is equal to tlie difference be- tween the frequencies thereof, then if we calculate the exact required frequency of each of the two members of an interval and from this calculate the frequency of their lowest coincident partials, w^e can easily and at once take the difference be- tween the two latter, and whatever this differ- ence be, that number of beats per second will be heard between them when sounded together. Therefore if we tune the two members of the in- terval so that we hear just that number of beats per second between them, we have tuned cor- rectly. It then remains only to calculate these true values for the different tones of the piano and thus to establish proper beat-rates everywhere. Miller's Researches. There is nothing unusual in all this really, for of course all tuners tune by 70 Modern Piano Tuning. counting beats, whether they call the process by this name or another. The point I am making here is that this process is the proper and natural process and that it is capable of being established mathematically, as has been done by Mr. J. C. Miller of Lincoln, Neb.; whose researches I am happy to be able to make use of in this book, as will be seen later. We have now discussed to such an extent as is necessary for our present purposes the behavior of piano strings in vibration ; and have discovered that this discussion, if properly understood, is found to give us all needed assistance in both tun- ing and voicing, provided we can calculate the necessary frequencies of the tones required on the piano. We already know ^ that the piano does not permit pure tuning of the diatonic scale but that a system of compromise must be adopted to ac- commodate the inequalities of the diatonic scale to the unyielding 12 keys of the piano's octave. The system of Temperament used for this pur- pose, called the Equal Temperament, is now so firmly ingrained in practice that it is in fact the real basis of all modern music; rather than the diatonic scale, which indeed is now little more 1 Supra, Chap. I. On the Vibration of a Piano String. 71 than an artificial abstraction. Of this, however, I shall speak in the next chapter. If the present chapter has seemed at all involved this is only because I have had to treat an in- volved subject in simple language and small space. Still, all I have said here has been necessary and forms part of the argument which I am develop- ing as to a system of piano tuning and tone-regu- lating; based on science and not on guesses or rule-of-thumb — and a good deal easier than if it were so based. For, indeed, among all the ridiculous supersti- tions of the human mind, none is either commoner or more absurd than that which covers with con- tempt the efforts of pioneers to formulate and apply scientific method. In truth, to do things scientifically is always to do them in the easiest as well as the best, way; and your ^'practical man," untainted with one touch of theory, wastes time and energy in equal proportion. Chapter III. TEMPERAMENT. We have reached the central position in the science of tuning. What has gone before has been enough to show that one cannot obtain a series of pure diatonic scales, in the quantity required for the performance of music, with a key-board com- prising only twelve keys to the octave. The par- ticular method adopted in Chapter I for the pur- pose of showing the truth of this assertion might of course be matched by a dozen others; without altering the facts in the least. For example, I might have pointed out that an ascending series of perfectly tuned perfect Fifths, although nominally equal to seven Octaves, yet actually exceeds them. I might have shown that three major Thirds should be equal to an Octave, if tuned pure one above the other ; but that in fact they fall considerably short thereof. There are many other possible illustra- tions; but I have already shown, in the simplest 72 Temperament. 73 manner, that some form of compromise is needed if pianos are to be tuned so as to make the per- formance of music in all tonalities tolerable de- spite the defective and inadequate 12-to-the-octave key-board. The word Temperament is generically used to indicate any one of the many such systems that have been, at one time or another, proposed and used. It must be remembered that the present type of key-board dates certainly from the 14th century and has scarcely undergone any change in details — positively none in essentials — during all that time.^ This is an amazing commentary on the slowness of the human mind and its hatred of change. It is a fact that the width of an octave, even, has remained the same for certainly three hundred years. And the same slowness of de- velopment is true in other details.^ Influence of the key-hoard. The truth implied 1 A terra-cotta model showing a rudimentary form of key- board used with an Hydraulikon or water-organ, has been found in the ruins of Carthage, and is assigned to the second century A. D. Cf . A. J. Hipkins' "Introduction to the Key-board Instru- ment Collection," Metropolitan Museum of Art, New York. 2 The great organ at Halberstadt, Germany, built in 1361 by the priest Nicholas Faber, had a complete chromatic key-board, but with very wide keys. However, sixteenth century clavichords are preserved showing key-boards essentially identical with that of the modern piano in width and even in moimting. 74 Modern Piano Tuning. in Chapter I may now be realized completely : that the key-board has always exercised a distinctly enslaving influence upon the development of music. If we were not chained to the 12-note key- board by the tradition of music teaching and of piano making, we should soon have a substitute, as easily taught to the hand, whereby at least the grosser imperfections of any temperament sys- tem might be avoided. But to hope this is to hope too much. Meaning of Temperament. Actually, the word Temperament means ' ' tuning ' ' ; nothing else. Its derivations from the Italian and thence from the Latin, show this clearly. To ''temper" sounds is to tune them. And this fact indicates that the necessity for a compromise from purity was rec- ognized very early and that just intonation has never been even near accomplishment in ordinary practice. In fact the system of Temperament now in use is probably the best that has yet been contrived, although it has had one rival whose claims are not to be despised. Equal Temperament. The twelve keys within the octave must, of course, represent amongst themselves the various degrees or steps of rela- tionship existing within that interval. Seeing Temperament. 75 that we cannot gain purity of ratio with only twelve keys, it follows that we must divide up the octave in some way that will admit, as adequately as may be, of performing required music in a toler- able manner. Equal Temperament is the name given to a system of dividing up the octave into twelve equal parts. This being the case and the pitch proportion of the octave interval being 1 : 2, it follows that the proportion from semitone to semitone in equal temperament is 1 r^y or 1 : 1.0594631, correct to seven places of decimals. This ratio is the ratio of the equal semitone, upon which the system is based. The Equal Tempered Scale. This being so, we have only to select some standard of pitch for some one tone and calculate up and down there- from by the simple process of multiplying or divid- ing, semitone by semitone, by the factor 1.0594631. The octave of course remains the one interval which retains its purity. This is so, because we must have a system of some sort and the octave provides a foundation therefor. Hence the octave remains pure, and so if we once calculate the equal tempered pitch of the 12 semitones in one octave we can obtain that of any one of the tones situated in any other octave by multiplying by 2 76 Modern Piano Tuning. for eacli octave of distance upwards or dividing by 2 for each octave of distance downwards. Thus we may say that Equal Temperament is a system in which the octave interval is tuned pure and all other intervals are tuned in such a way as to produce a tone-series of 12 equal parts within each octave. International Pitch. The nominal standard now recognized for the basis of pitch in the United States is A3 = 435. This is the same as the French Normal Diapason, from which indeed it is taken. Assuming this as our standard, we have the following frequencies for the A throughout the compass of the piano, beginning at the lowest : A-, - 27.1875 A — 54.375 Ai - 108.75 A. = 217.5 A3 — 435 A, - 870 A5 -1740 A« -3480 The piano's scale in equal temperament. With the above figures as our standard of measurement, and multiplying for each semitone upwards by the Temperament. 77 equal semitone ratio, we get the table on the next page, showing the complete range of frequencies for the entire 88 notes of the piano.^ Object of the Table. My object in setting forth this Table is not to confuse the student but to enable him to see how a system of tuning in Equal Temperament may easily be worked out; one far simpler and considerably more likely to lead to correct practice than any other based on guess. The Table is the preliminary essential in the argu- ment now to be set forth. By examining the Table we observe that if any column be taken, the figures from top to bottom thereof represent the progression of frequencies in the sounds of an ascending octave. All columns to right of any such column are ascending octaves and all columns to the left are descending octaves. From column to column we may proceed by either multiplying or dividing by 2 at each column. The octave interval is pure and the others are 1 In reality the names used for the tones in the equal tem- pered scale are incorrect, since they are the same as those of the pure diatonic scale. For purposes of convenience we continue to say C, B flat, G sharp and so on, whereas it would be more ac- curate simply to number the septave C to B as 1 to 12. How- ever, seeing the musical notation still sticks to the old key-sys- tem, though this no longer means anything in point of char- acter, the old names are respected in the table, the sharps and flats being noted as coinciding. (^ 93 o .>* • 00 ; • • eo 4) > o o • • .(MOO'*aOOOCOODO > o 'Tiicoi— locor-icoocgococa ; ; ; ;oo^(Mco 1^ (M 1-^ -c<]in'^i-; ; ; ffi t-^ in CO cj oi (m' cc in i~-^ o 'i^ " (McoTjHincDt^oooiO^cc-* i-lrHr-(i-HnHr-<>-H,-li o • ; ; •>*' CO oj CO F-H !» ^' (ffl oq CO in (m' ; COCOt^t-COOOOCiOO^tN i-H 1— 1 .— 1 1— 1 c Octave • • • CO in t-- (M t^ in c-1 t- • • • O l?I C<1 ■^_ t--; >-; I--; M; CO CO CO o • c^i -t CD co" o co' in" 00 I-H -+ t-I »-i ; cocococoTtiT»<-<*' 365.33 G 387.97 A 435.3 Ap ....411.00 A 431.08 B 483.60 Bl? 456.66 B 484.97 O3 517.3 C 513.75 CJf., ...544.12 Dl> 548.00 Equal Tempered C Scale ( Chromatic ) c, . > • ..258.65 CJ- -Dl> ..274.00 D ..290.2 DS- -E^ ..307.5 E ..325.9 F . .345 3 F#- -GJJ ..365.7 G ..387.5 G#- -AP ..410.5 A ..435. A#- -Bi> ..460.8 B ..488.2 0, . .517.3 c#- -Dl> ..548. D ..580. D, .580. 1 The minor scale has not been considered because its difference from the major is merely in the detail of intervals. The argu- ments already made apply with equal force to the minor scale. See supra. Chap. I, 80 Modern Piano Tuning. major scale built on the same Cg = 258.65, tlie sec- ond in a pure major diatonic scale built on the tem- pered major second to C (D), and the third a pure diatonic major built on the tempered D flat. The pure diatonic scales are worked out from each on the basis of the ratios of the diatonic scale major {supra Chapter I) ; and the object of the comparison is simply to show what effect the Equal Temperament has on purity of intonation. Advantages of Equal Temperament. These tables show clearly some of the peculiar defects of the Equal Temperament; but they show also some of its peculiar advantages. For it will be seen that at the cost of some perceptible disso- nances in certain intervals — dissonances which we shall shortly calculate definitely — we gain the abil- ity to perform music in all tonalities, by aid of the traditional 12-note key-board. Disadvantages of Equal Temperament. At the same time we must not lose sight of the fact that in reality the Equal Temperament is a comprom- ise, and a loose compromise, with fact. If it were not for the organ and piano, the imperfections of Equal Temperament would be more easily per- ceived; but the dynamic powers and immense Temperament. 81 harmonic resources of these two instruments have endeared them to musicians and have concealed the roughness of their intonation. No one who has read the previous chapter and understands how to listen for beats, however, can long endure the intonation of the organ on such intervals as minor thirds. The sustained tones of that instru- ment bring out beats very clearly and produce a generally distressing effect for delicate ears. Of course, the truth is that most of us are so used to tempered intonation that we recognize nothing else and know of no other possibility. Yet the fact remains that whoever has heard one of the few experimental key-board instruments that have been constructed to play in pure intonation has been entranced with the sweetness of music thus played. It is far more beautiful than tempered intonation and in fact seems to impart to the music of these instruments a new sweetness and concord. So long, of course, as the manufacture of pianos and organs is stressed rather on its industrial than on its artistic side we shall probably have to remain content with Equal Temperament. But it might as well be observed that if the piano and organ were out of the way, music throughout the 82 Modern Piano Tuning. world would be on some basis of tuning other than Equal Temperament within ten years. ^ Meanwhile we must be content to tune in Equal Temperament as well as we can, knowing that when such work is well done it is very satisfactory and serves well the requirements of modern music and modern musicians. Meantone Temperament. Before going on to consider the method of tuning in Equal Tempera- ment, however, I should like to mention the imme- diate predecessor of the Equal Temperament ; the famous Meantone Temperament, which flourished from the 16th to the early part of the 19th century and may be occasionally found to-day on organs in obscure European villages. This system con- sists in tuning a circle of fifths equally flat, in such a way as to leave all the thirds major nearly pure. In order, however, to be used for all re- quired keys, it is necessary to have extra key- levers, for the flats and sharps of adjacent tones are not identical. For perfect performance in all tonalities, not less than 27 tones to the octave are iThe reader who doubts this miglit consult Ellis (App. 20 to Helmholtz), Helmholtz, chapter 16, Perronet Tliompson, "Theory and Practice of Just Intonation," and Zahm, "Sound and Music." My own book, "Tlioory and Practice of Pianoforte Buildin<^," con- tains a close analysis of the requirements of Just Intonation, Temperament. 83 required, but tlie greater number of tonalities can be used with 16 keys to the octave ; the additional tones being for D flat, E flat, A flat and B flat. The ordinary 12-tone key-board would give, of course, starting from C, only the circle of Fifths, which when transposed to the same octave result in the following scale : C, C#, D, D#, E, F, F#, G, Gj, A, Ajf, B. Unfortunately, in this temperament, C# will not do for D flat, D# for E flat, G# for A flat or A# for B flat. These tones of course have to be incor- porated somehow and in some 18th century organs were built into the manual by dividing up some of the black keys, which were cut across the mid- dle with the back half slightly raised above the front. The mean tone system gives a ''sweet" and harmonious effect for nearly all keys, with 16 tones to the octave, although of course this num- ber still lacks 11 tones to make it quite adequate. However, even with 12 tones to the octave, an ex- periment in meantone temperament can be tried, and will sound veiy attractive so long as one keeps within the range of keys allowable. To make the best of the key-board we have, the following method may be tried. Start with C and tune the 84 Modem Piano Tuning. major third C — E perfect. Then tune the fifths from C round to E by Fifths and Octaves, equally flat, testing until the right degree of flatness is ob- tained. All other notes can be had by tuning pure major Thirds and pure Octaves. By this system it is possible to play in the keys of B flat, F, C, D and A major, and G, D, and A minor. The reason, of course, is as stated below. This is a very use- ful experiment and if tried out carefully will en- able the student to play old music in the tuning for which it was intended; an experience sometimes most illuminating and delightful.^ The ''Beat" System. I have mentioned these things because I am anxious to have the student understand that the Equal Temperament is not the only possible system of tuning. But to get now definitely to the method of tuning in Equal Temperament, which is the system which the tuner to-day uses universally, let us see what is the nature of our problem. The Table of frequencies (Table I) suggests the method we shall use. We know ^ that beats afford 1 The student might consult the extremely useful and interest- ing article, "Temperament," by James Lecky, in Grove's "Diction- ary of Music and Musicians." 2 Supra, Chapter II. Temperament. 85 us a simple and accurate way of judging the devia- tion from consonance of one tone sounded with an- other. Since we cannot trust the unaided ear to tune successively a series of equal tempered semi- tones, we make use of the method of comparing one tone with another. Thus we have only to as- certain the number of beats that are produced by the members of various intervals in equal tem- perament, beating against each other, and then to tune these intervals by counting their beats. Beats arise between coincident partial tones and therefore if we lay out a series of intervals from some given standard tone and calculate the co- incident partial tones in each, we can by subtrac- tion find out how many beats there are heard when that interval is rightly tempered.^ Experience shows that it is easiest to tune by Octaves, Fifths and Fourths; by Fifths and Fourths for the Oc- tave of tones, usually Fg — F3, chosen for the ** bearings" or foundation work and by Octaves up and down thereafter. The other intervals in- volved are best used for testing the correctness of the work as it proceeds. Such testing is best 1 Compare Chapter II, "Coincident Partials," to find what par- tials coincide in any interval. 86 Modern Piano Tuning. done by means of major and minor Thirds and major and minor Sixths, whose rates of beating in equal temperament the tuner must therefore know. Beats in Equal Tempered Intervals. The fol- lowing Table (Table III) gives the number of beats per second in the ascending minor Thirds, major Thirds, Fourths, Fifths, minor Sixths and major Sixths from each degree of the equal tempered scale between Co and C^ inclusive. The rates are, for purposes of convenience, made correct only within .5 vibrations per second. In other words, where an accurate calculation would show any beat-rate as some whole number plus a decimal greater than .5, the rate has been made the next whole nuinber. For instance, 19.73 is counted as 20; while the same course has been adopted for rates where the decimal correctly is less than .5. For instance, 9.31 is made to read 9.5. On this plan the error may be less than .1 or more than .4 vibrations per second. Inasmuch, however, as the tuner will find his powers extended to the utmost in estimating the beat-rates of Fourths and Fifths at the figures given, and with this relatively large error, it has been thought better to adopt this course. For suggestions as to counting beats and other o • 03 ;^ CO lO 0>rtOC»00»0 0»00»OOOiOOO . 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C'*? l. L »** L O** 1 ** "** '">** " " B J 'j1o<;g«cf«oO«Q«<;^^QP.f.-^« o I « I L i« I '- I '..I I 1 '" I. L l„ 1 ^ f^ fM f^ <5 <; o o O O P^ fe m ft Ph P^ <5 <1 O f^ (X -2 coCT>0'-<«Ti 19 I9a 19b Figure 16. 1. Top. 2. Iron Plate, covering wrest plank. 3. Treble tuning-pins, 4. Side. 5. Muffler-rail and muffler felt. 6. Hammers. 7. Ilammer-rail. 8. Action. 9. Arm. ' 10. Digitals or Keys. 11. Key-Bed. 12. Truss. 13. Toe. 14. Sound-board. 15. Iron Plate. 16. Sustaining Pedal. 144 The Modern Piano. 145 17. Muffler Pedal, 20. Muffler Trap-work, 18. Soft Pedal. 21. Action. 19. Trap-work. 22. Soft Pedal Lifter. 19a. Bottom Kail. 23. Action-bolt. 19b. Bass bridge. 24. Bass Tuning Pins. 19c. Treble Bridge. various parts. In figure 15 are shown the ex- ternal or visible parts of an upright piano with the proper name for each appended. The various case parts of the grand piano are of course largely similar, but the different posi- tion of the scale necessitates modifications, which involve some changes in names and positions of parts, as shown on page 147. Names of Internal Parts. In order to provide the reader with a list of correct names for the vari- ous internal parts of the piano, the illustration on page 144, figure 16, shows an internal front view of an upright piano. The rear view shown on page 146 indi- cates the position of the various elements in the back frame and the rear of the sound- board. The grand piano, figure 18, page 147, cannot so well be shown as its internal parts are hidden by the solid case. The differences, such as they are, which exist between the two types, however, are thoroughly explained in the pages which follow. Figure 17. 1. Top Block of Back, behind wrest-plank. 2. Limiting Rim of Sound-board. 3. Posts. 4. Ribbing. 5. Surface of Sound-board. 6. Bottom-rail of Back. 7. Limiting rim of Sound-board. 146 Figure 18, 1. 2. 3. 4. 5. 5a. Top. Top-Stick or Prop. Case. Key-Bed. Leg. Pedal-Frame or Ly 6. Pedal Frame Brace 7. Pedal Rod. 8. Key-Slip. 9. Key-Block. 10. Fail-Board. re. 11. Music Desk. 147 148 Modern Piano Tuning. Materials Used in Piano Construction. Woods : Mahogany. Walnut. Oak. Circassian Walnut. Bird's Eye Maple. Maple. White Wood. White Pine. Spruce. Pear. Holly. Sycamore. Cedar. Mahogany. Leiatheks : Doeskin. Elkskin. Buckskin. Fext and Cloth: Green and White Baize. Tone Felt. Damper Felt, hard. Damper Felt, soft. Flannel. IVOBY. Celluloid. Iron. Steel. Bbass. Gbaphite. Used In Veneers for Cases. Veneers for Cases. Veneers for Cases. Veneers for Cases. Veneers for Cases. Veneers for Cases. Wrest-Planks. Backs. Hammer moldings and shanks. Hammer rails, dowels, etc. Body of case work. Key Frames and keys. Soimd-boards. Various small action parts. Various action parts. Key-rail cloth, punchings. Hammers. Bass dampers. Treble-dampers. Casework punchings, fall-board 8tri])s, name-board strips, stringing. Tops of white keys. Fronts of white keys. Iron plate, action brackets, lx)lts and general hardware. Action angle rails, plates, trap- work springs, etc. Action-springs, pedal feet, rods, Lubrication of action, etc. The Modern Piano. 149 Various other materials are used in small quan- tities, for individual manufacturers have their own special methods which require special mater- ials. But the above includes the principal ma- terials common to all pianos. Finish. Modern pianos are elaborately finished with a highly polished surface. The base of this finish is several coats of varnish, which are rubbed down and then re-varnished with what is called a ''flowing" coat of very heavy varnish. This is again rubbed down, first with pumice stone, felt pad and water, then with rotten stone, felt pad and water and then with the hand. The final finish is given by rubbing with lemon oil, which is lastly wiped off with cheese cloth wrung out in alcohol. Although this finish is very beautiful it does not retain its brilliancy long under domestic condi- tions. In the remarks on piano repairing I have made several suggestions concerning the repair of damaged varnish work. This brief description of the modern piano has been intended to furnish the student only with an explanation of the relation of the various parts to each other and the correct functions of each. More thorough studies are made in following 150 Modern Piano Tuning. / chapters of certain elements which the tuner re- quires to understand in completeness and the present chapter will be perhaps most useful in providing a convenient peg on which to hang them. Although it fulfills so humble a purpose, however, it will not be without its value if it im- presses on the reader's mind the great truth that the piano, as it stands, is by no means to be re- garded as the fruit of sudden inspiration but rather as the contemporary stage in a long proc- ess of evolution. The history of the instruments which preceded the piano in point of time, and which in system are its ancestors, shows plainly that the invention of the hammer action by Cristofori in 1711 was merely the culmination of a long series of efforts on the part of many great craftsmen, looking towards the production of a musical stringed instrument capable of doing for domestic use what the organ has always done for the church; namely, furnish complete command over all existing resources of harmony as well as of melody. The piano as it stands to-day is the crown of three centuries of endeavor; but it is by no means certain that it will not yet be modi- fied much further. No one can pretend that the piano is a perfect instrument. Its tempered in- The Modern Piano. 151 tonation, its rather hard unmalleable tone, its lack of true sostenuto, all represent defects that must in time be improved out of existence. Meanwhile, we have to take the piano as we find it, realizing that after all it is a very fine and very wonder- ful instrument.^ Incidentally, it is a matter for congratulation that the modern development of the piano is almost wholly an American achievement ; and that European makers are confessedly inferior to the best of their American colleagues. Why this should be so is another matter; but it certainly is so. 1 The reader who desires to study the extremely fascinating liis- tory of the piano may find an extensive literature on the subject. Hipkins is the best authority by all means. See bibliographical note at the end of this volume. Chapter VII. SOUND-BOARD AND STRINGS. Quite as characteristic of the piano's individu- ality as the hammer action itself, is the apparatus of resonance, or, as we more usually call it, the sound-board. The piano is a stringed instrument and thus claims kinship with viols and lutes and all their descendants ; but ever so much more it is a resonance instrument and a percussion instru- ment. In fact, the true character of the piano cannot be rightly apprehended until we have real- ized that the string-element is really overshad- owed to a considerable extent by the sound-board. The piano is just as much dependent upon reso- nance as upon the prior vibration of the strings. Without the sound-board the piano would have neither power nor color to its tones. Moreover, variations in the quality of the sound-board ma- terial in its construction and in the skill of its de- sign involve parallel variations in the tonal values of pianos, of such marked and distinct charac- 152 Sound-Board and Strings. 153 ter as, almost without any special physical in- vestigation, to convince us that we must accord to the combined tone-apparatus which we call the sound-board and strings, entirely individual pe- culiarities and functions. In fact I propose in this chapter to consider the sound-board and strings together as one complete structure, which for want of a better term, we might name the ''tone-emission apparatus" of the piano. In this and in what follows, I do not wish to be considered dogmatic, and certainly have no intention of composing vague and involved disquisitions on the subject-matter. Practical throughout this book is proclaimed to be; but it is impossible to talk practically about the piano's sound-board and its strings, unless we have a solid basis of fact on which to found our theories. In- deed, in this particular case, as in many others, the one sure method of going astray is to rely on rule-of-thumb or traditionary notions; as the experience of numberless persons who have tried to improve the sound-board, most clearly, if pain- fully, indicates. Beginning therefore with a clear discussion of the phenomena seen in the action of the sound-board and the strings, I shall try to work out the bearing of these upon the facts of 154 Modern Piano Tuning. piano construction as they affect the piano tuner in his work, the pianist in his playing and the piano in its durability and value. Definition of tone-emission apparatus functions. The object of the tone-emission-apparatus may be described as follows: to produce the charac- teristic piano tone, through the vibration of the strings in response to the percussive action of the hammers thereon, and through the resonating functions of the sound-board, whereby the original string wave-forms are combined, amplified, and transformed in quality as required for the pur- pose indicated. That is not a neat definition perhaps, nor is it uncommonly accurate in all its parts ; but for the present it is perhaps the truest description that can be assimilated. Later on we shall improve and refine the details with better understanding. Piano Tone. The feature of the piano which distinguishes it generally from all other musical instruments, and specially from all other stringed instruments, is the peculiar character of its tone. This is, to an extent, of course, hard and un- malleable. It possesses neither the plasticity of the violin tone nor the bitter-sweet gayety and lightness of the guitar. It is solid, yet evanescent, Sound-Board and Strings. 155 hard yet capable of infinite gradation in inten- sity. Lacking the serenity and majesty of the organ diapason, it is pre-eminent in obedience to touch. The pianist cannot indeed sustain his tones, nor swell or diminish them at will. Here both organ and violin surpass the piano. But the pianist can color his tone almost as widely as the violinist, and withal has a touch control over dynamics which the organ entirely lacks. Thus the tone of the piano, as brought forth by a good performer, has qualities highly attractive, which, combined with the convenience of the instrument, its capacity for complete musical expression in all possible harmonic relations, and its moderate price, have made it supreme in popularity. Let us then see just how this peculiar tone is pro- duced. Acoustical Definition of Piano Tone. Speaking from the view-point which we have adopted in Chapter II, it may be said that piano tone is the effect of a wave-form induced by hammers strik- ing upon heavy high-tension stretched strings at pre-determined points on the surface thereof; these waves having definite forms which are modi- fied by the resonating power of the sound-board. The first important feature is that the piano tone 156 Modern Piano Tuning. is produced by the strings being struck; thus dis- tinguishing the piano from all other stringed in- struments. The string is struck. As we have already found out ^ a string stretched at high tension and struck by a piano hammer, is thrown into an extremely complex form of vibration. This vibrational form consists of the resultant of a number of simple forms, which in turn are the effect of the string's vibrating in various segments as well as in its whole length. In short, the fundamental tone of the string, together with partial tones correspond- ing to at least the following five divisions,^ sound together whenever the hammer makes its stroke. The exact number of concomitant partials depends, partly upon the amplitude of the vibration, which depends in turn upon the intensity of the blow, partly upon choice of the point of contact of hammer on string, and partly upon the stiffness and weight of the string. "Touch." ''Touch," of course is an impor- tant element in the control of the exact shape of the wave-form. Tone-color or character, as we are aware,"* depends upon the wave-form, and 1 f^upra. Chapter IT. 2 See Cliapter II, "Resultant Motion." ' ' 3 Cf. Chapter II. Sound-Board and Strings. 157 that means upon the number and prominence of the concomitant partials. That, in turn, from the ''touch" point of view, means the hammer velocity in connection with the rebound thereof. That is to say, control over the wave-form of the string, as finally emitted through the medium of the sound-board, rests, so far as concerns the per- former, upon his manner of manipulating the ham- mer so as to vary the length of time required for it to travel from the position of rest to the string, and back ; or in other words, and more roughly, in the force and rapidity of the actual excitation of the string. Sound-Board Vibration Demonstrated. So much for hammer and string; but how about the sound-board? I have indicated that the part played by the board is not only important but decisive. This may be experimentally demon- strated. Suppose that a long thin rod of spruce wood is made up, sufficiently long to extend the length of one room and into another. Spruce is the wood from which piano sound-boards are made. Suppose that one end of this rod is doweled into one of the ribs of a piano sound- board so that it touches the rear surface of the board and thence runs into the next room, all in- 158 Modern Piano Tuning. termediate doors being stopped off so that ordi- narily no sound will come from one room to the other. If the open end of the rod be now brought into contact with the sound-board of another piano, leaving the dampers of this second instru- ment raised, the tone of the first piano when played will be reproduced note for note but in diminished volume, from the surface of the second sound- board. The same experiment may be made by using a violin as the ''receiving instrument." This experiment shows that the sound-board of the piano has independently the power of vibrat- ing in all the extraordinary complex of motions that arise, not only as the resultant wave of the complex motion of one string, but as the combined resultant — the resultant of resultants — of the mo- tions of many simultaneously excited strings. The motion of a string may be compared with the operation of several forces pulling in different directions. The resultant of these forces — that is, the direction in which the net value of all the forces when compounded, is seen to lie — can be determined mathematically. So also we know that the complex vibration of one string combines into a single complex or resultant curve.^ And so also 1 Supra, Cliapter H, Sound-Board and Strings. 159 we can see that the complex vibrations of two strings, if impressed together upon a sound-board, must combine into a further resultant; a process which can be carried on indefinitely. Thus, whilst we see on the one hand that the sound-board must be capable of complex forms of motion, we can also perceive that the mechanical realization of such forms is neither inconceivable nor even particu- larly difficult to apprehend. Analogy of the Monochord. If the suggestions I have made here have any value, they must tend to give us a reasonably clear conception of a theory which may account for the peculiar operation of the sound-board and may fix definitely its place in the economy of the piano. If, in fact, we keep steadily in mind the truth that no matter how many strings may be struck at any given moment, nor how consequently complex their motions may be, these motions always must express themselves on the sound-board as a single resultant motion, it becomes clear that such resultant motion is re- sponsible for the tone; and nothing else. In the circumstances, we may, without unduly stretching the comparison, suggest an analogy with the monochord. This, as we all know, is a single string stretched between a hitch pin and a 160 Modern Piano Tuning. tuning pin over a small sound-board, with a move- able bridge which can be shifted so as to change the vibrating length of the string whenever and however desired. Now, this string has in itself the possibility of producing all the tones which can be had by shifting the bridge. No matter how the bridge be placed and therefore no matter what segment of the string be vibrating at any time, it is the same string. The same string vibrates always, but the moving of the bridge selects the particular segment which is affected. So also with the sound-board and strings of the piano. The sound-board is a true vibrator, whose opera- tions are representable as resultant motions of the string vibrations. The strings are selecting vibrators, impressing their own individual vibra- tions upon the sound-board, either singly or in combination. When a single impression is made, the board repeats the motion exactly as trans- mitted to it. When a complex of impressions is made, this develops instantly into a resultant mo- tion, compounded of all the motions; or as we might better say, being the geometrical sum of all the motions. Sound-Board a True Vibrator. If this be a plausible hypothesis, from the mathematical view- Sound-Board and Strings. 161 point, it is just as plausible mechanically, for while it may be hard to conceive the sound-board mak- ing a thousand different kinds of motion at once, it is not hard to conceive it making a single re- sultant motion; nor is there any mechanical rea- son why it should not. For if we consider that the sound-board is a table of spruce, forcibly arched by ribbing on its back, and then so secured to the piano as to be always in a high state of tension, and if further we keep in mind that the impressibility of the board is immensely increased through its close contact with the great battery of high-tension strings communicating with it through the bridges, we can see that we have in a well-made piano sound-board nothing less than an extremely sensitive vibrator, a whole musical in- strument, ready to sing as soon as it is kindled into life by the operation of the property of resonance. The sound-board of course is a resonance instru- ment, and it is only necessary to understand just what this phenomenon means in Sound, to com- plete our apprehension of the sound-board's be- havior in use. Resonance. As I said above, the sound-board is the true tone-maker, whilst the strings are the selectors or selecting vibrators. The board is the 162 Modern Piano Timing. central telephone station, while the strings are respectively the various subscribers' entering and outgoing lines. The strings are the nerves, the W board is the brain. A dozen analogies suggest themselves. But, in any case, we cannot stop here. We must know how the board can receive the impressions which are transformed into re- sultant motions. What, in fact, is this Reso- nance 1 Resonance is the property which sonorous bod- ies possess of impressing their vibrations upon other sonorous bodies. In the case of the tone- emission apparatus of the piano, the sound-board is placed in contact with the battery of strings stretched above it, which pass over wooden bridges glued on the surface of the board, pressing upon these latter with a heavy down bearing. The strings are brought over the bridges between pins which impart to them also a side-bearing as they cross. Thus it may be seen that the sound-board is in the most favorable condition to receive any vibrations that may originate in the strings. If it can be shown that the vibrations of a string can actually be imparted to the sound-board, and can cause that apparatus to undergo a resultant vi- bratory motion compounded from these vibra- Sound-Board and Strings. 163 tions, then we shall have the theory of the sound- board demonstrated. Now, since resonance is a property possessed by all substances which may form sonorous bodies, it will be understood that we are not here discuss- ing any uncommon quality of the piano sound- board. Seeing that the physical nearest cause of sound sensations is the performance of vibra- tory motion by solid bodies, it follows that reso- nance must take place wherever that vibration can be transmitted. If then we have a body of some material thrown into vibration, it is easy to see that all other bodies of similar material in con- tact with it must also vibrate. Whether their frequency is the same as that of the original body depends upon the comparative masses and other qualities of the two. All elastic substances are capable of transmitting vibrations, themselves partaking of the vibratory motion in the process ; and so also if the two bodies in contact be of dif- ferent material, it follows that vibratory motion may be transmitted from one to the other, so long as both be elastic enough and contact be main- tained. Actual physical contact, indeed, may sometimes, under favorable conditions, be elimi- nated, and the atmosphere alone be competent to 164 Modern Piano Tuning. transmit the pulse from one body to the other, as it does from the body to the ear. This latter po- tentiality is translated into fact only when each of the bodies is very favorably situated for the purpose and extremely sensitive to vibratory im- pulse. The resonance boxes of two adjacent tun- ing forks furnish an example of these latter quali- ties. We see therefore that there is no mechanical or physical reason why the sound-board should not at least receive the vibrations of the strings. The question therefore becomes this; does the sound- board reproduce them after it has received them; and how? Composition of Impulses. We have already seen (supra) that the most satisfactory hypothesis of the sound-board's functions is that which con- siders it as a true tone-maker; but the mind does not always grasp easily the idea of the apparently stiff and unresponsive sound-board reproducing and amplifying the complex vibrations of the strings. Yet a simple illustration will show that this is quite possible. Suppose we secure somewhere a heavy ball, or a metal weight, like a ten pound scale weight, and suspend it from a cord so as to form a pendulum. Sound-Board and Strings. 165 If now the cord be gently agitated until it settles into its normal period of vibration, we can deter- mine just what its natural frequency is. Hav- ing done this, we may allow the pendulum to come to rest again, and then begin to direct against it puffs of air from the mouth, timing these so as to correspond with the vibratory motion of the pendulum. For several seconds this will have no effect, but if the work be kept up, gradually it will be observed that the weight begins to stir. Let the work go on, being careful to blow on the weight only when its direction of motion is the same as that of the breath; that is to say to blow on it only when it is moving away from one. By de- grees, if the puffs of air are timed as directed, the weight will begin to swing back and forth in its regular period and at its regular amplitude or width of motion. Thus we have an experimental demonstration of the mathematical fact that if a series of small equal forces be periodically ap- plied to a given resistance through a given elapsed time, at the end of that time the total force ap- plied has been equal to the sum of the small forces delivered in one unit of time corresponding to the period of one force. To take a concrete in- stance, if a series of taps, each one ounce in weight, 166 Modern Piano Tuning. be delivered at the rate of one per second until, say, 160 of them have been made, the resistance has been operated on with a force, at the end of 160 seconds, equal to a force of ten pounds (160 ounces), operating through one second. Thus we see also that it is quite possible for even the most delicate and minute vibratory motions not only to be imparted to a stiff sound-board but also to throw that board into resultant motion. For if we consider that the middle tones of the piano are produced by frequencies running from 200 to 800 vibrations per second we can easily see that what is possible in the extreme case here described is more than possible — ^nay, is inevitable — in the case of the specially prepared, highly elastic and ten- sioned sound-board, especially when we remember that the strings, being struck, are set in relatively violent agitation, and communicate a relatively more powerful vibratory impression than can be had by blowing with the breath, on a far more re- sponsive resistance than the weight, and at many times the possible blowing speed. Considerations like these, although they do not actually demonstrate the hypothesis of sound- board behavior here adopted, do strengthen it and tend to confirm it. Sound-Board and Strings. 167 To sum up, we may say that the sound-board and strings of the piano together constitute the tone- emission apparatus, that the sound-board is the main vibrator or tone-maker, that the strings are the selecting vibrators, and that the vibrations of the sound-board are resultant single vibrations due to composition of the complex of vibrations proceeding from the strings, just as the latter themselves are resultants of the complex of seg- mental vibrations which take place in the string when it is struck. I do not claim for this hypo- thesis that it is above criticism, but I am certain that it meets the facts more fairly than any other I have yet seen. In making this analysis I have wished to pre- pare the reader's mind for the critical examina- tion of sound-board construction, and especially to show reasons for some of the peculiar methods that characterize that construction and have been worked out by piano makers experimenting often in the dark. The problem of practical construc- tion is to provide a resonance table that will not merely take up in resultant vibration the im- pressed vibrations of the strings, but also will properly amplify these as well as reproduce their forms. In other words, it is not enough for the 168 Modern Piano Tuning. sound-board to reproduce the characteristics of the tone, but to amplify it; make it loud enough. We need quantity as well as quality. Amplification. Amplification of the wave- forms is of course a natural consequence flowing from the large mass of the sound-board and the consequent relatively great mass of adjacent air which can be put in vibration. The tones origi- nally impressed by the wave-forms of the strings are therefore intensified. Coloration of Tone hy the Sound-Board. We know that inasmuch as most piano strings are struck well above the seventh node, the seventh partial is a definite member of the partial tone pro- cession in the piano string's wave-form. The presence of this partial tone, however, is, on a thoroughly well-made piano at least, scarcely per- ceptible in its influence on the tone color, although when it is markedly present in any other tonal combination, its tendency to promote harshness is at once discerned. This partial and its mul- tiples, as well as the ninth and others above it which are not eliminated in the upper regions of the piano on account of the high striking point, would have a much more distinctly hardening ef- fect on the tone than is the case, if it were not for Sound-Board and Strings. 169 the fact that a properly made sound-board un- doubtedly modifies these and other odd-numbered partial tones, at least as to their intensity. Thus we have another function of the sound^board which must be considered, namely the tone-qualifying function. Proper Vibration of the Sound-Board. It is evident from what has already been said that the piano sound-board is a sensitive vibrating instru- ment and therefore must possess a proper period of vibration all its own. That this is so is plain from the facts of the case. The board is arched, or crowned, by means of ribs planed arch-wise and glued to the back of the board, so as to draw the front surface into tension and press the rear into compression. It is then fastened into the wooden back of the piano by being glued along its outer edges, so that it remains permanently in such a way that it is continually in a "live" condition, ready to vibrate. But it is also necessary to take into account the fact that the piano sound-board is covered by an iron plate, which bears the strain of the stretched strings. If we examine the iron plate and sound-board of a piano after stringing, we shall see that the entire structure thus formed, as well as the wooden back, is in a condition partly 170 Modern Piano Tuning. of compression and partly of tension. Hence tlie whole structure has its own regular period of vi- bration and its own proper tone. The object of sound-board design therefore must be to take advantage of the proper vibration of the board, plate and back together, and to see that the relative importance of each element is re- tained, without any one being unduly prominent. The fact is, of course, that since the sound-board is the true tone-maker, and since the iron plate and back are in such close contact with it, each of the two latter exert a constant modifying influence on the vibratory activity of the board. In short, the various materials of which the back-structure (board, plate and back) are made, all exert their individual influences, so that the ultimate vibra- tory period and composition of the wave-form proper to the sound-board arises out of all these forces compounded. Hence the question of the dimensions and design of each of these elements is almost equally important. I have made this digression because it is im- portant that the tuner should understand the rea- sons for differences in tone-quality as between various pianos. I shall not go into small detail regarding the design of these elements because Sound-Board amd Strings. 171 that is the province of a technical treatise on piano construction and has been treated else- where.^ The following remarks are appended, however, treating generally of the influence of the parts mentioned. Influence of the Iron Plate. The cast iron of the plate is of course considerably stiifer and more rigid than wood. Its weight-for-bulk is also much greater ; or, in other words, its specific grav- ity is represented by a higher index. Now it is well known that the vibratory form of any body which is enough under tension to induce suscepti- bility to vibrative influences is modified by the factors of density and rigidity. On the whole, any increase in density and rigidity tends to produce a wave form in which the higher partials are un- damped. The more '* yielding" structure of wood, as it were, has a damping effect on the less powerful partials, or rather, perhaps, is incapa- ble of so elaborate a subdivision under the in- fluence of the string vibrations. Hence the wood of the sound-board will, if left to itself, act as a damper on all the feebler partials of the strings, however many may have been left after the re- bound of the hammer. The tone quality, there- 1 Cf . "Theory and Practice of Pianoforte Building." 172 Modern Piano Tuning. fore, is founded on a partial-tone series scarcely extending above the eighth, with perhaps a trace of the multiples of the even numbered partials. Iron, however, modifies this procession by taking up the higher partial vibrations of the strings and reproducing them in amplified form. At least this is the most plausible explanation of the plate's activities, for it is certain that the more iron we have in close touch with the strings, at the ex- tremities and on the bearings thereof as well as around the sound-board area, the harder and more '* metallic" is the tone; which of course means the existence in the tonal complex of high dissonant partials. Thus it is plain that the iron plate should be so designed as not to overload the struc- ture, and especially so as not to usurp all the functions of bearing. Wooden upper-bearing bridges are often useful in a piano which otherwise would produce a harsh and metallic tone. Ex- cessive bracing or barring and undue massiveness are also bad features. In fact, we may say that the plate should be as light as possible ; the lighter the better so long as it is strong enough to stand the string strains. This of course greatly de- pends on the precise tensions at which the strings are stretched, which again depends on the dimen- Sound-Board and Strings. 173 sions of the strings. But, as we shall shortly see, scientific design tends to emancipate us from the false gods of excessive tension, hardness of wire and "bing-bing" tone.^ Influence of the back. The technical impossi- bility of producing an iron plate of the ordinary thin-sheet type, strong enough to bear the entire strain of sound-board and strings, without at the same time being too enormously heavy, has neces- sitated the use of a very massive wooden back.^ This back, of which I have already given some description, is extremely large and clumsy, and necessarily so.^ Its effect on tone can only be de- scribed as deadening; for there is no doubt that the natural vibrations of sound-board and plate are very much damped by the drag of the back. On the whole, therefore, we can only wish the ut- most success to the inventors who have been try- ing during the last twenty-five years to furnish us with practical substitutes for the wooden back ; although it should not be overlooked that the plate vibrations are not to be encouraged so much as those proper to the sound-board. The inventions of Wm. Bauer of Chicago point the way to a suc- 1 See infra, String Dimensions, et seq., in the present chapter. 2 Cf. supra, Chapter VI. 3 See the previous chapter. 174 Modern Piano Tuning. cessful solution of this problem, unless I am much mistaken. Dimensions of the sound-hoard. The sound- board is limited, of course, according to the size of the piano, and therefore no particular rules can be given for length and breadth, or even for shape. It is to be observed however that the size of the piano and the tension and other features of the scale will require parallel modifications in the size and thickness of the board ; that is in the vi- brating area. But this is a matter which, in the nature of the case, must be determined by experi- ment. The point is that the board must be free to vibrate, in the particular situation created by the other conditions of the piano. If it is too heavy it will vibrate feebly on light playing, whilst with heavy playing its vibratory form will incline to be too much in its own proper period, thus smothering the resultant vibrations selected by the strings. If it is too light it will respond in light playing too readily and so again its proper vi- bration will intrude, whilst on heavy playing it will be unable to respond strongly enough to pro- vide sufficient support to the strings. Thus the thickness must be graduated to the size. In prac- tice piano makers have found it well to vary the Sound-Board and Strings. 175 thickness of the board between the two extremi- ties. Thicknesses running from %" in the treble to Ya:" in the bass are usual. But these are ex- perimental matters and can be determined only experimentally. Ribbing. The sound-board must be ribbed in order to stiffen its surface and enable it to resist the various strains put on it. These strains are (1) the down bearing of the strings; (2) the ten- sion of the strings; (3) the opposed tension and compression of upper and under surfaces due to the crowning. The crown is necessary in order to give a proper bearing and also to resist the down- ward pressure. It is likewise useful in promoting the necessary tension for free vibration. The ribs are planed into curved surfaces where they are glued on to the board, so as to produce the crown, which also is further promoted by being glued on to slanted ''linings," as they are called, in the back struc- ture. It is customary to use from 12 to 14 ribs and these should be placed so as best to sustain the strains without being too heavy or having too much of a damping effect. No other rules can or need be given in this book.^ 1 For a general discussion of these points cf. "Theory and Practice of Pianoforte Building." 176 Modern Piano Tuning. Bridges. The position and curvature of the bridges are entirely governed by the string de- sign. No special descriptions therefore need be given here, except to remark that it has become customary to build up the bridge structure of cross banded veneers of hard wood, so as to avoid any tendency to split. The pins, which are driven into the bridge to give side-bearing to the strings, rep- resent an archaic survival from past days, in fact from the days of the harpsichord, and there is no doubt that it would be a great deal better to use an agraffe, or drilled metal stud, such as is found on the upper bearing bars of grand pianos (and in some uprights also). False beats in strings are often generated by faults in the pin- ning, whereby twists in the wire are produced. The bridges must be high enough to give a good down bearing and wide enough for a good side bearing. They should never be cut to permit the treble brace on the plate to pass through, but the plate design should be modified accord- ingly. A cut treble bridge always means a bridge that does not transmit the string vibrations prop- erly to the bridge, and invariably involves bad tone, and rapid break-down. The greatest enemy to the conservation of piano tone is the degenera- Sound-Board and Strings. 177 tion of the board under string pressure ; a process promoted by a cut bridge. Tuners may take it as true that a cut bridge means a bad piano. Bridges should not be brought too near the edges of the sound-board, lest the elasticity of the board in response to the vibrations transmitted by the strings be rendered valueless for those situated at the ends of the bridges. In tight places, if the string length is to be preserved (as always it ought to be), an extension bridge may save the day, as may be observed interestingly in the small 4 foot, 8 inch Brambach grand, at the bass end of the treble bridge. Bass bridges can usually be treated best on the extension system, as bass strings are nearly always too short anyhow. These remarks will be principally useful to the reader of this book in making clear to him the cause of piano tone-production and the reasons for differences in tone quality between pianos of ap- parently equal grade. I shall now briefly con- sider the string-scale. Functions of the String. In Chapter II I have discussed at length the physical properties of piano strings. It is now only necessary to remark that the object of the strings is to select the par- ticular wave-form which the sound-board is to 178 Modern Piano Tuning. amplify. The wave-form must first be created by the string vibration; and therefore the dimen- sions, weight and method of stringing are of the utmost importance. String Dimensions. Elsewhere I have made a tolerably complete study of string dimensions/ and here, therefore, I may be brief. The propor- tion of pitch from octave to octave is as 1:2 but since strings have weight and weight increases with length, this proportion will not hold good in designing string lengths. Piano makers, attempt- ing to compensate for the factors of weight and tension, have produced various scalings of string length ranging from the proportions 1 : 1.875 to 1 : 1.9375 for each octave. In other words, instead of doubling the string lengths at each octave, each string is made 1% or 1^%6 as long as its octave above. Intermediate lengths should be worked out, one by one, in proportion. Practice dictates almost universally a length of 2 inches for the highest treble strings. Gages. It is a very clumsy and altogether un- pardonable sin to change the gages of wire used in a scale when putting on new strings, unless it is obvious that some fatal defect in tension propor- 1 Cf . "Theory and Practice of Pianoforte Building," p. 48 et seq. Sound-Board and Strings. 179 tions exists. Evenness of tension is a desider- atum always aimed at, but not often attained; mainly through lack of inclination to calculate closely. But the tuner should very carefully fol- low the gage of wire when re-stringing, for it is usually to be taken for granted that the piano as strung represents the best gaging that could be devised, considering its scale. The wire sizes used in piano making range from gage 12 (some- times used in the highest treble), down to gage 26 for core wire on the heaviest bass strings on large pianos. In determining what string gages to use, piano makers should attempt to obtain an even pull for each string from end to end of the scale. On the whole, the average strain of 160 pounds per string, which is common to the mass of American pianos, is too high, and a general lowering of gage would be a good thing in all probability. The high tension piano has never fulfilled the promises so lavishly made for it thirty-five years ago. Heavy wire means higher tension. Tensions are already too high, which simply means hard, thin, metallic tone, superficial glitter and coldness. The modern piano already has much to answer for in this respect. Striking Point. This is another matter not al- 180 Modern Piano Tuning. ways considered with sufficient care. In a good piano the point at which its hammer touches each string is chosen scientifically, for there is no more important detail in piano design than this. I have already discussed this subject in an earlier chapter (Chapter II), but it may here be observed that the tone quality of a piano is very closely asso- ciated with the position of the hammers in relation to the strings. The tendency in modern pianos is to make the striking point excessively high. For my part I should like to see a return to the ancient fashion of low tension strings and low striking points. Of course, as we all should real- ize by now, the necessary tonal re-inforcement of the short upper strings must be brought about by raising the striking point. But this point also is treated elsewhere (Chapter II). Commercial pianos take all these things for granted with a refreshing but somewhat disastrous naivete how- ever, and it is to be hoped that readers will realize that in these details and the care that is taken over them rests the difference between good and bad piano making. Bass Strings. The use of steel, brass or cop- per winding for the purpose of overweighting strings artificially, so as to make up for necessary Sound-Board and Strings. 181 shortening of true length requirements, is as old as piano making, and older; nor has any special improvement been made in the last half century save as to closer winding and lessening of slippage. It is still far too much the fashion for piano mak- ers merely to send to the winders a pattern show- ing their string lengths, leaving the weight of the strings to chance, skill or tradition. In fact, of course, the weight of a covered bass string is just as important as the length of a treble string ; for reasons which must by now be apparent to every reader of this book. It is therefore most advisable to consider the question of weight, with its intimate relation to tension whenever consider- ing the improvement of the tone of a piano by put- ting on new bass strings.^ Copper vs Steel. On the whole I think it is fairly well established that copper winding is bet- ter than steel for bass strings ; for the reason that the greater specific gravity of copper makes a thin- ner wire available to produce a given weighting. Excessive bulk is to be avoided in bass string mak- ing. Of course, copper tarnishes and in moist 1 Consult, for complete discussion of these points, "Theory and Practice of Pianoforte Building" (p. 48 et seq.) , and to some ex- tent Chapter II of this book. 182 Modern Piano Tuning. climates gets covered with verdigris, perhaps more quickly than the tinned steel wire rusts; but I doubt whether the difference in favor of steel is enough to justify any preference, especially as, for the reasons above noted, copper is tonally better. The so-called **iron" covering wire is to-day usu- ally a soft steel wire.^ To sum matters up, it may be said that the fol- lowing points are important in any consideration of a string scale. 1. Accurate proportioning of lengths, measured string by string. 2. Careful graduation of wire thickness to as- sure equality of tension from one end of the scale to another. 3. Placement on the bridges with enough space for each string to vibrate freely. 4. Avoidance of grounding bridge extremities right on the edge of the sound-board. 5. Avoidance of too much iron on bearing bridges. 6. Accurate weighting of bass strings. In setting down these facts about the string 1 But the subject is highly controversial, as the discussions of the Chicago Conference of Piano Technicians in 1916 plainly showed. Sound-Board and Strings. 183 scale, I have purposely avoided going into com- plete details; partly because the vibrations of a piano string and the details of stringing have al- ready been treated in this book, and partly be- cause I have elsewhere, in a volume still in print, also discussed them quite thoroughly.^ From the tuner's view point all other necessary information is to be found in preceding chapters. The discussion of the sound-board has been pur- posely more complete because accurate informa- tion regarding its functions is not so readily avail- able. Practical details are discussed in the chap- ter on piano repairing {infra). 1 "Theory and Practice of Pianoforte Building," p. 28 et seq., p. 48 et seq., etc. Chapter VIII. THE ACTION AND ITS EEGULATION. The movement or ''action" which translates the motion of the finger-impelled key of the piano to the hammer, has been developed within the past fifty years to a high state of perfection. Funda- mental work was mainly done in Europe, where Erard established the principle of double repeti- tion which distinguishes the modern grand piano, and Wornum devised the tape-check which makes the upright action efficient in repetition and re- liable in attack. Although these revolutionary in- ventions date back about eighty years from the present time (1917) the enterprise of contempo- rary makers was unequal to any immediate recog- nition of their superiority, so that for a long time both grand and upright pianos were fitted with less efficient movements ; until the example of the more courageous amongst them, especially in the United States, showed quite unmistakably the im- mense superiority of double repetition and the 184 The Action and Its Regulation. 185 tape check. From tliat time onwards — that is to say during the last thirty-five years — the use of the modern grand and upright piano action has be- come universal throughout the world, while we may say that, so far as concerns the United States and Canada, there is almost complete standardiza- tion of the two types. Our descriptions therefore may be considered as being of general applica- tion. Technical Knowledge of Action principles. The experience of fifteen years' constant contact with piano tuners convinces me that a thorough ac- quaintance with the scientific and mechanical fea- tures of the piano action is uncommon amongst them, save in a most elementary sense. I am proposing therefore to carry out, in the present chapter, a careful mechanical analysis of piano action, followed by an equally careful description of its modern forms and a general explanation of the methods of regulating these. The discussion will, I hope, be not only professionally useful, but the reverse of tedious. Functions of the Action. The functions of the piano action may be described as follows: (1) to convey to the hammer a motion which shall carry it toward the string for the purpose of inflicting a 186 Modern Piano Tuning. blow thereon, (2) to trip the hammer immediately before its actual contact with the string, so that it instantly rebounds without blocking the vibration, (3) to permit the repetition of the hammer blow without complete release of the key and (4) to damp the string vibration immediately the key is released. These functions are of course identical for all forms of piano action, whether horizontal or vertical. It is obvious from what has been said, therefore, that the piano action may conveniently be con- sidered as divided into the following main ele- ments (1) the hammer, (2) the escapement, (3) the key and (4) the damper. From the beginning all piano actions have possessed the 1st, 3rd and 4th of these, and in almost all cases a more or less satisfactory mechanical solution of the 2d has been carried out. The method of arranging these ele- ments now to be described was first successfully worked out by Erard in 1821 for the horizontal, and by Wornum in 1826 for the vertical, piano. Let us now consider how these various elements are co-ordinated. I shall begin with the grand piano. The Grand Action. Erard 's principle is to-day universal in grand piano making, but the particu- The Action and Its Regulation. 187 lar form in which it is generally carried out to- day was developed by Herz from Erard.^ The il- lustration given herewith (No. 19), shows a modem grand piano action manufactured by Messrs. Wessell, Nickel & Gross of New York. The parts, arrangement of parts and method of regulation are quite typical of the very best Amer- ican practice. The terminology may be considered as correct and as following the practice of the best American action makers. Operation of Grand Action. The student should now follow the argument by means of a working model, or by the simple process of re- moving the action from a grand piano and study- ing its motions. Pressing slowly the key of the action we observe that the rise of the rear end thereof affects the capstan (7) which lifts the wip- pen (11) through contact with the wipp en knuckle (8). On this wippen are pivoted the repetition lever (19) and the jack (sometimes called '*fly") (13). By lifting the hammer shank (27) up and away from its cushion (24) it will be seen that the 1 Cf. "Theory and Practice of Pianoforte Building," p. 96 et seq., Encyclopedia Britannica article "Pianoforte," 9th, 10th and 11th editions, and "History of the American Pianoforte," by D. Spillane. Figure 19. 188 The Action and Its Regulation. 189 1. Digital or Key. 20. 2. Key Frame. 21. 3. Key Leads. 22. 4. Front Rail Pin and Punch- ing. 23. 5. Balance Rail Pin and 24. Punching. 25. 6. Back Rail Cloth or Felt. 26, 7. Capstan Screw. 27. 8. Knuckle of Wippen. 28. 9. Bottom Rail of Action. 29. 10. Supporting Flange of Wip- pen. 30. 11. Wippen. 31, 12. Knuckle of Jack or Fly. 32, 13. Jack or Fly. 33, 14. Regulating-Screw Rail. 34, f Jack-regulating Button 35 15.^ and Screw #1 regulat- t ing escapement. 36. ( Jack-regulating Button 37. 16.- 1 and Screw #2, regulat- 38. ( ing oscillation of Jack. 39, 17. Spoon (Jack Stop). 40, 18. Repetition Lever Support. 41 19. Repetition Lever. Repetition Lever Spring, Spring for Jack or Fly. Repetition Lever Regulat- ing Button. Repetition Lever Stop. Hammer Cushion. Top Action Rail. Hammer Flange. Hammer-Shank or Stem. Knuckle of Hammer. {Repetition Lever Regulating Screw. Hammer-head molding. Under-felt of Hammer. Top- Felt of Hammer. Back check wire. Back check head. Damper Lever. {Damper Lever Flange and Spring. Damper Lever Leads. Damper Block. Damper Wire. Damper Head. Damper Felt. 190 Modern Piano Tuning. top of 13 works in a groove in 19. Moreover, tlie upper surface of 19 bears against the hammer knuckle (28) the weight of which and of the ham- mer, depresses 19 until 13 also is in contact with 28. When, however, the key is depressed it will be noted that the lifting is first done by 19 and that 13 comes in to play only after 19 has begun to lift the haimner. As the key is further depressed 13 lifts on the hammer and pushes it up to the string until tripped by its knuckle (12) coming in contact with the regulating button (15). The momentum of the hammer carries it up the rest of the way to the string, whence it immediately re- bounds and is caught by the back check (33 and 34) which holds it until the key is released, when the hammer is again supported by 19, which holds the hammer up while 13 slips back under 28. The function of 19 then is seen to be that of assisting repetition, for by using it, the hammer may be again and again operated through the jack (13) without the finger entirely quitting the key. As may be seen by practical test on the action, so long as 19 holds up the hammer by means of the expansive strength of 20, just enough to enable 13 to slip back into place (which last operation is performed very quickly through the agency of 21), The Action and Its Regulation. 191 the stroke may be repeated; and therefore it is plain that the key need only be lifted enough to afford the finger a secure stroke. Eeally, then, 19 is the repetition lever in fact as well as in name and through its agency the escapement which otherwise would have to be affected by quitting the key and giving it time to rise entirely, is effectually performed. Comparison ivith Square Action. The old square piano, still to be found once in awhile, pre- sents in its action an interesting comparison with the above. Here will be seen the difference be- tween single and double repetition. In the square action, the repetition lever is omitted and the jack can only find its way under the hammer butt safely, when the key is allowed to rise almost to its full height in front. Thus the finger action must be higher and the execution of rapid passages be- comes difficult if not impossible. The Back Check. There is, however, one other extremely important element which so far has only incidentally been mentioned. This element is com- mon to all types of piano action, grand, square and upright alike, and is found in even the earliest successful pianos. I refer to the back check (33 and 34). The object of this is to catch and hold 192 Modern Piano Tuning. the hammer firmly on its rebound, thus assisting the recovery of 19 and 13. Even in pianos like the square, or older makes of grand, one always finds the back-check, whether the double-repetition device be present or not. Indeed, the inventor of the pianoforte action, Cristofori, to whom belongs premier honors as father of piano making, cer- tainly mastered the necessity for the back-check in the course of his experiments, for he devised them, in almost modern shape, and built them into his last pianos. This may be seen by examining the Cristofori piano now standing in the Metropolitan Museum of Art, New York, the date of which is 1720. The back-check, then, is as old as the piano. This fact alone shows its essential value, for not otherwise would the necessity for something like it have been so quickly discerned. Cristofori, of course, was an uncommon genius, for in his last actions (1726 and later) he had also an under- lever, not unlike the repetition-lever of the modern grand piano, and very much like the under-lever of the '*01d English Square Action" so-called; the object whereof is to steady the hammer and impart elasticity to the blow. It will be observed that the back-check comes into action when the hammer, rebounding from the The Action and Its Regulation. 193 strings, is descending towards a position of rest. The spring of the repetition lever would naturally throw the hammer back towards the strings again, and thus keep it dancing up and down instead of bringing it sharply to rest. Of course, the back check is to be carefully adjusted so as to catch the hammer at just the right point in its arc of travel. Thus the back check performs two func- tions, (1) it catches and holds the hammer on its rebound, where the repetition lever alone could not hold it and (2) it allows the repetition lever to lift the hammer again the moment the key is re- leased. In other words, since the back check works from the key direct, it follows that the least raising of the back end of the key releases the check from the hammer, whereupon the repeti- tion lever does the rest, as described above ; but the check is necessary to prepare the hammer for the action of the lever. The operating or sound producing part of the grand piano action may be described by saying that the key moves the repeti- tion lever, the lever moves the hammer and then lets the jack move it further, the jack moves the hammer to the string and then trips it, the check catches the hammer on rebound, and the lever lifts it the moment the key is released; whereupon the 194 Modern Piano Tuning, cycle of motions may once more be set in mo- tion, to be repeated as often as the key rises at the back enough to ease the back check from the hammer head. Turning Points. Thus the grand action ap- pears, in its sound producing parts, as comprising six centers and six radii, describing six arcs of turning. All piano actions may be similarly con- sidered. The Damper Action. The function of the damper (40) is to rest on the strings when the key is not in use and so prevent any vibration of the string, especially to prevent any sympathetic vi- bration which might be produced by the vibration of another string having partials in common. As will at once be observed, however, the damper is so positioned that when the key is in motion, and has descended about one-third of its total dip, the damper lever (35) begins to lift and with it also the damper head, so that by the time the hammer is about to make its stroke, the damper is well clear of the string. Upon the return of the key to its position of rest, the damper is allowed to fall back on the string, being pressed down thereupon by means of the spring in the damper lever. Some European actions are to be found with The Action and Its Regulation. 195 dampers which normally press up against the un- der side of the strings by means of springs and are drawn down when the key is pressed. Such are the Erard, which retains the original action in- vented by Sebastian Erard in 1821, and the Broad- wood of London, the latter being the oldest of existing makes. Damper pedal. The damper action can be en- tirely raised from the strings, independent of the operation of the piano action, by means of the damper rod (not shown in illustration), which runs underneath the line of damper levers and is con- trolled by the right hand pedal of the piano through suitable trapwork usually placed under the key-bed. General Construction Practice. The piano ac- tion in all forms is a wooden machine. Numer- ous attempts to devise a satisfactory action of metal have so far been uniformly failures, largely because the peculiar requirements of lightness, independence of lubricants and low frictional re- sistance seem to present insuperable difficulties. Although, therefore, the stickiness, dampness and liability to warping which naturally characterise wooden machinery of any sort render the piano action somewhat unreliable and distinctly trouble- 196 Modern Piano Tuning. some at times, it is not likely tliat much change will be made in the future, unless indeed some entirely new principle is discovered. On the whole, how- ever, the wooden piano action, especially in its grand piano form, is a wonderfully efficient piece of machinery. Being in effect a series of centers, with radii therefrom moving through arcs of circles, the piano action requires numerous pivotal points. These are now universally provided by means of flanges carrying brass center-pins, working in bushed holes, on which the levers turn. These flanges have been always of wood hitherto but for the last fifteen years there has been a con- stant and steady drift towards brass or other metal forms ; and there is no doubt that the piano of the future will use such centers altogether; if only because they are more rigid, less likely to loosen at the bushings and more easily ad- justed. The woods used in the piano action have been briefly mentioned already ^ and here it may prin- cipally be said that the practice of the best makers has not noticeably varied in a good many years. Hard woods such as maple, beech, and sometimes iCf. Chapter VT. The Action and Its Regulation. 197 oak, are used where strength and rigidity are the requirements, as for instance in hammer butts, hammer shanks and supporting rails. Key frames are usually white pine and keys them- selves the same wood, particularly chosen for straight grain. The key frame and keyboard are to-day as they were a century and more ago, at least as to essen- tials. No particular progress has been made, ex- cept that we have better felt, larger pins for front and balance rails and accurately machined mor- tises and holes. But otherwise there is nothing of importance to record. The felts used in piano actions are especially manufactured for the purpose, the principal varie- ties being the very fine close-textured red-cloth used for bushing and the spongy green and white material used for punchings. Card-board and paper punchings are also used, for fine work under the keys, as described later. The brass center-pin is universal and attempts to substitute other material for it have not suc- ceeded, although recent experiments throw much doubt upon the question of comparative durabil- ity as between brass and steel wire. What is true of pins in this respect is even more true of 198 Modern Piano Tuning. the springs, which are always made of brass, but which, in grand pianos especially, seem to collapse and lose their ''life" very soon under modern conditions. It would probably be a good thing if experiments looking to the substitution of steel springs were made ; but the trade is conservative here, as everywhere. Capstan screws are also of brass always, but the remaining hardware is either cast-iron (action frames, screws, etc.), or steel (damper rods, etc.). Detail Variations. Older grand pianos are of- ten found (if made prior to about 1890) to have wooden rockers with short extension rods of wood, in place of the capstan screw. The method is not admirable, mainly because it renders the action less accessible. Wooden action frames were also common in the old days, and wooden action rails are still almost universally used, although modern makers are beginning to see the advantage of at least support- ing these rails by metal bars. The construction of the repetition lever and of the wippen in general is subject to considerable variation of practice. Some makers (Steinway, Schwander) use a single spring, with double or single bearing. Sometimes the travel of the jack The Action and Its Regulation. 199 is limited by a metal spoon as shown in Figure 19 (Wessell, Nickel & Gross), and sometimes by a wooden post (Schwander), whilst in some actions (Steinway), no adjustable means are considered necessary. The greater number of modern grand piano actions are provided with tensioning screws whereby the strength of the wippen springs may be adjusted more surely than would be possible by any method of bending. But older actions are usually without this adjustment. Steinway grand pianos are distinguished by the use of an octagon head screw in place of a capstan screw, which necessitates the use of a special wrench for turning them. The same makers use metal sheathing for their action rails, which are of special design. The cushion on the wippen, above which the hammer is normally held, has given way in some grand actions to a fixed, independently supported hammer-rail on which the shanks rest as they do in an upright. Some of the Schwander actions are of this type. Strauch Brothers, also, have made some grand actions like this. Soft Pedal. These last, however, are made spe- cially for the purpose of substituting a lift of the hammer-line by the soft pedal for the usual shift 200 Modern Piano Tuning. of the key-board. The Isotonic soft pedal action by Kranich & Bach is of similar type. Sostenuto Pedal, On most modem grand pianos, each damper-lever is provided with a tongue of felt projecting from it. In front of the line of tongues is a brass flanged rail which can be rotated by depressing the middle pedal (pro- vided for that purpose). After a key or keys have been struck and their dampers raised, the pedal may be depressed before releasing the keys, and the flanged rail thus turns, catching the felt tongues and holding up the dampers. The keys may then be quitted. This device is useful in get- ting tone-color and adds to the tonal resources of the piano most markedly.* Regulation of the Grand Action. The processes which together constitute the adjustment or ' ' reg- ulation" of the grand piano action are not com- plicated when studied systematically and in order. To describe them is by no means difficult ; and in- deed the only difficulty is to get enough prac- tice to be able readily and rapidly to perform the various processes. In order to simplify as much 1 Many other small detail variations may be found amongst the work of individual makers, but for general remarks along these lines see Chapter X. The Action and Its Regulation. 201 as possible what follows, I shall simply detail in order the various steps taken in regulating the action of the grand piano, so that the reader may be able to see what is done and why. A first necessity, however, is some consideration of the question of action ** touch" considered from the viewpoint of the pianist. "Touch." It is important that the pianist should have a piano with an even feel to the keys, uniform depth of touch and uniform resistance so far as is possible. The practice of makers in this respect has greatly varied since the birth of the piano, but curiously enough the most modem ideas in regard to depth and resistance are again vir- tually the same as those of one hundred years ago, having descended from the excessive heights at- tained in the middle nineteenth century, when piano makers vainly attempted to make pianos large, heavy and loud enough to suit the piano- thumping school of musicians, now happily out of fashion. Depth of Touch. The pianist considers depth of touch from the standpoint of convenience. He wants the touch to be deep enough to give him a good **feel," and shallow enough to permit of rapid passage-work. General practice now ac- 202 Modern Piano Tuning. cords the key a touch-depth (dip of the front end) of % inch. The bass end may be a little deeper, but on the whole this is not essential. Touch-depth, however, the piano maker must consider in connection with rise of the rear lever of the key. Moreover, it naturally follows that as the front dip is to the rear rise, so is the length of the front lever (front-rail pin to balance-pin) to the length of the rear lever (balance-pin to cap- stan). If therefore the requirements of any ac- tion are such that special height of rise is re- quired, the position of the balance-pin must be shifted accordingly. Usually, however, a rise of Yi inch for the back is found sufficient. Taking this as a basis, the following simple calculation gives the other proportion : Depth of front dip %'\ Height of back rise 14". Front Lever : Back Lever : : Front dip : Back Else. But, % : 1/4 : : 3: : 2. .'.Front Lever : Back Lever : : 3 : 2. If, however, the proportions between dip and rise are altered, so also the length proportions be- tween front and back lever are affected. Length of Keys. In grand pianos of normal The Action and Its Regulation. 203 size the key lengths have finally been settled at about 15% inches from front rail pin to capstan. Short grands sometimes have to carry a smaller key, and in this case, to preserve the true front dip the proportionate lengths must still be as above, for if any change is made on the mistaken idea that some fixed length instead of a fixed pro- portion is to be followed, the entire key propor- tions will fall to the ground and the touch will un- doubtedly be bad. By retaining the proper pro- portions as indicated above the short key will be effectual enough, although it must be remembered that the shorter the key the less the leverage for an equal touch depth. Resistance. The practice of the best makers has finally settled the resistance or touch-weight at 2^ ounces approximately. Some variation between the extreme bass and treble ends is permissible and desirable. In fact it would be well to consider a resistance in the extreme bass of 2% ounces, graduated to 2% ounces in the middle and to 2^ ounces in the extreme treble. Changes in resist- ance may be made by drilling the body-wood of the keys and putting in small round pieces of lead where required. The piano maker should always carefully ascertain the weight required to depress 204 Modern Piano Tuning. each key when the action is in contact with it and having done this adjust accordingly by putting lead in the back of the keys to increase the resist- ance, or in front to lessen it. Order of Regulating. Following the general factory practice we may consider the regulation of the grand piano action in the following order -} 1. Key frame, and keys. Key-shift and soft pedal. 2. Action. 3. Dampers, damper pedal and sostenuto pedal. Keys and Key Frame. 1. Keys are removed from frame, which then is fitted with felt punch- ings for front and balance rails and strip of cloth for back-rail. 2. Keys are replaced and eased off, by being tested for clearance on front and balance rails. Each key should fall back when lifted, naturally and readily, but not loosely. Key-pliers are used for squeezing the bushings wider when needed. If keys are too loose, bushings may be squeezed to- gether by punching with a wooden punch. 3. Key-frame is then placed under action {same 1 For the sake of clearness, it will be necessary to include certain processes actually classified as part of the preliminary Action-finishing. The Action and Its Regulation. 205 having been previously adjusted in finishing room when capstans were placed in each key) and gen- eral level of key-frame in relation to action is noted. 4. Action being removed again, a piece of lead is placed at rear of each key, having same weight as resistance of action. This holds keys up in front and down in rear. Keys are then carefully straightened by knocking over balance-rail pins slightly when needed, then spaced by bending front rail pin where needed, and lastly leveled. This latter operation is performed by putting under extreme treble and bass keys, over front-rail pin, wooden block measured exactly equal to calculated depth of dip. Straight edge is then put over keys on line immediately above blocks and general level of keys adjusted up to the extremes. If too high, key frame may be planed off where balance rail is screwed in, or if too low, balance rail may be ''built up" by putting strips of cardboard be- tween balance rail and bottom of key-frame in same places. 4. Key frame is then replaced in piano with keys taken out where soft-pedal shifting lever touches frame. This lever is closely adjusted so that the key frame moves as soon as pressure is 206 Modern Piano Tuning. put on pedal. Points of contact are black-leaded with powdered black-lead and burnished with heated steel bar. Spring which retracts key frame is also tested and adjusted if necessary. Action. 5. Action being replaced on keys, ham- mers are adjusted so that length of stroke is not more than 2 inches from end to end. (This is the action-finisher's work originally and regulator merely looks it over). Each hammer must then be adjusted to rest over its cushion about %2 inch. Capstans are adjusted accordingly and care taken to see that the hammers are level. 6. Jacks are then adjusted so that hammer trips up at about %2 inch from the string {here prac- tice varies but close regulation is desirable). This is done by turning regulating button of jack. 7. Jack is regulated by turning button and screw on repetition lever so that jack normally rests in middle of groove in repetition lever. Usually a line on groove is marked to show right place. 8. Back-checks are regulated so that (1) they stand even and straight in line, (2) catch the ham- mers firmly without any slippage even on hard blows and (3) catch hammers when same have descended on rebound about Ys inch from the The Action and Its Regulation. 207 strings. Use only proper bending iron or bend- ing pliers for this work. 9. Eepetition Lever is regulated; (1) spring is made strong enough to cause the hammer to dance a little and lift slightly when back-check is re- leased. Most modern actions have screw tension adjustment, but otherwise tension may be changed by bending wires with hook; (2) rear of lever is set low enough to permit plenty of space between it and its travel-limiting hook, so that the jack may rest about Vm" below the level of the grooved end. This is usually done by means of regu- lating button (Figure 19) ; (3) height of rise of repetition lever under hammer-knuckle is regu- lated by Repetition Lever Regulating Screw (No. 29 same illustration), so that rise of Lever is stopped when hammer is still about %2 inch from the string, or (which is nearly the same in practice), a little before the jacks trip off; just enough before to give the jacks about Vs inch lift by themselves before tripping. After-Touch. 10. Action and keys being in piano, keys are tested for evenness of dip. This is best done by means of wooden block of proper depth whereby each key may be tested from ex- treme bass up, by placing block on top of key and 208 Modern Piano Tuning. then depressing. If block sticks up too high take out punchings underneath front ; if block sinks be- low level of key-top put more punchings under- neath. Paper punchings are used for this work. 11. Testing for after-touch is then done. After- touch is the slight lifting of hammers which should take place when keys are gently released. If properly regulated, the release of the key imme- diately releases back-check and repetition lever lifts hammer slightly. To make after-touch right, put enough punchings under each key to make sure that hammers will not release from back checks except under very hard stroke; and then take out from this about 3^2 inch punching depth. This will leave the necessary after-touch.^ Dampers and pedal work. 12. Dampers must lie square on strings and their wires work freely in bushings. 13. Each damper lever must be regulated so that the line of dampers, when lifted by the sustaining pedal, lifts all together evenly and looking like one piece. 14. Damper wires must be regulated so that lift 1 It is often necessary and always better, to regulate the black keys separately and with the white keys removed. The Action and Its Regulation. 209 of dampers does not exceed /4 inch in bass and a little less in treble. 15. Damper lever line is to rest above rear of keys at such a distance that key has performed about Vs of its dip before dampers lift. 16. Damper lift rail or rod operated by sustain- ing pedal is to rest closely in contact with damper levers. 17. Sustaining pedal trap-work is to be regu- lated to eliminate nearly all lost motion, leaving just a suspicion for the greater ease of the foot work. 18. Sostenuto pedal-work is to be regulated so that felt tongues on damper-levers are level and are free of flanged rail until same is turned, when they are caught by same if keys belonging to them have been depressed and held down. This is an outline — not entirely perfect, for this would not be possible in a book — of the process of regulating grand actions. I now pass to consid- eration of the action of the upright piano. The Upright Action. Familiar to most of us as the upright piano undoubtedly is, one can only wonder that the stock of public information about its action is so generally inadequate. It has been my experience to find that even tuners are by no 210 Modern Piano Tuning. means guiltless of ignorance in this respect, and that the real meaning and inner refinement of the upright action are almost as much a closed book to many of them as anything else one could men- tion. Crude and rule-of -thumb methods of regu- lating and repairing, handed down by tradition and practiced by men themselves unable to ap- preciate the piano from the performer's stand- point, are not calculated to improve either the durability of the piano or the reputation of the tuning profession. It is therefore without any further apology that I devote space to an analysis of the upright movement as painstaking as that which we have just finished. Figure 20 shows the modern upright action, to which is appended a complete terminology as fol- lows. The illustration is of an action by Wessell, Nickel & Gross of New York. Distinctive Features of Upright Action. The upright piano action is in two parts, separated from each other and only in mechanical contact; namely the keyboard and the action proper. These two can therefore be handled separately in a convenient manner. The hammer does not fall back by gravity, and The Action and Its Regulation. 211 so must be assisted by the provision of an en- tirely new element, the bridal-tape (No. 20), as well as by the hammer spring (No. 36). The hammer-line rests against a hammer-rail and the soft-pedal operates by swinging this rail to bring the hammers nearer to the strings. This creates lost motion between capstan and abstract, which in some actions is taken up by special devices. There is no special repetition lever. Operation of Upright Action. The key being depressed at its front end, the rear end rises, lift- ing the abstract (8) and the wippen (13). The rise of the wippen lifts the jack (17) which swings the hammer butt (25) carrying the hammer, until tripped at its knuckle by the button (22). Trip- ping of the jack throws it out of contact with the hammer, which moves forward to the string by its own momentum, and rebounds, assisted by the spring, till it is caught and held by the back check (19) working against the back-stop (24). When the key is released, the hammer is pulled back by the tape, which also assists in the retraction of the jack. This latter important part of the process is further assisted by the peculiar shape of the leather-covered hammer-knuckle against which the Figure 20. 212 The Action and Its Regulation. 213 1. Key. 22. Regulating button and 2. Key frame. screw. 3. Key lead. 23. Jack stop rail. 4. Front rail pin and punch- 24. Back stop. ing. 25. Hammer butt. 5. Balance rail pin and 26. Hammer shank. punching. 27. Hammer molding. 6. Back rail cloth. 28. Hammer top-felt. 7. Capstan screw. 29. Hammer under-felt. 8. Abstract. 30. Wippen flange. 9. Abstract lever. 31. Spoon. 10. Abstract lever flange. 32. Middle action-rail. 11. Lower action rail. 33. Damper lifting rod. 12. Action bracket. 34. Damper lever. 13. Wippen. 35. Hammer and damper 14. Jack flange. flange. 15. Jack spring. 36. Spring rail spring. 16. Jack loxuckle. 37. Spring rail. 17. Jack. 38. Damper wire. 18. Bridle wire. 39. Damper block. 19. Back check. 40. Damper head. 20. Bridle tape. 41. Damper felt. 21. Regulating rail. 42. Action bolt. r^^ '» lc= ^1 - ^ „.| """^ r " 1 J 2 214 Modern Piano Tuning. jack bears. When the key has already risen enough to bring the parts here described into play and start them on their arcs of turning, the spoon (31) presses against the damper lever (34) and the damper is pushed away from the spring. When the key is released, the damper is retracted with it till it against presses against, and damps, the string. The action of the upright is somewhat simpler than that of the grand and the absence of a repetition lever is felt in the higher finger ac- tion and less delicate repetition. Nevertheless, if properly regulated, this action is efficient and rapid. Comparison of the Upright with the Grand Ac- tion. The characteristic feature of the upright action is the bridle tape. The value of this tape lies mainly in the slight extra pull it manages to impart to the hampaer butt when the hammer re- bounds from the string, and after the back check has caught the hammer and been released by the release of the key. The tape would not have any special value but for the fact that the hammer, having been caught by the back check, naturally would hang a little on the release thereof, if it did not receive the gentle pull caused by the fall of the The Action and Its Regulation. 215 wippen with which the bridle tape connects it. The tape is, in fact, to the upright action what the repetition lever is to the grand. Until these two features had been devised and applied to their corresponding actions, the piano was an extremely imperfect instrument. The modern upright piano owes its present touch effect to the tape just as the touch delicacy of the grand is due to the repeti- tion lever. Of course the grand action is the more delicate and responsive of the two, for it possesses the double repetition. This the upright cannot have, not to mention the fact that the fall of the hammer through gravity is of course far more effective than its retraction by springs. The up- right action blocks more easily than does the grand, and finger movement must be higher to secure repetition. Detail Variations. The metal flange is coming into its own even more rapidly on the upright ac- tion than on the grand. The first step in this di- rection was taken some years ago when Wessell, Nickel & Gross brought out the continuous brass plate with flanges, carrying each section of ham- mers on one plate. This did not prove to be the required solution, but the individual brass flange has since come forward and appears to be per- 216 Modern Piano Tuning. fectly satisfactory. Certainly it does make the action more rigid and durable. Metal rails or metal reinforcements to wooden rails are also coming into use and these are like- wise an admirable improvement. Some actions (Schwander) are provided with an extra spring in the jack, called a repetition spring. The same makers have eliminated the ordinary spring rail and in place of it have a separate sup- port for each spring in the back of the hammer butt, fastened to a loop cord secured in the flange. Lost motion attachments are common. These consist of a mechanical movement whereby the rise of the hammer-rail, on the depression of the soft pedal, causes a proportionate lengthening of the abstract, to fill up the gap which would other- wise be left between capstan and abstract. Many attempts have been made at various times to eliminate the tape and provide for reliable repetition by other methods. The ideas of Con- over Brothers, of Luigi Battallia and of many others might be mentioned, but modern practice in this respect chiefly centers about the ''Master- touch" action of Staib-Abendschein and the Am- mon *'non-blockable" action of Christman. One principal objection to the tape is its liability to The Action and Its Regulation. 217 destruction by mice or other domestic pests. Other upright actions often have props fixed in the keys instead of the more modern abstract. These are adjusted by turning the wooden button up or down on its wire. Pedal Actions. The soft pedal of the upright piano merely swings the hammer rail in an arc so as to bring the hammers nearer the strings. The damper pedal operates through a damper- lifting rod (33) whereby the bottoms of the damper levers are thrown forward, tilting back the dampers from the strings. A third pedal is usually found. Sometimes this operates to draw down a rail from which depends a strip of thick felt, so as to interpose the felt between hammers and strings and muffle the tone. This is called a ''muffler" pedal. Another form is an auxiliary damper action operating on the bass dampers only, while another kind still is an adaptation to the upright of the grand sostenuto pedal. A fourth and last is a mere duplicate of the soft pedal. Unhappily the majority of com- mercial upright pianos have no more to show for their middle pedal than this blank. Materials. All that has been said on this sub- ject in the sections relating to grand actions is ap- 218 Modern Piano Tuning. plicable to the upright, and I shall therefore con- tent myself with referring the reader to them, suggesting also that he study the various repre- sentative actions he meets with, for the purpose of discovering at first hand the practical facts of ma- te-rial and constructional usage as displayed by manufacturers. In this case, as in all others, prac- tical first hand knowledge is priceless. Regulation of Upright Action. Certain parts of the work of regulation are identical in method with what we have already learned concerning the similar processes in the grand action, but the dif- ferences in design between the two bring about such differences in parts and functions of parts that a separate description is necessary every- where save in one or two instances ; as will now be seen. 1. Keys. The preliminary work of felting, eas- ing, leveling and spacing keys is done just as be- fore described in the sections on the grand action. This work, in the present case, may be done with- out removing the action from the keys, so that it is unnecessary to put lead pieces at the backs of the keys to hold them up. 2. Hammer-hlow. This is regulated to be about l%o inches. Regulation is made by putting felt The Action and Its Regulation. 219 cushion between hammer-rail and action brackets. 3. Lost Motion. Lost motion between capstans and abstracts is taken up. Correct adjustment is indicated when the hammers lie freely on the ham- mer rail, neither forced above it nor with a gap in the action below them. As long as the back-checks move without moving hammers, there is lost mo- tion; but it is advisable to leave a little, a very little, play, so that the jack is not hard up against the hammer knuckle. 4. Back-checks. Back-checks are straightened by means of the back-check bender or a pair of bending pliers, so that each check lies squarely in front of its corresponding stop. 5. Back-checks are lined up so that each check catches back-stop when hammer has descended about one-third of its total drop on rebound. 6. Let-Off. Jacks are adjusted for the trip of the hammers, which is done by turning regulating screws, using a regulating screw driver. Ham- mers should trip at a distance of from ^ inch (bass end) to Vs inch (treble end) from the strings. 7. Bridle-Tapes. Bridle-Tapes are adjusted to lift wippens evenly and all together. This is tested by hammer rail up and down, so that bridle 220 Modern Piano Tuning. tapes lift and drop accordingly. Adjustment is made on bridle-wires. 8. Bridle-wires are adjusted so that they do not knock against back-check wires and lie straight and square. 9. Dampers. Dampers are adjusted so that they lie square against strings. 10. Rise of dampers is adjusted by moving damper-rod back and forth, so that it may be seen whether all dampers begin to move together. Ad- justment is made by bending spoons. Dampers should lift not more than about M inch from the strings and their movement should begin when key is about one-third of the way down. 11. Sustaining Pedal. The sustaining pedal ac- tion is adjusted to lift the damper-rod promptly. Adjustment is made on the trap-work at the bot- tom of the piano or between top of pedal rod and damper rod. 12. Soft Pedal. Adjustment is made at ham- mer-rail. 13. Middle Pedal. See supra in reference to grand actions. 14. Touch. All instructions regarding laying of touch in the grand action apply here to the up- right. The Action and Its Regulation. 221 The foregoing descriptions are sufficient for the purposes of this book. It has been my intention mainly to give the reader a good working knowl- edge of the grand and upright piano actions in the light of their functions. Purposely I have given most space to the grand because that one is least understood; whilst everything said about its prin- ciples can at once be applied to the upright. The upright action is a series of turning points, just as is the other. The upright has almost the same parts and the same adjustment. But uprights are more familiar and hence better understood. Regulating Tools. It is impossible to do any good work in piano action regulation without ap- propriate tools. The most important of these, with which the student should not fail to provide himself, are : ^ Long and short narrow-blade screw drivers Very fine screw driver, for grand actions Regulating screw driver Key pliers Bending pliers Small regulating screw driver for grand actions Key spacer Damper bending iron Spring adjusting hook 222 Modern Piano Tuning. Spoon bending iron Parallel pliers Capstan screw iron Hexagonal wrench for Steinway actions. Professional regulators, who operate in piano factories, use, of course, a much wider selection of tools, often including many devised by their own ingenuity. But the traveling tuner cannot expect to carry an arsenal of tools with him, nor indeed to burden himself with one single not actually in- dispensable piece. Yet the selection suggested above while it may at first seem formidable in quantity, really represents an irreducible mini- mum, below which the judicious worker cannot and will not, go. Chapter IX. THE HAMMER AND ITS RELATION TO TONE. The hammer is the ''characteristic" of the piano ; its sign and symbol. It was exactly the in- vention of the hammer, and of a movement to con- nect it with the key, that made the harpsichord into the pianoforte. The object of the labors which led Cristofori to his epochal application of a principle until then regarded as practically un- realizable, was tonal gradation. He sought a keyed stringed instrument of music susceptible to dynamic control through variations in the stroke of the fingers upon its digitals. He was looking for something better than the harpsichord could give him; something better than the light thin tinkle which represents the ultimate achievement of any harpsichord, no matter how beautifully made. No increase in the vigor with which the harpsi- chord key is depressed will do m'ore than gently pluck the string. Thin, rippling, tinkly, the tone of the harpsichord and of its kindred claviers could not always suffice for the full satisfaction 223 224 ' Modern Piano Tuning. of musical art. True, the harpsichord persisted for nearly a hundred years after Cristofori be- gan his work in the little shop among the outbuild- ings of the Medici Palace at Florence ; but on the day he produced his martello ^ and the crude move- ment which connected it with the key, not only was the piano born, but the harpsichord was doomed. Henceforward, percussion instead of plectral vibration was to be the characteristic of keyed stringed instruments. The two hundred years that have elapsed have brought no change in principle, although they have seen much improvement in detail. The piano hammer remains precisely what it was. Changes in the materials of which it is made and improve- ments in the mianner of its manufacture have been produced as part of a gradual general refine- ment of our conceptions of the piano and of its true place. These conceptions have brought about improvements in manufacture, which have been accompanied by parallel improvements in the machinery of manufacture. But the principle re- mains to-day as it was two hundred years ago. Function of the Hammer. Fundamentally, the piano hammer consists of a rounded cushion of 1 i.e., hammer. The Hammer and Its Relation to Tone. 225 some flexible resilient material mounted on a wooden molding and provided with a right angle stem, the other end of which is connected with the piano action. The object of the hammer is to ex- cite the strings into vibrations. We know that string excitation may be carried out in many dif- ferent ways. When percussion is the method, two elements immediately present themselves for con- sideration. The string may be struck with greater or less vigor, whilst also the manner in which the blow is delivered, as regards place on the string, nature of the material, and so on, may be varied so as to produce variations in the color of the tone. In short, the hammer not only may control the comparative strength of the emitted tone but also to a large extent its color. Now we have already discussed at considerable length the influence on tonal character involved in choice of the point of contact of the hammer with the string. The reader will now wish to consider questions as to the material of the hammer, and the methods of treating this material so as to produce in each individual case the best tone. It will be advisable to consider the question of ma- terial and workmanship first. Material. The first hammers were wedge- 226 Modern Piano Tuning. shaped wooden blocks covered with hard leather and topped with a softer skin, like that of the elk. In the time of Beethoven the covering material was still leather, although an oval form had been developed. The felt covering which has long sup- erseded all others was developed during the nine- teenth century, principally through the work of manufacturers in the United States, where ma- chines for covering the moldings were first suc- cessfully made and used. The present hammer consists of a wooden molding of approximately pointed shape over which is stretched a strip of hard felt known as the under felt. This is glued in place and over it is fastened in the same way a thicker strip of softer felt called the top felt. The two strips of felt are cut oif large sheets, and glued on to the hammer moldings in one piece ; the moldings themselves being also in one piece. Thus a whole set of hammer molding is turned out complete, and receives a strip of under felt nearly as wide as the whole set of hammers, which in turn receives a strip of top felt. The solid set is then taken out of the machines and sawed into separate hammers. The sheets of felt are of different weights, run- ning from 12 to 18 lbs. per sheet or even higher. The Hammer and Its Relation to Tone. 227 Hammers are known as 12-lb., 14-lb. or 18-lb. ham- mers according to the weight of the sheet from which their top felt is taken. The sheets themselves are prepared in tapering form so that the thickness runs from greater to less in a constant gradation from one end to the other. In this way is preserved the gradation of thickness in the hammer-felt from bass to treble of the piano. Bass strings, of course, require the heavy hammers and treble strings the light ones. Felt. The peculiarities of hammer construc- tion must be considered definitely if we wish to become acquainted with the reasons for the some- times peculiar behavior of hammers under usage. In the first place, it should be observed that felt is a very different thing from woven or spun fabric. Felt is the result of pressing together layers of wool in such a way that the fibres, which are ser- rated or jagged, fasten into each other and form a solid mass, which cannot be torn apart and which possesses in a high degree the qualities of flexi- bility and resiliency, together with strength and durability. At the same time however, it must be remembered that felt is a material which is really at its worst when under tension ; yet hammer-felt is continually in tension after the hammer is 228 Modern Piano Tuning. manufactured. The felt sheet is stretched over a wooden molding, with the result that the whole outer surface of the sheet is subjected to consid- erable tensional strain, which tends constantly to pull the fibres apart; fibres which have in effect merely been pressed together in the process of felting and which therefore are susceptible of rup- ture under strain. This peculiarity of the felt hammer is seen in sharp relief when a piano has been used any length of time. But even before this, even in the fac- tory, the processes of tone regulation invariably expose this imperfection. In order to understand how this is so, however, we must see what that process is and how the condition of the felt af- fects tonal result. Tonal Properties of the Hammer. An ideal piano tone-color can, of course, be expressed in terms of a definite wave-form. This form, we can safely assert, differs not in essentials in any pianos made anywhere. All piano makers of all nations are agreed, generally speaking, upon the kind of wire used, the points of contact, the em- ployment of felt hammers and the general taste of the modern ear for piano tone; or rather for what we have come to accept as good tone for a The Hammer and Its Relation to Tone. 229 piano. Now experiment shows that a wave-form produced by the vibration of a strong fundamental with the following five partials in diminishing strength and if possible with no seventh and no partial above the eighth, represents the ideal. At least, the very best piano tone — the kind of tone which is universally accepted as refined, pure and noble, is a tone which, when analyzed, is seen to be expressible in these terms. Such a wave-form gives such a tone. But the practical requirements of piano making render the attainment of this simple object very difficult. In the first place, it is not regarded as practical to place the hammer contact-point at Vi of each string-length throughout ; though why this should not be practical it is very hard to say. However, that piano makers will not do this is the key to the further fact that the seventh par- tial is an ugly and perpetual reminder, in the com- plex of piano tone, that science and piano making do not yet quite agree. In the second place, the high tension and density of the strings themselves are very favorable to the production of the higher partials, especially those above the ninth. If the hammer struck the string at H, the seventh partial and its multiples would be abolished. If also the 230 Modern Piano Tuning. wire were on the whole softer and the tension lower, than are usual, the 9th and high partials would diminish in amplitude and consequently their influence on tone would be diminished.^ Now it is plain that the hammer must also enter into the complex as an influence of more or less power. Putting aside the question of contact points, which after all is a matter for the scale draftsman and not for the hammer-maker or the tuner, we are reduced to three considerations: (1) the hardness or softness of the underfelt; (2) the hardness or softness of the top-felt and (3) the size and shape of the hammer. Let us con- sider these. Under felt. It is of course plain that the under felt must be relatively firm and hard, simply be- cause the necessity exists of interposing an effec- tive cushion between the hard wooden molding and the contact surface. It is equally clear that the function of the underfelt is, just as much, that of "backing up" the softer top felt. Top felt. The function of the top felt is to in- flict the blow on the string in such a way as to 1 The published proceedings of the Cliicago Conference of Piano Technicians for 1917 contain some interesting discussions of this point. The Hammer and Its Relation to Tone. 231 produce the necessary wave-form required. Now, it is plain that the softer the top felt may be, the less quickly will it rebound from the surface of the struck string. Now a soft top felt of course will be one in which the fibres will be relatively more detached on the top ; a condition partly aris- ing from the fact that the top felt is stretched at high tension over the under felt and molding. The cushion of soft fibres thus formed will tend to cling to the surface of the string a little longer than if it were perfectly smooth and hard. This clinging will have the effect of damping off at least some of the high partials which originate around the point of contact of the string. When it is understood that the hammer, even when new, presents a relatively blunt surface to the string, the above can easily be realized. Soft and Hard Felt. It now becomes plain that : 1. The softer the top felt the less complex will be the wave form and the more mellow the tone quality, due to damping of high dissonant par- tials. 2. The more sharply pointed the contact sur- face, the smaller is the actual mass of felt presented to the string and the fewer are the up- per partials around the contact point to be damped 232 Modern Piano Tuning. by the contact. Hence, a pointed hammer, other things being equal, means a less mellow and more complex tone. 3. The greater the velocity of travel to the string, the more rapid will be the rebound, since action and reaction are equal and opposite. Therefore the harder the hammer-stroke the less mellow will the tone quality be, other things being equal. 4. For the above reason, also, a lighter hammer will rebound more quickly than a heavy hammer on a light hammer-stroke and the heavy hammer will rebound more quickly on a stroke powerful enough to move its weight freely and derive the velocity-advantage thereof. TJie Voicing problem. The business of the voicer is to exert such influence as can be exerted by treatment of the hammer-felt, upon the tone- quality of the piano. Fundamentally, the tone- quality is settled long before the voicer sees the piano. The design of the scale, the general con- struction of the piano, the choice of striking points for the hammer; these and many other details have already determined the tonal quality before any treatment of the felt is considered. The sole business of the voicer then is to smooth The Hammer and Its Relation to Tone. 233 out, to improve if lie can, what has already been set forth; and if he cannot improve, at least to put the best appearance upon things and to make sure that the piano goes out into the world under the most favorable tonal conditions. That is the voicer's business, and he effects his results by the processes of hammer-treating which I de- scribe below. Prior Condition of the Hammer felt. In the first place, let us keep in mind that the top felt is less than an inch deep over the under felt and molding at the point of contact in the bass, and tapers down until it is hardly thicker than the felt of a hat, at the highest treble. This top felt is fastened over the under felt and molding in such a way as to stretch the upper surface whilst com- pressing the parts nearest the under felt. Now it is plain that a structure like this must be more or less uneven in texture and certainly rough on its surface. It is also easy to see that any attempt to remedy these conditions through a process of working up the texture of the felt must take into consideration that the cushion is in a condition of both tension and compression, with a constant tendency towards pulling apart its fibres and dis- rupting its structure. 234 Modern Piano Tuning. Smoothing the Surface. Now it is obvious that before any sort of judgment can be formed rightly regarding what may have to be done to a set of hammers in order to provide the best possible tonal result, the surface of the top felt must be made as smooth and as even as possible. This the voicer does by a process generally called ''filing." A strip of cigar box wood is taken, about wide enough to cover the surface of a hammer when laid over it, with some space to spare, but not wide enough to interfere with the hammers on either side. This strip may be made of any suitable wood, but the kind spoken of is particularly convenient and easy to obtain. The strip is made about seven inches long. Several of these strips are obtained and covered with sandpaper by the simple ex- pedient of cutting a strip of the paper to the same width and twice the length and then gluing it over the one edge and down both sides. The loose ends are trimmed off where the hand grasps the instru- ment. Some of the strips are covered with No. 2, some with No. 1 and some with No. 0, sandpaper. Filing. The ** sandpaper file," as it is called, is used for the purpose of rubbing away the rough uneven particles and fibres of the felt so as to produce an uniform surface. The technic of the The Hammer and Its Relation to Tone. 235 operation may easily be acquired, but practice and patience are requisites to success. The action is laid on its back away from the piano, if this be an upright, or is taken out with its keys if it be that of a grand, and placed on a table or bench. The operator sits with the backs of the hammers near- est to him. Taking one of the hammers between his thumb and first finger he raises it above the line of the others and grasping the file in the other hand so as to leave as much of the sandpaper avail- able as he conveniently can, he draws the file along the striking surface of the felt, beginning at the bottom of the under side of the hammer and draw- ing the file in a series of light strokes towards the top or crown where contact is made with the string, leaving the actual crown untouched. In this man- ner he smooths out the surface, rubbing away the rough outside crust of the felt and drawing this latter up to a curl at the crown. By so doing the position of the crown is indicated and any flatten- ing of it avoided. Then the hammer is attacked in the same way on its other side and the smooth- ing out again terminated at the crown, so that now the hammer looks like a bald head with a little tuft of hair at the very top ; a sort of Mohammedan top- knot. In doing this apparently quite simple work, 236 Modern Piano Tuning. however, it is well to remember that (1) the strokes must be made with the file absolutely square on the surface of the felt, or else the result will be a crooked surface. (2) The file must be drawn just with enough pressure to take off the rough outer crust or skin but not hard enough to make dents in the surface or disturb the shape. Careful prac- tice is therefore necessary, as well as a good deal of patience. Moreover, the high treble hammers which have so little felt on them must be very care- fully treated, or the felt may be all filed away, leaving a bare spot showing the wood underneath. This first smoothing is done with the No. 2 paper. First Needling. The voicer now turns to the needles. Having given the surface of the ham- mer a preliminary smoothing out, he must attempt to produce an uniform texture in the interior. The object of so doing is to furnish a cushion for the immediate contact with the string, which shall be relatively resilient and uniformly yielding, against the harder under felt and still harder molding. This upper cushion however, must not be mushy at the crown or actual place of contact, nor must its surface be broken up and its fibres disrupted by unscientific jabbing with needles. On the contrary, the object is to work the in- The Hammer and Its Relation to Tone. 237 side of the felt so as to leave the outer surfaces as far as possible intact, whilst conforming to the re- quirements noted here. The voicer therefore uses a needle holder con- taining three No. 6 needles, set in a row and pro- jecting not more than one-half inch from the handle. This handle should be of such thickness that when grasped as if it were a dagger with the point of the blade (the needles) downwards, it may be held without cramping the muscles. Thus grasped, it is used to stab the felt, in the manner following : The hammer to be treated should be supported upon a block laid under its stem, so as to raise it above the line of hammers. Such a block is usually made wide enough to support three ham- mers at a time. The needle is firmly grasped in the right hand whilst the left hand steadies the hammer. Strokes are made by firmly pressing the needles down into the felt, on each side of the crown alternately, as far as they will go, not stab- bing hard but pressing firmly, avoiding the crown and gradually working down on each side thereof to the very bottom of the top felt. The needles should enter the felt like the spokes of a wheel, of which the under felt represents the hub. 238 Modern Piano Tuning. It is necessary for the voicer to estimate from time to time the condition of the felt and the progress of his work. At the beginning, before he has filed the hammers, he will of course have tested the general condition of the tone and will also have estimated the hardness of the felt. His work must continue until the interior of each ham- mer is in an uniformly resilient condition, with- out uneven lumps anywhere, but especially with- out any picking up of the surface or tearing of the fibres, and without touching either the crown or the under felt. "Picking Up." The abominable practice of "picking up" the felt by digging with the needles as if one were digging potatoes out of the crown of the hammer, cannot be too strongly condemned. It does the very thing which should not be done ; weakens the already tightly stretched sheet of felt by breaking the fibres and crushing the structure at its surface. The consequence is that the entire crown is soon broken up, its indispensable firm- ness destroyed and contact made mushy and in- effective, whilst the interior of the hammer is left virtually in its original state. Thus the purpose of voicing is entirely missed. The needle-work should be done as indicated and in no other way ; The Hammer and Its Relation to Tone. 239 continuing until it appears by the *'feel" of the felt that each hammer is well worked inside. Trimming the Crown. The voicer now trims off the felt tuft or "top-knot" on the crown of each hammer with his sandpaper file and replaces the action in the piano to test the tone. It will then be found, probably, that the quality is more or less mellow, but that there is much unevenness, some hammers being harder than others. The voicer therefore tests the tone quality by first running over the piano, a few hammers at a time, with a soft touch and then in the same way with a hard touch. The tone quality ought to be the same in both cases. Also the tone throughout should be of even mellowness. To remedy the unevenness the voicer uses his needles as before on the faulty hammers, again avoiding the crown, until the tone quality is evened up on a moderate touch. He then tries each hammer on a hard stroke and if the tone quality hardens when the stroke of the key is very strong, the voicer takes a needle holder containing two % inch fine needles and with these takes a few ''deep stitches," as they are called, down into the top felt ; avoiding the under felt and the crown. This will remedy the trouble, which 240 Modern Piano Tuning. was due to the interior not having been worked sufficiently. Second Smoothing. The hammers are now smoothed again, with finer paper on the file, and any specially hard hammers that may have been noted are needle-worked until they are in good shape. The action is then replaced in the piano. The '*Dead" Tone. If the work has now been done rightly, the tone will be mellow and even on all kinds of touch, but with a sort of ^'deadness." One feels that it needs to be livened up ; and this can be accomplished in the following manner : Ironing. The action being again taken out, each hammer is carefully ironed with a hot iron. This tool is best made from an old l^/^ inch chisel, of which the blade has been cut off below the edge. Let this be heated until a drop of water touched to it evaporates and then let each hammer be well pressed with this on both sides. One side is held with the hand whilst the iron is pressed into the other side, working so as to direct the pressure upwards towards the crown and bring the felt in the same direction. This is done on both sides of each hammer until the felt is well scorched and blackened. The file is then applied again and the scorched The Hammer and Its Relation to Tone. 241 felt cleaned off. The action is replaced in the piano and if the work has been well done the tone has been ''livened up" and made clear. The Crown Stitch. If there is any unevenness still to be noted in the tone quality, or especially if any hardness be observed anywhere, one or two gentle pressures into the felt, down through the crown with a single fine 1-inch needle, will remedy the trouble. This, or something equivalent to it, is the proc- ess of voicing as carried out in the best factories. Qualifications of the Voicer. A good ear for tone-quality is the principal qualification neces- sary for the voicer. The mechanical technic is soon acquired when the necessary feeling is there. To know what are the physical requirements of piano tone is of course the business of the de- signer, just as the same man should also know how to insist on the various works of construction being carried out according to his prepared de- signs; but even so the voicer himself should be equally scientific and equally able to take upon himself the function of a critic. For instance, the voicer may perceive that the striking distance is somewhat wrong, and in that case it is his duty to insist on changes being made 242 Modern Piano Tuning. which will remedy the conditions. It is his duty to watch carefully all points of the design and construction which have relation to tone, and to suggest such improvements as his own knowledge leads him to discern. These are counsels of per- fection, but they are necessary nevertheless. A fine ear for tone-quality may be acquired by patient study of the physics of piano construction and by constant practice in the art of voicing. No other possible road can be recommended or even suggested. The aim and end of voicing is to make the piano sing beautifully, and only con- stant work on the piano makes this idea possible of realization in one 's mind ; an indispensable pre- liminary to its realization in concrete form. The Ideal. The ideal piano tone is that in which a wave form excluding the seventh and all par- tials above the eighth as far as possible shall be evoked uniformly under all conditions of touch. It is the object of the piano hammer to make this tone possible ; and of the voicer to carry out the technical processes necessary to prepare the ham- mer for its tonal work. The matter of repairing old hammers, and cog- nate matters relating to the care of the hammer in used pianos, are discussed in the next chapter. The Hammer and Its Relation to Tone. 243 The rules here laid down for the work of voicing are of course based on the practice of factories; and the tuner who studies this chapter is expected to understand that his practice must be modified in accordance with the condition in each case. Old pianos cannot always be treated exactly as described in this chapter, although every one of the rules and directions here given for each of the processes described and explained, is to be fol- lowed, at all times. This is important: to follow the entire process may sometimes be out of the question, but every time a needle or a file or an iron is used, the directions given above should be remembered ; and, as far as possible, followed out. Care of Tools. One point remains. In using his tools the voicer should be careful especially about keeping the sand-paper files always covered with fresh paper, and about renewing the needles whenever they become dull at the points. Worn sand-paper and blunt needles prevent good work and cause waste of both time and energy. Chapter X. REPAIB OF THE PIANO. Definition. Piano repairing, for the purpose of the present chapter, is held to include all the work that the tuner is called on to do on upright or grand pianos after they have taken their places in the purchasers ' homes. In chapters which have gone before I have said a good deal about the technical processes of piano construction and ad- justment, but these remarks have been concerned with the piano in course of manufacture. The special subject of repair and adjustment of used pianos deserves and requires a special chapter. Square Pianos. The square piano is obsolete, but I have included at the end of this chapter some brief remarks on certain peculiarities of these old instruments. Classification of the Subject. In order to make the subject more intelligible, I have adopted the following classification, marking out the subject in subdivisions and discussing the particular topic 244 Repair of the Piano. 245 of adjustments and repairs specifically for eacli. (1) Tuning pins, wrest plank and strings, (2) sound board and bridges, (3) action and keys and hammers, (4) pedal action and trap-work, (5) var- nish. Tuning-pins and Wrest-planh. Old pianos often suffer from what may be called a sort of general break-down of structure and this is es- pecially noticeable in the wrest plank or tuning pin block and in the frame work which supports the same. One symptom of such troubles is found in loose tuning pins. Sometimes old pianos can- not be drawn up to pitch without breaking strings ; or again often they will not stand in tune even when their strings are pulled up. 1. Loose pins. Tuning pins, of course, are held by the frictional resistance they develop against the cross-banded wood of the wrest-plank. If the wrest-plank holes have been worn through long use and much tuning, the pins will very likely be too loose for effective resistance to the string-pull. In this case, the obvious remedy is to hammer them a little farther into the block. If, however, this does not effect the required remedy, the tuner should either insert a larger pin or else put in a metal friction tuning pin sleeve. This consists of 246 • Modern Piano Tuning. a thin fluted brass tube, fitting over the tuning pin and driven with it into the wrest plank hole. A worn hole can be filled up in this way and a com- plete new surface provided for the old pin to work in. A pin thus treated will tune perfectly, stand in tune for a long time and eliminate all driving of the pin or other make-shifts. 2. '* Jumping" pins. These may also be rem- edied by the use of the above mentioned device, or else by the expedient of removing the defective pin or pins, and blowing a little powdered chalk into the wrest-plank hole. The cause is usually grease or oil which has soaked into the wrest-plank through some carelessness on the tuner's part; thus producing one of the most annoying of piano troubles. Pins that jump cannot be manipulated in fine tuning, and much the same is true of pins that are too tight. 3. Broken Pins. The best way to handle a pin which has been broken off at the eye is with the tuning pin extractor, which is a short steel head like that of a tuning hammer, but provided with a reversed thread tapped in it. The extractor is placed on a handle of its own or can be had to fit on to a tuning or T-hammer. It is worked by screwing it down reverse way on to the broken Repair of the Piano. 247 stump of the tuning pin. This cuts a thread on the stump and grips it tightly enough to enable the operator to pull it out of the wrest-plank, which is done by gently turning it in the plank hole un- til it is loosened enough. One must be careful not to get the head so firmly fastened into the stump of the pin that it cannot be unscrewed therefrom. It is best, in fact, to turn back on the pins a Kttle way after starting the thread and to keep on doing this from time to time whilst the thread is being cut. 4. Wrest plank holes split. The holes in the wrest plank in old pianos sometimes are split across the mouth and it is occasionally necessary to block them up and re-bore them. In doing this, maple dowels should be used for the plugs, which are driven in with glue. The hole is first reamed out somewhat and a dowel driven in to fit tightly, so that when the hole is again bored for re-inser- tion of the pin there will be enough dowel left to act as a bushing all around. 5. Wrest plank split. It is better not to touch wrest planks that are split unless one is very sure of what one is doing. Old pianos with open wrest planks sometimes give way at the gluing between the wrest plank and the back posts ; that is to say 248 Modern Piano Tuning. along a line parallel with the hammers from bass to treble, so that the entire wrest plank pulls away from the back, carrying the strings and tuning pins forward with it. If such a case is met with the tuner may sometime be able to repair the plank as follows : Loosen up all strings, screw wrest plank back into position by hand screws, and leave same tightened in place. Eemove all lag-screws. Bore out lag-screw holes right through wrest plank and out at other side of back. Procure threaded square-head bolts of suitable diameter to fill lag- screw holes and long enough to stick out at other side, together with washers for head and tail of same and nuts to tighten at back. Have at least five such bolts and if there are not enough lag- screw holes for this purpose, bore out extra holes through plate and wrest-plank if necessary to af- ford further protection. Loosen hand-screws. Pour^glue (hot) along and into the crack between back of plank and back post of piano. Screw up hand-screws again. Insert bolts with washers on at heads, driving them well through till threaded ends emerge at back. Put on washers and nuts at back and turn same down as far as they will go. Tighten hand-screws further to take up slack when bolts are turned in. Leave hand-screws on Repair of the Piano. 249 about four hours. Then take screws off, tighten bolts further if nuts will turn, clean off glue, file off ends of bolts or cut them off with cold chisel and file clean, if they stick out too far, draw up strings again, tune. This method will often suc- ceed perfectly. Don't try to use liquid glue. 6. Strings Rusted. Do not rub oil on strings if they are rusted. They may be cleaned by rubbing with end of a hannner-stem dipped in whiting, using alcohol to moisten. Eust at the bearings near upper bridge or on the agraffes or on the belly-bridge pins or at the hitch-pins may some- times be remedied by the use of a little oil care- fully brushed on. But the use of oil on wire is not generally permissible. 7. Tuning pins rusted. The coils of strings around tuning-pins can be cleaned, as well as the pins themselves, by the use of a string and pin polisher, a device whereby a rag carrying metal polish is pushed in and around the coils where the hand alone cannot go. 8. Strings false. False beats have already been referred to {supra, Chapter II), but the tuner will often find that his ingenuity is strained to overcome the clashing between several strings, each of which generates false beats. It is some- 250 Modern Piano Tuning. times possible to tune one string against the other, as it were, so as to play off one set of false beats against another. In bad cases, remove the old wire and string. 9. Bass strings "Dead." Bass strings some- times go ''dead," losing all their beauty of tone and emitting a dull hollow sound. Try loosening string, putting hook in hitch-pin eye, twisting string a few times and replacing as twisted. This will often take up a loosening in the covering wire that is a frequent cause of dead tone. In bad cases, remove and replace with new strings. 10. Bass strings rattle. This is usually through loosening of the covering wire or of the pins on sound-board bridge. (See page 252.) Remedy accordingly. 11. Treble strings rattle. Causes are as above. Sometimes pressure bar is loose, but be wary of tightening too much. 12. Obtaining new bass strings. Bass strings must be made to order. In getting new ones, send along old strings, whether one, a few, or a whole set. 13. Defects of iron plate. Apart from screw- ing down the bolts on an unstrung piano the tuner Repair of the Piano. 251 can do virtually nothing with defective plates save send them to the factory. Broken plates can be re-welded by the oxy-acetylene process. Sound-Board and Bridges. 14. Sound-hoard split. Small splits are not dangerous and do not affect tone unless they cause the board to loosen at the edges. Splits are caused by alternate com- pression and expansion of the wood due to weather and cognate conditions. If it is neces- sary to repair a split, open same up with sharp knife till it is even from end to end, and insert a ''shim" or short strip of sound-board lumber, which may be obtained in quantities from any fac- tory, using hot glue and driving well in. Shims I are triangular in cross section and are driven in sharp edge do^\^l. When dry, they must be trimmed off and smoothed down. 15. Ribs loose. Sound-board ribs are glued in place. If they spring out of place they must be screwed down by drilling small hole into rib from front of sound-board and then driving screw from same side into rib, through the board, with a bridge button at head of screw to take up uneven thrust. Glue brushed over surface of board where rib has sprung also helps screw to hold. 252 Modern Piano Tuning, 16. Sound-hoard rattles. Usually in grand pianos the trouble is that something has dropped onto the board. Get a long strip of steel like a cor- set steel, fasten little pad of cloth on one end and explore surface of sound-board theremth, thus moving dust and grit, pins, pennies, etc. In the\ upright piano, the fault is usually looseness Af| bridges, or splits. Of course these same (jondi-, tions occur in the grand piano to( 17. Bridges rattle. Stpin'g^s rattle cm, bridges when pins are loQser^ Drive pins in furtnar and file over if necessary. In bad cases put in longer pins. If bridge is split, saw out split section to depth of bottom of pins, and send to facfory. New part will be returned bored and pinned, ^eady to be put back in place, which should be done with glue and screws. Bridges also rattle when but- tons behind are loose or when they have sprung from surface of sound-board. Re^iedies are obvious. ' '^ 18. Bass bridge loose. Bass bridges sometimes come away from the sound-board, especially when they are of the extension variety. If extensioi bass bridge splits in half, remove bass strings and re-fasten with glue and screws. Repair of the Piano. 253 Action, Keys and Hammers. 19. Defects of up- right action. Flanges rattle. Flanges being loose, ham- mers "click" when striking strings. Hammers "click" when striking strings. Hammers loose on cen- ters. Hammers don't strike squarely. Center bushings worn. / Centerpins too tight. Bridle tapes missing. Bridles squeak on wires. Tighten. Tighten. Hammer heads loose on stems, back- stop stems loose in back-stops, ham- mer stems loose in hammer butts. Remedy : — re-glue. If center is split, put in new ham- mer butt. If pin is loose in flange, use larger pin or new flange. Tight- en flange. — — -.. Stems are twisted. Heat stems with alcohol lamp and bend hammer heads backward into position. Cut strip of bushing cloth triangular in shape, coming to point at apex. Twist same to shape of cone, and spread on some glue. Push point in through flange holes whence old bushings have been removed. Pull through as far as required. Then cut off bushing cloth, trim and let dry. This can be done on several flanges at once. Push pin in and out a few times, or try smaller pin. Don't ream bush- ing if you can help it. Don't oil bushings. Usually this means mice. Cut away old stumps of tape and insert new tapes with tape inserter. If no in- serter is available, cut groove in bottom of butt, near where tape goes in, with hack saw, fold tape over and glue in groove. See that length is right. Remove from bridle wires, clean off all rust. Replace. 254 Modern Piano Tuning. Keys stick when de- pressed. Keys stick on balance rail. Keys rattle and shake. Keys sunk in middle. Keys rub in front. Keys sink. Key Level uneven. Lost motion. Back checks block. Hammers block. Repetition bad. Dampers buzz on strings Dampers don't rise. Bass dampers catch. Jack action feeble. Ease front rail mortise with key- pliers. Ease balance rail mortise. Re-bush mortises, using bushing cloth and wooden plug to hold cloth whilst drying. New key top but- tons can be had in sets for old keys. Replace worn punchings on balance rail and re-level.i If necessary, build up key-frame with card-board under balance rail. Re-space and straighten. See Chapter VIII (regulating). 2 Straighten on strings. Bend damper spoons. Straighten dampers and re-bend wires. Strengthen springs under jacks. 20. Defects of grand action. Nearly all the above remarks on the upright action apply also to the grand, but the following additional instruc- tions are also useful. Hammers out of line. Hammers don't check. Hammers re-bound too high. Hammers strike loosely. Hammers squeak. Re-space. Re-bend back checks. Regulate repetition lever to trip a little lower. Contact roller Tmder hammer butt is flattened. Re-leather. Contact roller worn bare. Springs in action worn through felt bushings. Rust on springs. Remedy accord- ingly- iSee pages 20.5 and 218. 2 Pages 218-219. Repair of the Piano. 255 Dampers stick. Bushings in rail are swelled. Dampers don't damp. Straighten on strings, clean felt, regu- late fall. Keyboard rattles. " Key blocks not tight down. Or key- frame warped. In latter case, glue cardboard between frame and key- bed. 21. Trap work in upright pianos. Old style wooden trap work often shakes, rattles and suf- fers from lost motion. Use black-lead for squeaks between springs and wood, and soap for trap-pins. Oil pedal bearings when same are of metal and take up lost motion at adjusting points on trap work. See especially whether soft pedal rod shakes at top or rattles. This is a common de- fect. Use felt punchings for taking up lost mo- tion where no screw adjustment exists. Vaseline on coiled springs stops squeaks. 22. Trap Work on grand pianos. The only dif- ference is in the fact that the grand trap-work is placed in a separate lyre. Sometimes the pedal foot sticks in the lyre, or there is lost motion due to worn bushings. The trap levers are usually found under the key bed and in modern instruments a screw adjustment on the lifting rods permits the taking up of lost motion. Other diffi- culties can be remedied the same as for the up- right. 256 Modern Piano Tuning. 23. Varnish. Blue look on case. Bruises. Light scratches. Deep scratches. Renovating old case. Polishing varnished case. Oiling off case. Due to moisture and dust combined. Avoid polishes. Simply wash off case with soap and water and dry with chamois leather. Fill in with melted sealing wax, if deep, then cover with film of melted shellac, which sand paper down, and touch up with French varnish. To polish same, rub with powdered pumice stone and pad, using water to moisten, finish with rotten stone and pad and then with hand mois- tened with rotten stone and water. Oil off as below ("Oiling off case"). Rub down with powdered piunice stone and finish as above. Touch up with French varnish if necessary. Fill with shellac and proceed as above. Scrape off old varnish, then smooth case with sandpaper then with pum- ice stone rough. When surface is clean, re-varnish two coats rubbing varnish, two days apart, rub down rough with pumice stone and wa- ter, flow over with flowing varnish and then polish, as below. After flowing coat has dried (5 days) rub down with pumice stone pow- der, water and felt pad till all parts are flat. Then run out scratches with rotten-stone, water and pad. Finish with hand till brightened up. Oil off as below. Parts being cleaned of powder, etc., rub lightly with cheese-cloth on which has been poured some lemon oil. When this has been done well, wring out another cheese-cloth in alcohol and Avipe off lemon oil. Al- coliol must be almost dried off be- fore using cloth. Repair of the Piano. 257 Checking of varnish. This occurs in all pianos after ex- posure to domestic conditions. Re- polishing with pumice-stone and thence as directed above will often remedy. But varnish always checks. 24. Ivory polishing and repairing. Ivory keys get yellow. They may be scraped down white again with ivory scraper or by fastening down en- tire keyboard in front after removing sharps and then rubbing back and forth with wooden block covered with No. 1^ sandpaper. To polish, rub ivory with whiting and alcohol. Touch up sharps with French varnish. To replace badly worn or loose ivories, take new strip of ivory, and after making some deep scratches in wooden top of key to assist glue in holding, spread over wood some glue whitened by mixing a little whiting in the glue pot. Put ivory on and fasten with ivory clamp or by wrapping tightly with string. But clamp is best. Never try to use liquid glue. There is an ivory cement on the market. 25. General remarks on the square piano. Al- though very few square pianos remain in use, the tuner sometimes has to work on these old instru- ments yet. The principal defects may be sum- marized as follows : 258 Modern Piano Tuning. Defects of sound-board and bridges. Defects of case. Defects of action. Hammers loose. Hammers don't strike squarely. Hammers twisted. Hammers rattle. Hammers worn. Jacks sluggish. Excessive lost motion in action. Keys rattle. Dampers rattle. Dampers stick. Dampers don't damp. Sound-board sags in middle some- times enough to cause hammer rail to touch it. Pins in bridges loosen. Bridges split. Sound-board splits. Wrest-plank sometimes sinks so that it is necessary to pare off some of the under surface to enable ham- mer rail to have free space. Key bed often sinks in middle and lets do\vn touch of keyboard. Rem- edy is to build up under key frame. Tighten split flange, or if flange is fixed put in larger pin. But see that hammer moves freely. Re-space hammer butts. Bend stems over with alcohol lamp. Glue loose somewhere. Investigate and re-glue. Get new hammers by removing old ones and sending them in as sam- ples. Re-capping with leather is usually very poor policy. Springs are usually weakened. Re- place or strengthen. Screw up jack rockers but leave enough play to ensure jack getting back into place under hammer. See directions for uprights. Bushings of lifter wires are loose or worn. Bushings swelled. Heat lifter wire and push in and out of bushing till same is expanded. Probably damper levers don't co-act with lifter wires. Re-space. Other defects can be understood and remedied by study of previous instructions on upright and grand pianos. Repair of the Piano. 259 26. The Old ''English" Square Action. The old English square action is still occasionally met with. In this the hammer is supported by an under-hammer which is raised by the key and the regulation for the escapement of the jack is on the key. All parts are usually very small and deli- cate and instead of pinned centers there are often hinges of parchment or vellum. Great care is necessary in handling these old actions, which are usually much sunk and out of line, but the tuner will find that individually to study each case is the only sound advice that can be given. 27. Tools. The importance of good tools can- not be overestimated. There is no greater mis- take than to suppose that one can do good work with bad tools. Many special tools are manu- factured for the use of piano makers and tuners, and all of them are useful. Eegulating, especially, calls for many tools of special design, such as regulating screw drivers, spoon benders, key spacers, key pliers, wire benders and others of the same sort. Special conveniences are also to be found such as pocket glue pots, center pin car- riers, wire carriers and similar articles. The tuner should take pride in having the best possible tools and in carrying them most conveniently and 260 Modern Piano Tuning. accessibly. Some of tlie tool kits put up by vari- ous manufacturers, containing complete sets of tools for all kinds of outside work on pianos and player-pianos, are extremely attractive and prac- tical. I know ; for I have used them. My own experience proves amply the value of some advice which was given me when I started out as a tuner: ''Get the best tools, learn to use them skilfully and keep them in perfect condi- tion. This alone may not make you successful, but without this respect for, and care of, your tools you will never get anywhere. ' ' Nor can one atford to neglect the matter of ap- pearance. The tuner does much of his work in the customer's house. He is largely judged by the appearance of his clothes, by his manner, and like- wise by the workmanlike or unworkmanlike ap- pearance of his tools. A neat case of bright, clean, fine-looking tools is an advertisement: it is also an aid to efficiency. Chapter XI. ELEMENTARY PNEUMATICS. It is not my intention in the following chapters of this book to write an exhaustive treatise on pneumatics. Elsewhere I have subjected the piano player mechanism in its present condition to treat- ment of a technical sort at some length and to this other volume the reader is invited for a more com- plete survey of the facts surrounding the con- struction and operating principles of these mech- anisms. In the present chapter, I have indeed en- deavored to set forth simply and clearly the req- uisite facts ; but in a more condensed fashion. To treat the subject-matter again in all completeness would be to write another volume beginning at this page; but this is unnecessary, for the reasons stated. At the same time, I feel it proper to say that the reader who wishes to be thoroughly ac- quainted with the player mechanism, and is not satisfied merely to know that which every tuner 261 262 Modern Piano Tuning. must anyhow know to-day about players, should study the subject systematically.^ Need of Instruction. It is no secret that the arrival and rapid progress of the player-piano have been most seriously disturbing to those mem- bers of the tuning profession whose views are already formed and their methods more or less settled; in short, to the older and more conserva- tive tuners. It is safe to say that as late as the year 1896 very few tuners had ever given serious thought to the possibility of a mechanism for piano playing being developed at all; much less to the possibility of its becoming immensely important to the trade and a knowledge of it in some shape essential to success as a tuner. That this should ever happen would have been thought absurd; that it should happen within fifteen years would have been thought ludicrously impossible. Yet the impossible has become the possible, the ''could- not-be" has become the Is. The player-piano is with us; most of us have been caught quite un- prepared for it. Scope of these chapters. In the circumstances, seeing that already nearly one-half of the pianos 1 The book referred to is "The Player Piano Up-to-Date," pub- lislied by Edward Lyman Bill, Inc., N. Y., 1914. Elementary Pneumatics. 263 made in the United States are player-pianos and that the ordinary upright piano without player seems positively to be doomed, it is plain that one could not very well avoid writing some chapters on the player mechanism in a book like this. On the one hand, then, I have attempted to make sure that the information given here shall be always clear, accurate and intelligible ; whilst on the other hand I have not failed to remember that the tuner whose interest in the player is confined to attain- ing such acquaintance with it as will enable him to make necessary small adjustments and trace the cause of apparent defects in its performance, will neither require nor desire a lengthy treatise. To be accurate and intelligible whilst being also very brief is not easy ; but I hope that I have succeeded measurably well in carrying out this requirement. In this and the two following chapters, then, I undertake to set forth briefly (1) the funda- mental principles of pneumatic player mechanism (2) a general description of the modern player- piano in its pneumatic aspect and (3) such instruc- tions as experience shows to be most useful in the adjustment and repair of defects. The treatment is such that the reader will have no difficulty in following everything set down here. 264 Modern Piano Tuning. The Mechanism. The player mechanism, whether it be built right into the piano or placed in a cabinet detached therefrom, is self-contained and entirely independent of the piano. Usually to-day it is interiorly built, fitting into waste space within the case of the upright piano. It is also now fitted into grand pianos, but in its principal embodiment remains an addition to the ordinary upright, built within the case, but independent of and not interfering with the regular action, scale or sound-board. The player mechanism can be withdrawn from the piano case very readily and is in all respects separate from the musical instru- ment itself. The function of the player mechanism is to render musical compositions by playing upon the piano action, either through the keys or directly upon the abstracts or wippens thereof. The player mechanism runs on power furnished by bellows blown by the performer. Various means for expression are provided, con- trolled either automatically or at the will of the performer, the objects of which are to permit, as required, variation of speed, use of damper lift, loud and soft stroke of hammers, and division of melody from accompaniment parts. Elementary Pneumatics. 265 All these requisites are made possible by the use of simple auxiliary devices. The selection of notes for the performance of a composition is undertaken by the aid of a web of perforated paper, spooled on a core and called a "music-roll.'* Source of Power, The power for operating the player mechanism is furnished by bellows oper- ated by the feet of the performer through treadles. The operation of the bellows system is not at all hard to understand. In fact, the entire player mechanism works on a system so generally simple that, once its principle is grasped, the reader can reason out immediately the method of operation and the function of any part. Pressure and Weight of Air. The air of the atmosphere in which we move and which we breathe is invisible and virtually intangible. Yet it is just as much to be reckoned with as so much iron or wood. Its density is less than that of the other materials mentioned, but is measurable nevertheless. Scientific observation has proved that air, like all forms of what is called matter, has weight. A column of air one inch square and the height of the atmosphere has a weight of very nearly 14.75 pounds or 236 ounces ; so that we may 266 Modern Piano Tuning. say that the air of the atmosphere exerts a pres- sure at its bottom (the surface of the earth), of about 14.75 pounds per square inch. Expansion. Air is a gas and all matter in a gaseous state has the property of expanding con- tinuously to fill any space in which it may find itself. This expansive property together with the weight of air is the foundation of the operation of all pneumatic machines. The air normally fills at normal pressure all closed spaces capable of containing air. It is everywhere and always present at normal pres- sure, unnoticed and unconsidered, until by some artificial means it is either rarefied or condensed. Then work can be done by means of it. If a closed bag, which is normally filled with air according to the natural facts of the case, be shut off and closed so that no more air can get into it from the outside, and if then the bag be enlarged, without any more air being allowed to flow into it, the contained air will have to expand to fill up the enlarged space. In so expanding, the air is acted on like the rubber in a rubber band which is stretched. It becomes thinned out, so that any cubic inch of it now weighs less than a cubic inch of it weighed before it expanded. Hence the pres- Figure 21. Essential parts of player mechanism, pneumatic open; (not to scale) 267 "'^^ v-'-" ' • ."n ^^fe^ Pedals Figure 22. Essential parts of player mechanism, pneumatic closed; (not to scale) 268 Elementary Pneumatics. 269 sure exerted by any quantity of it is less after ex- pansion than before. Hence, again, the atmos- phere outside, which has retained its normal pres- sure of 14.75 pounds to the square inch, is able to exert an effective pressure on the outside walls of the bag, because the inside pressure is reduced owing to the expansion of the bag; and hence the balance between the outside and inside air is dis- turbed. Disturbance of Balance. The player mechan- ism operates entirely through this disturbance of balance as between the atmosphere and bodies of air contained within enclosed spaces. Look at the illustrations on pages 267 and 268, which show the various parts of a player mechan- ism drawn out in the simplest possible way to show the operation of each part, but not drawn in pro- portion or according to any particular existing player. In fact the object of the drawings is to show only the operation of the principle. Simplest case of pneumatic mechanism. At the bottom of the illustrations will be observed the bellows with two ''exhausters," operated by the foot pedals, and one ''equalizer." One of these exhausters is open and the other closed. But let us suppose that the player is in a state of 270 Modern Piano Tuning. rest with, therefore, both foot pedals untouched and both exhausters closed. The compression springs behind the exhausters hold them closed normally. Well, now, the exhausters being norm- ally closed, the reader will observe that (1) the outside air can find its way into the ''pneumatic" through the channels and the top of the valve; (2) the long channel from tracker bar, over which the perforated paper moves to the valve pouch, will also contain any air that may have flowed into it when a perforation in the paper was registered with the tracker bar hole ; and (3) through the lit- tle ''vent," which is just a pin hole in a cap, the at- mosphere flowing in from the tracker bar will also fill the reduced pressure chamber and therefore the entire bellows system, which is in connection with it. This is the normal or at rest condition. Operation of Exhausters. If now, the foot is placed on a pedal and one exhauster pushed open, see what happens. Assuming that the tracker bar channel is sealed by the paper for the moment, as when no note is being played, it will be seen that the operation of the exhauster simply means that the whole inside cubical content of the player is enlarged by the exhauster being opened; the player, in fact, being made larger inside by just Elementary Pneumatics. 271 the volume of the exhauster. True to its nature, therefore, the air in the various parts of the player expands equally to fill up this space. But the il- lustrations show that a flap or strip of leather covers the openings between the inner wall of the exhauster and the interior of the player. This strip, however, is pushed aside by the rush of normal-pressure air into the empty opened ex- hauster, which continues until the pressure on either side of the strip is equalized. Therefore a quantity of air filling the exhauster, but at lower than normal pressure, is now trapped in the ex- hauster, since it cannot get back through the door which it opened once and is now holding closed (the strip) ; for this door is held shut by a spring just strong enough to keep it against the pressure on the inside of the player, and further, is of course held by the pressure now in the exhauster. But, the exhauster being now all the way open, and the pedal all the way down, the heavy compres- sion-spring outside tends to close the exhauster again. Besides, the foot-pressure is now natur- ally released for the return of the pedal. There- fore the exhauster begins to close and in closing squeezes the air inside it, which is trapped there and cannot get back inside the player, until it is 272 Modern Piano Tuning. enough compressed to force its way out through the outer strip or flap into the atmosphere, being forced out by the closing of the exhauster. Once squeezed out, the exhauster is shut, and anyhow no more air can get back in through the strip or flap which presses on the outside of the exhauster. Therefore we see that one opening and closing of the exhauster has withdrawn a definite quant- ity of air from the interior of the player and has expelled it into the atmosphere. Therefore a ** partial vacuum," as it is called, is set up inside the player; or, in other words, the pressure of all the air inside the player has been lowered. Valve. This being the case, the atmospheric pressure on top of the valve holds it down firmly on its seat and shuts off the reduced pressure chamber from the outer air, whilst conversely the pneumatic is open to that air and therefore re- mains at rest. Reduced-pressure Chamber. Thus the situa- tion when the pedals are being operated is as follows: Pressure of air is being constantly re- duced, inside the player, in the reduced-pressure chamber, in the tracker bar channel (though on account of the smallness of the vent, to a smaller degree), in the trunk channel between bellows and Elementary Pneumatics. 273 pneumatic action and in the equalizer. Now sup- pose that a hole in the paper registers with the tracker bar hole : Operation of Valve. Immediately, the atmos- phere, which has of course, been pressing against the paper, finds its way down against the reduced- pressure air, through the tracker channel and un- der the pouch, losing a little by the way through the vent. The pouch being larger than the top of the valve button, rises against the pressure on the button, and lifts the valve spindle with its buttons. At once, as may be seen, outside air connection with the pneumatic is shut off, whilst connection is simultaneously made between the pneumatic and the reduced pressure chamber. Hence the heavy normal air in the pneumatic ''falls" by its own weight into the reduced pressure chamber, re- ducing the pressure in the pneumatic. The atmos- phere therefore presses against the moving wall of the pneumatic, closing the same and putting the piano action into operation. When the perforation passes over and the paper again seals the tracker bar hole and channel, the normal air under the pouch and in the channel no longer is re-inforced by supplies from the outside and in consequence (since the bellows are oper- 274 Mod&rn Piano Tuning. ated continuously and the reduced pressure cham- ber always therefore is in a state of partial vacuum, being never in contact with the open air except at times through the very small vent), this normal air in the channel '* falls" into the re- duced pressure chamber as quickly as it can ''fall" in through the vent (air being elastic in all direc- tions, can ''fall," as I call it, up as well as down). Therefore, partial vacuum again exists in the chan- nel and under the pouch, so that the valve-stem is no longer held up with its buttons but again sinks down and is held down by the atmospheric pressure on its top button. Therefore again the pneumatic is shut off from the reduced pressure chamber and placed in contact with the atmos- phere, so that it fills with air at normal pressure, and forthwith opens. This operation may be re- peated over and over again, quite as rapidly as the piano action can operate, and in fact, even more rapidly; provided the necessary sequence of perforations is present on the paper roll. This is the operation of the player mechanism. But we have yet to speak of one important ac- cessory; the equalizer. Equalizer. The equalizer is a reversed ex- hauster. Normally it is held open by a spring. Elementary Pneumatics. 275 It is also, as will be seen, connected pneumatically with the remainder of the bellows system and with the upper action of the player. When the exhaust- ers begin their work, the air in the equalizer ex- pands along with the rest and part of it moves out- ward to the air, so that the pressure in the equal- izer is also reduced. If the pressure is enough reduced to overcome the expansive power of the spring (which never exceeds 8 ounces per square inch of area on the moving wall of the equalizer and usually is much less, so that a displacement of about 3 per cent, of the contained air is enough to enable the atmosphere to balance the spring and neutralise it), then the equalizer starts to close. Whilst closing, it does no effective work, but is in fact a drag on the bellows. When, however, owing to an increase in the number of tracker bar holes open, or to slowing up of the pedaling, or increased speed of the motor, or to any other cause, the effectiveness of the exhausters is reduced for a time, the equalizer, forced by its spring, begins to open; and in opening becomes, of course, an- other exhauster, automatically displacing air from the player and holding it till the exhauster can take care of it and expel it. This is the function of the equalizer. 276 Modern Piano Tuning. Of course, the reader is well aware that there are many variations on the simple system here described, but all depend on exactly the same prin- ciples, whether one or another kind of bellows be used, whether single or double valve system be adopted, and whether the most elaborate or the simplest expression devices be provided. In the next chapter, I discuss the general varieties of construction amongst the players usually met with. Motor. The motor system is equally easy to understand. As will be seen by the illustration on the next page, the motor consists of small bellows called ' ' pneumatics, ' ' mounted on a block which is perforated with one long tube running through it from the bellows, provided with ports called ** suction ports" which penetrate to the outside of the remote surface of the frame. Each pneumatic is also provided with a port which runs between its interior and the outer surface of the same block. A slide valve slides over the pair of ports belonging to each pneumatic and is con- nected with a crank shaft by means of a connect- ing rod, the pneumatic itself being also connected to the crank shaft. Operation of Motor. Now, when the bellows are operating below and the suction port is in pneu- rmtumajtic op Cotnnec\irtoUo Index. 333 Clavichord, stringed instrument, keyboard of, 73 footnote Comma, interval, 33 Condensation of sound-pulse, 61 Conover Bros., piano makers, 216 "Crash-bellows" in player, 287 Cristofori, B., inventor of piano, 150 his back-check, 192 his hammer, 223 Curve of sines, 7 D. Damper, of grand piano, 194 regtilation of, 208 of upright piano, 220 "Delicacy of ear" defined, 128 DiflFerence of one vibration, 65 E. Ellis, A, J., F.R.S., translator of Helmholtz, 35, 82 footnote, 94 history of musical pitch, 19 "Electric player," see Automatic Player Equalizer in players, 274 operation of, 275 Erard, P. S., piano maker, 184, 186 Erard piano, 195 Errors, accumulation of, 112, 127 Expression in player-pianos, 264 Expression governor in player, 290 description of, 291 Expression governor — continued operation of, 293 regulation of, 319 F. Faber, N., organ maker, 73 foot- note Felt for piano hammers, 226 nature of, 227 See also Hammer-Felt Fifth, musical interval, 21 ratio of, 22 Fourier, J. B., mathematician, 52, footnote his theories, 52 Frequency of vibration, 15 G. Galton, Sir F., anthropometrist, 18, footnote Galton whistle, 18, footnote Gate-box, see Tempo-box. Goetschius, Dr. Percy, musical theorist, 24, footnote Graphite, use of, 314 Grove's Dictionary, musical en- cyclopaedia, 84 Gulbransen, A. G., player in- ventor, his player, 290, 299, 302, 303 H. Hagaman, Dr., inventor, 94, footnote Hammer of piano, 137 contact with string, 55 description of, 224 334 Index. Hammer — continued development of, in U. S. A., 226 felt for, 227 "filing" of, 234 functions, 224 light vs. heavy, 232 material for, 225 tonal properties of, 228 voicing of, see Voicing Hammer-blow on upright piano, 218 "Hammer-felt" of piano, 226 under-felt, 230 top-felt, 230 soft and hard, 231 condition prior to voicing, 233 (See also Hammer and Felt.) "Hammer-rail-lift" on player pianos, 295 floating type, 296 Harpsichord, ancestor of piano, 223 nature of its tone, 223 Helmholtz, H. L. F., Acousti- cian, 17 footnote, 19, 35, 82 footnotes, 94, 97, foot- note Hipkins, A. J., musical techni- cian, 73, 151, footnotes "History of the American Pianoforte," historical work, 187 footnote, 329 Hydraulikon, ancient instru- ment, 73, footnote Impulses, composition of, 164 Interference of eoimd, 67 Intervals of musical scale, ad- vice to tune pure, 96, 122 used for tests, 126 wide and narrow in equal temperament, 89 Intonation in music, impracti- cability of pure, 31 Just intonation, 94 Intonations, comparison of, 79 study of, 93 Ivory, polishing of, 257 repair of, 257 Jack of grand piano action, 206 of upright piano action, 219 Key of piano action, of grand piano, 202 regulation in grand, 204 of upright piano, 218 remedies for defects in, 254 Key-board, influence of, 73 Key-pliers, use of, 204 Kimball, W. W. Co., piano makers, their player, 301 Koenig, Dr. R., Acoustician, 18, 97, footnote Kranich & Bach, piano makers, their soft pedal, 200 Leakage in pneumatic player action, 311 results of, 312 precautions against, 313 Index. 335 Leakage — continued in valve boards, 321 Lecky, Jas., musical theorist, 84, footnote Left hand in tuning, 121 for grand pianos, 122 Lost motion in upright piano action, 219 M. Materials for player repairing, 327 (See also under Felt, Piano, Player, etc.) Mayer, Prof. A. M., Acoustician, 61 Method, note on, 92 Metronome for coimting beats, 107, footnote Miller, J. C, Acoustician and Tuner, researches of, 69 his tables, 88 Monochord, analogy of, 159 Motion, harmonic, 49 resultant, 49 Motor of player, 276 adjusting speed of, 314 adjusting valves of, 315 cloth for, 322 old, reclothing, 321 operation of, 276 parts of, 276 speed of, 314 transmission of, 301 troubles of, 314 various types of, 301 Motor governor of player ac- tion, 278 adjustment of, 289 Motor governor — continued description of, 288 operation of, 280 Muffler of piano, 141 Mutty, L. J. Co., player supply makers, their cloth gages, 322, 323 Music Trade Review, piano trade journal, 88 Music Trades Review, London, piano trade journal, 88 Musical instruments, their im- perfect tuning, 33 Mute, 125 Muting of strings, 123 N. Needham cabinet player, 308 Nodes, in string vibration, 48, 65 Noises, 3, 4 Notation, acoustical, 29, foot- note 0. Octave, musical interval, 21 in equal temperament, 76 tuning of, 98 Organ, intonation of in equal temperament, 81 Oscillation or semi-vibration, 15 Overstringing in bass of piano, 132 Partials in string vibration, up- per, 16 336 Index. Partials — continued influence of, 54 coincident, 67 series from C, = 64, 53 series of, 54 Patches, in player repairing, 320 Pedals of piano, 139 sustaining, 140 "loud," 140 soft, 140 sostenuto, 140, 200 regulation of, 209 soft of grand, 199 Kranich & Bach soft, 200 of upright piano, 217 of upright soft, 217 of upright damper, 217 of upright middle, 217 regulation of damper pedal, 220 of soft pedal, 220 of middle pedal, 220 of player piano, 270 Penduliun for counting beats, 106 experiment with, 164 Pendulum-clock, 106 Perforated sheet or music roll, 265, 273 Perforations, marginal, in sheet, 303 Phase, in Acoustic phenomena, identity of, 64 difference of, 64 Piano or pianoforte, as acous- tical instrument, 38, footnote action of, see Action case-work on upright, 141 Piano — continued development of, 150 finish of, 149 grand, illustrated, 147 highest sound of, 17 illustrations of, 143, 144, 146, 147 iron plate of, 133 defects of, 250 keys of, see Keys lowest sound of, 16 materials of, 148 a percussion instrument, 131 polish of, 149 range of modern, 18 strings of, see Strings soundboard of, see Sound- board in theatres, 125 tone of, see Tone tone-emission, apparatus of, (see Tone Emission Ap- paratus ) upright, names of parts, 141, 142, 143, 144, 145, 146 varnish of, 149 wire of, see Wire wrest plank of, 117, 133 square, see Square "Pianoforte," article in Ency- clopaedia Britannica, 187 Pin-block of piano, see Piano, Wrest plank of Pipes, musical, vibration of, 54 Pitch of sound, 14 lowering of, 124 raising of, 124 imiform, 125 Player-piano, 284 description of, 285 Index. 337 Player — continued lacks power, 317 maintenance of, 311 old, 324 repair of old, 324 Player, cabinet or exterior, 284, 307 action of, 308 bellows of, 307 expression in, 308 motor of, 308 repair of, 326 Player-Piano Up to date, book, 326 "Pneumatic," power unit of player mechanism, 270 ciphering, 318 cloth for, 322 collapse of, 273 cracks in, 321 repetition of, 274, 317 silent, 319 "Pneumatics" science, 201 need of instruction in, 262 summary of facts in, 282 Pneumatic playing mechanism of player-piano functions of, 264 operation of, 269 regulation of, 320 repair of, 310 Pneumatic power, source of, 265 Pneumatic stack of player mechanisms, 298 assembly of, 299 Polishing, 149, 256 Position in tuning, 123 Pouches of player mechanism, 323 Pouches — continued leather for, 323 repairing of, 323 "Pounding" in tuning, 123 Practice by student in tuning, 100 Pressure of atmosphere, 265 effective, for player, 282 on valve, 272, 274 Price & Teeple Piano Co., their player, 290 Purity in timing, measure of, 97 Pythagoras, Greek physicist, 20 R. Range of musical sounds, 18 Ratio, chromatic, 33 (also see Interval) Reduced pressure chamber of player mechanism, 272 Refinishing of case-work, 256 Reflection of vibratory motion, 49 Reisig, Aug., Acoustician, 107, footnote Repetition of piano action, 184 double, 184 of player action, 317 adjustment of, in player, 317 Replacement of parts on player piano, 320 Re-roll in player piano, 297 Reservoir of player, see Equal- izer Resonance of sound, 66 in piano, 161 sympathetic, 40 Re-wind, see Re-roll 338 Index. s. Saw, noise of, 7 Scale, in music, 20 chromatic tempered, 19 diatonic, 20, 22, 24 equal tempered, 75 equal tempered on piano, 76 minor, 79, footnote natural, 22 relations of degrees of, 25 "Scale" in piano making, 131 Schwander piano action, for grand, 198 for upright, 216 Screws, overdrawn, 324 Semitone, chromatic, 32 "Sensations of Tone," book, 17, 97, footnotos Shellac, use of, 313 for leaks, 321 Silencer in player-piano, 297 Simplex cabinet player, 308 "Sixty-five note" players, 306 Slide valve in player, squeaky, 323 Soft expression { see Expression- governor) Soft-pedal, pneumatic, in play- er-piano, 295 Sound, science of, 4 as sensation, 4 loudness of, 12 mechanics of, 5 musical, 9 pitch of, 14 quality of, 54 transmission of, 9 vibration of, 9 "what is sound," 2 Sounds, extremes of musical, 16 highest on piano, 17 lowest on piano, 16 lowest audible, 16 musical, 3 properties of musical, 11 Sound-board of piano, 134 bridges of, 136, 176 character of, 152 crown of, 135 defects of, 251 dimensions of, 174 influence of back on, 170, 173 influence of plate on, 170, 171 as resonance instrument, 161 use of, 135 ribbing of, 175 tone coloration by, 168 vibration, period of, 170 proper of, 169 of, shown, 157 as vibrator, 135, 160 with strings, one structure, 153 Spillane, D., musical historian, 187 Spool-box in player-piano, 302, Springs in piano action, 198 in player action, treatment of, 323 Square style of piano, 244 is obsolete, 244 old English action of, 259 repairs on, 257 Staib-Abendschein Co., New York, their Mastertouch piano action, 216 Standard Pneumatic Action Index. 339 Co., New York, their player, 287 Steinway & Sons, New York, piano makers, 198 their grand action, 198 Strauch Brothers, New York, piano action makers, 199 their grand piano action, 199 "Striking distance" of hammer, 56, 179 String, musical, 36 definition of, 36 division of, 42 experiment on, 46 length of, 43 pitch of, 43 thickness of, 43 tension of, 43 variable factors in, 45 vibration, simultaneous, of, 59 weight of, 43 why it subdivides, 45 Strings, of piano, bass, 132 defects of remedied, 249 description of, 116 dimensions of, 178 false, 249 functions of, 177 gauges of, 178 hang on bridge, 122 material of, 57 proportions of, 132 striking point of, 179 struck, 156 tension of, 58, 133 tones of, 38 winding of, in bass, 180 String polisher, tool, 249 "Style" in tuning, 127 Sustaining pedal, pneumatic, in player, 294 troubles of, 319 Technicians, conference of, 182, footnote Temperament in tuning, mean- ing of, 74 necessity for, 34 use of word, 73 Temperament, equal, system of tuning, 70, 74 advantages of, 80 a compromise, 95 definition of, 75 disadvantages of, 80 octave rates, 75 semitone ratio, 75 Temperament, meantone, sya- tem of tuning, 82 Tempo or speed, in player piano, 280 control of, 280 valve for, 281 Tension of piano strings, 58 Tests in tuning, method of. 111 of octave, 102 by thirds and sixths, 103 by tenths, 104 Test-roll for player-piano, 314 "Theory and Practice of Piano- forte Building," Book, re- ferred to or mentioned in footnotes, 35, 45, 82, 130, 134, 135, 171, 175, 178, 183, 187 Tliompson, General Perronet, musical theorist, 82, footnote 340 Index. Time, unit of, 15 Tone, quality of musical sounds, acoustical definition for piano, 155 the ideal, 241 of piano, 154 of piano is compound, 39 of string, 38 Tone color, meaning of, 156 Tone coloration by sound board, 168 Tone-emission, apparatus of, for piano, 153 definition of, 154 Tonometer of Koenig, 19 Tone regulation, see Voicing Tools for player work, 327 for regulating, 221 care of, 259 for tuning, 119, 123, 125 for voicing, 234, 237, 240, 243 Touch in piano action, 137 after touch, 207 control of, 155, 156 depth of, 201 regulation on grand, 201 regulation on upright, 220 Tracker-bar of player piano, 300, 302 Tracking-device of player-piano, 303 Trapwork in piano action (pedals), 139 defects in, 255 Treadles of player piano, 286 Treble, tuning of, 127 Tubes in player piano, leaky, 324 metal, 324 Tubes — continued old rubber, 324 Tuning of piano, basis of, 34 of unisons, 98 of octaves, 101 of treble, 127 solid, 120 (see also Temperament, Oc- tave, Unison, etc.) Tuning-fork, pitch measuring instrument, its sound, 5 vibrations of, 6, 38 Tuning hammer, tool for tun- ing, 119 length of, 121 manipulation of, 119 position of, 121 Tuning-pin in piano making, 114, 118 bending of, 120 turning of, 120, 244 sleeve for, 244 Tyndall, Professor, Acoustician, 9 U. Unison, in music, 20 tuning of, 98 V. Vacuum, in pneiunatics, defini- tion of, 272 partial, 272 in reduced pressure chamber, 273 Valve, in player-piano mechan- ism, 272 of motor, 315 Index. 341 Valve — continued operation of, 273 pouch of, 270, 273 pouch defective, 317 primary, 299 secondary, 299 sticking of, 313 travel of, 318 Varnish for pianos, 149 defects and remedies, 255 Vent, of player piano mechan- ism, 269, 271, 297, 298, 316, 318 Ventral segments, in acoustics, 49 Vibration, in acoustics, com- plex, 41 double, 15 laws of frequency, 44 semi, 15 simple, 37 simultaneous, 59 Voicer, in piano making, his qualifications, 241 as critic, 241 Voicing, process of treating piano hammers, etc., 59 ■process of, 233 crown stitch, 241 "the dead tone," 240 deep stitches, 239 filing, 234 ironing, 240 Voicing — continued needling, 236 needle holder, 237 "picking up," 238 problem of, 232 prior condition of felt, 233 sand paper file, 234 smoothing, 234 technique of filing, 235 of needling, 237 trimming the crown, 239 W. Wave-length in acoustics, 63 Welding for plate repairs, 251 Wessell, Nickel & Gross, piano action makers, 189, 199, 210, 215 Wilcox & White Co., see Ange- lus Wire for piano strings, 57 density of, 58 gauge of, 179 high tension, 179 Womum, R., piano maker, 184 Wrest plank in piano, see Piano defects of, 247 Z. Zahm, Rev. J. A., Acoustician, 82, 97, footnotes \ A .y '■•».:^>**«w«Mf"^ ^^j^iW'" .et^'' 1/ iSANCElfj> <^\MmO/^ ^lllBRARY^/: -^^-^A -^ ^ 4^_1. '■^ ^ UNIVERSITY OF CALIFORNIA LIBRARY Los Angeles This book is DUE on the last date stamped below. OCp 6 » '^'- '^> '~A ■ij ,.4../, % OUAFtER. LOAN mi #-- DEC 41981 24131 1S3^ M(4^ .\>* jr sm ^>iV i'^ Semi -Ann. Loan »m SEPl 1982 BfC'D MUS-LIB '^UG 2 5 158 JAN - 9 198^ FEB 6 1984. 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