A o o A 1 2 33 55 2 > 5 1 4 JO > ^ 2 4 o 3 ^ il'M f'' piis fiasiiisiusi SOUND AND ITS RELATION TO MUSIC v,\ CLARENCE G. HAMILTON, A.M. ASSOCIAlJv I'ROFluSSOK t)F MfSIC AT WKIJ.liSI.KV C()r,LH(iK BOSrON OLIVER DITSON COMPANY N]<;\V YORK CIIICAG) CHAS. H. DITSON & CO, LYON & HEALY MADE IN U. S. A. ' Copyright. MCMXII By Omvkk DiTSox Company Inie))iatio!ial Copyright Secured DEDICATION To my very dear friend Professor Hamilton C. MacDougall PREFACE Every intelligent musician should be familiar with the physical laws which underlie his art. In the following pages will be found a compact statement of these laws and of the chief facts, theories and experiments in accordance with which thev have been formulated. The nature and transmission of sound, its various elements and manifestations, the musical materials derived from it and the application of these mate- rials in the construction of instruments are some of the matters discussed. In order to facilitate further reading in regard to any of the subjects broached, references are given at the end of each chapter to correlative parts of important works on acoustics, of which a list is appended. Abstruse mathematical works like those of Airy or Lord Rayleigh are excluded. Books are referred to in individual chapters simply by the last names of their authors Scientists and musicians have been slow in cooperating, and at times have even antagonized each other. It is hoped that in the future mutual helpfulness will take the place of distrust, and that due allowance may be made by either party for slight points of divergence between mathematics and aesthetics. That the present l)ook mav aid toward this result is the earnest wish of its author. Clarence G. H.vmiltox. \\'elli;slev, Mass., June, 1911. CONTENTS Pkefack V List of Kffekexce Books vii J. The Ohigix and TRAxs>rissiox of Sotxd 1 II. A'elocitv, Reflectiox. Refka(ti(jx AXi) Diffhactiox 12 III. Pitch 24 IV. T.OL'DXESS. I XTEKFEI^EXCE AXI) RfSI'LTAXT ToXES. , 37 y. Qtalitv 51 \'l. Kesoxaxce ')9 \'\ 1. Scales. Fxtek\als axd Chords 89 A'lII. The 1-".ak axd the A'oice 108 IX. Mi'sicAL Ixstkumexts 123 I xdex 147 LIST OF REFERENCE BOOKS Barnes, C. L. Practical ^Icoustics. Macmillan and Company. London, 1909. $1.10. Consists mainly of a series of exjjeriments. llAKTox, Enwix H. .-/ Text-book on Soioid. Macmillan and Company. London. 1909. $3.00. A highly technical treatise. Illustrated. Llaskkxa, P^iKTKo. Tlic Tlicovy of Sound. D. Appleton and Company, Xew York, 187f). $1.50. Readable and non-technical. Illustrated. Mroadhol'se. John. Musical Acoustics. William Reeves, London, l-'ourth editicjn, 1905. $3.00. "The Student's Helmholtz." Illustrated. Catchi'ool. Ei)ML-.\I). .1 Text-book of .Sound. W. IC Clive, London, 1894. $1.50. Somewhat technical in character. Illustrated. 1-lAKKis. T. V. Handbook of .Icousiic.'i. J. Curwen and Sons. London. Revised 1910. $1.25. A well-outlined treatment, with examination questions. Illustrated. Hkl.mholtz. 11. L. I". Tlic .Scusatio>is of Tone. Longmans, Green and Company, London. Third edition, 1895. $9.50 The standard work on acoustics, Lavigxac. .Xi-iiKKT. Music and Musicians. Henry Idolt and Company, London. Revisetl 1907. $1.75. The hrst part contains a concise treatment of acoustics. Pole. \\'illia.m. The J'lulosol'hy of Music. Triibner and Company, London, 1879. $3.00. Discusses the materials used in music. POYXTIXG AXI) TlIOMPSOX. .Souud. Charles Griffin and Comiiany, London, 1909. $2.75. Somewhat technical, I'ully illustrated. Stoxk. W. II. Elente.'tary I.esso>is on Sound. ^lacinillan and Company. London. 1895. $0.90. A compact treatise-. Illustrated. Tavi.or. Si:nLK\'. Snuud and Music. Macmillan and Company. London. 1883. $2.50. Written in an interestin.g style. T'l xnAi.L. Jim X. .Soioid. D. Aiipletdu and Comixmy. New Yf)rk. $2.00. ;\ standard ])r>pular work. Illustrated. Zah.m, J. A, Sound and Music. A. C. McClurg and Comiiany, Chicago, 1892. $2,00. \'erv readable and fullv illustrated. SOUND, AND ITS RELATION TO MUSIC CHAl'TER I Th]-: Okigix AM) Tka.xs.misskjx of Sound. TiikouGiiouT the recorded course of human histor}-, in- vestigations into tlie nature and properties of sound have occupied the attention of philosophers and \ , ... n ■ Investigations scientists. As early as the sixth centurv 1j. L.. of sound- 1 ^ 111 r ' 1- phenomena. lythagoras demonstrated the laws of sounding strings ; and it is probable that his researches were founded upon data derived from the h^gyptians. Others of the (Ireek philoso])hers, as well as those of following centurie.-. pro- pounded and s]5eculated upon the various and complex acoustic problems, sometimes giving to them answers which have after- ward been found logical and demonstrable. It wa> onK during the intense scientific activity of the latter half of the nineteenth century, however, that a reallv competent exposition 'of the subject appeared. Tn 1862 the distinguished German scientist Helmholtz (1821-1894) published his epoch-making work on The Sensations of Tone. This was supplemented bv the labors of other enthusiasts, such as Tyndall (1820-180,3) in England and Koenig ( 18.32-1901 ) at Paris. 1'}- interesting and convinc- ing experiments these men succeeded in clearing \\p m_\-steri(nis points which had bahfied the wits of sages for centuries, and in bringing to light manv facts destined to aid immea. music. Idle fundamental ])ro|)osition upon which all these researches rest is that the physical basis of sound consists in a form of motion. This fact is so patent as scarcelv to need ^ . t ' - Sound a form further dcmon>tration : we can easilv observe the °^ motion, whirring of thiC \iolin string a< it is agitated bv the Ikuv, and SOCXD. AM) ITS Rl-LATIOX TO Ml'SIC can feel the trembling of the bell after it has l)een struck by the clapper; nevertheless, a few simjile experiments nia\- still further attest its truth. Let a pith ball be suspended so that it hangs close to one of the ])r()ngs of a tuning-fork. (big. 1.) Jf now a A-inlin Ixiw c f c ^u- I't; drawn across the fork so as Proofs of ttiis from sounding ^,, i)roducc a toue. tlic ball will tuning-fork and ' ^'"■'"s- be thrown \iolently to one side. and will be repeatedly re])elle(l whenever it rebounds against the fork, thus showing that the fork is in a state of agitation while sound- ing. ( )r. let a chalked string be suspended over two bridges ./ and B (Fig. 2) in front of a blackboard, with one end of the string wound about a pin at C. which can thus regulate its tension. If the string be now plucked in the middle, its vibrations will be seen ])lain1y. and ^'"- '■ when the tension is increa>ed by ttirning the pin ( '. the^e vibrations will become still more rapid. liesides taking its rise in the motions of solid l)odies. sound ma\- also be prc^duced b_\- the shock t)ccasioned when a liberated gas comes violentlv into contact with Sound from ... , ' . Kases or from the au' ui au ex])losion, or even bv the confined air. ... , . ' . agitation of a se(|uestrated ])ortion ot the air itself, such as occurs in an organ pipe. -\n illustration of this latter phenomenon will be found on i)age 7S. bet us now return to our tuning-fork. Aflixing a little metal point to each prong and drawing thc>e ^ . ,. , points rapidlv over a i)iece of smoked bxammation of ^ ■ - ' glass while the fork is sounding. \\e produce a wa\v line, as in Fig. -v F.xaniining this line, we fmd that it is composed o{ regular curves which run alternatel}- to one side and to the other. Our deduction from this di-co\ery i> ^fews that each prong swings continuall_\- to and fro, in the the vibrations of a tuning- fork. SOr.M). .IM) ITS RliL.irioX TO Mr SIC 3 manner of a ])enduluni. Starting from a jHjint of rest, it is imj)ellefl b_\' the ^■iolin bow a given distance in one direction, where it becomes motionless for an instant. It then rebounds to its hrst position, and immecHatcl}- performs a simiUir e\'olu- tion in the o])])osite chrection. When it has again returned to its starting jjoint it lias made what is called a complete vibra- tion. If it should then stop, the air ^\■ould carry a single ex- ])losive blow to our ears ; but, impelled 1)\- the impetus which it has receix'ed, the i)rong continues to vibrate with ., . ,. '■ '^ Periodic les>ening force, until it returns t(j rest, or until ^''bration. the bow again agitates it. A number of vibrations of similar character thus occurring in regular secjuence are said to be periodic, and the sound which thev produce is of uniform pitch. Let us note that, in order to be capable of i)erforming such vil)rations. a bodv must pcx-^sess what is called elasticity, which means the power of rebounding to its original . ^ Nature of the position after some torcc has driven it to one property of . . - 1 • ■ • ■ elasticity. Side. An instance ot this action is seen m an ordinar\-, ela>tic banrl. W'c make u-c of this to hold objects together b\- the force which it C(^nstantl\- exerts after it ha? been stretched, and which, if allowed to do so, would snap it hack vigorouslv into its normal condition. 4 SOiWn. AXD ITS RIILATIOX TO MUSIC The vibrations of the tuning-fork which we examined were all simple: that is. they produced i)erfectl}- uniform cur\es on Tone and either side of the wavy line. As a matter of fnct, "°'^^- however, such simplicit}- is seldom founrl in the motions of a sounding Ijod}' ; for, as a general rule, these are accompanied h}- other vibrations of diiterent extent and rapidity, while sometimes a mingling of all sorts of motions takes place. The sound made !)}• the impact of the lingers upon the piano keys, for instance, is mingled with the musi- cal tones, as is the scraping of the violin bow acr()s> the strings, and the hissing of the air at the mouth of the organ pipe. When the vibrations are ])eriodic, and are cither ^-im])le or else accompanied b}" suljordinate vibrations which are in- distinguishable or have simple relations to the primal sf)und. the complete sound is said to be iiiiisica! in character, and its fundamental ettect is si)oken of as a tmic. According as the more complex or irregular \-ibrations become promment in the sotmd. does it lose in its musical value : and when all semblance (jf regularity has disapi)eared. tone \'ani-lic-. and the >t depend largelv tipon personal o])inion. When we incjuire, on the other hand, what kinds of ^Dunds are available for the use of the mu-ician. otiicr con.-ideration- c , ., arise. Mowever musical the tone, it must be i)Ut Sounds avail- ' able in music. jjif,, .^ jiracticablc fomi. The .-ound gi\cn out b}- the falls of Niagara, for instance, has lieen analyzed and found to have decided musical characteristics, -ince ii jjo^- sesses a stronglv-marked fundamental tone and liarnn iniou- accompanx'ing tones; but thi^ rich combination could hardl}' be intrcxluced into a musical com])osition. cxccjit b\ jirow. The sub-^titutes for an\- desired sounds of nature nui-^t be fi aind in either the human voice or artiticial nni-ical instruments. These latter have been de\-i-ed and elaborated to such an extent that the mridern comjio-er has at hi- command mo^t .it the socxn. ./AV ITS h'/iL.iriox to MCSIC 5 typical varieties of tone, each tlirous^h an adecjtuite compass of pitches. In his coni])o>itions. therefore, the musician makes use in the first i)lace of instruments hke the \-iohn, which can i)ro(luce tone i)ure in its make-U]) and steadv in its ])itcli. \' 1 1 1 • ' 1 - Types of .Next, ho\ve\er, lie emplo\"s >pecial means tor musical , . . ". , . . instruments. cm])hasizmi;' the element ot rlivtiiiii ; tor it niu>t be remembered that rcyuhir pulsation is as important a factor in musical structure as melodic beaut}'. Thus in>truments of l)crcus>ion are also necessar}-, in which an ex])losive sound mark.- off the dix'isions of time. Some of these instruments, like the kettle drum, have a distinct fundamental tone; while others, like the snare drum, give out merely a confused noise. Then, too, while the coni])()ser Ijases his work u])on conven- tional instruments, he feels at libertv to introduce those of a bizarre character, like the tam-tam, or queer elTects, like the rapping of the \'iolin bow on the wood of the violin, in order to express some extraordinarv conception. The sounds which he is least likeK- to em])loy are those which are unreliable in pitch, like tho.-e of the siren (page 26), since such sounds are subversi\-e of those dehnite intervals which form the sub- structure of music, and give to it stability For the present, we shall consider only those sounds which are produced Iw simple vibrations. We pass, therefore, to the discttssion of the manner bv Necessity for which these \'ibrations are a medium as a sound-trans- able to reach our ears, when mitter. Proof . . . . . of this. originating m objects en- tirelv external to oursch'es. (lenerally, the sound reaches us through the inter- vening air, and it can easily be shown that, while other media mav serve as sound-transmitters, a medium of some description must be employed for the purpose, and that without this, no sound can be heard. In SOUXD, .LXD ITS RELATIOX TO MUSIC Fig. 4 a bell 7", placed ui)on a plate that is connected with an air-pump, is kept sounding by means of a clock-work attach- ment // C'; and over the whole a bell-glass is placed. The sound at first continues with almost undiminished intensity, but as the air is exhausted by the pumi), the sound grows fainter, and when a practical vacuum is produced, it is in- audible. Care has been taken to place the clock-work upon a piece of non-conducting material, otherwise the vibrations would have been carried to the outer air by the plate itself. If, now, h}"dr()gen. which is fifteen times lighter than air, be admitted within the glass, a faint sound is heard. Hence we c(jnclude that the sound decreases as the medium through which it passes becomes attenuated. This latter fact has been further attested by experiments with other gases and vapors. Solids. altance, are enabled to hear distinctl}'. when the auditor\- nerve is unimpaired, bv holding an apparatus be- tween their teeth which catches the sound-vibrations from the external air, whence thc\- are conx'eyed to the ear through the intervening bones of the head. To understand how vibrations are imparted to the air b}- £ ^ounfling l.)od}', we must lirst remember that the air is com posed of an inconceivablv ».....4^....,,^ Action of a , ^ . , ' vibrating rod great uumbcr of particles or upon the air. ' . molecules, r(jughh- estimated as a million Ijillions to a cubic centimeter, or cube one side of which i< about three-eighths of an inch long. Placing a metallic bar . / -B in a vi>e E C ( Fig. 5 ). we set the free ])art ./ (" into a ])endulum-like motion by drawing it to one side at the ]:)oint .-l . If the free ])art has ijecn made long enough. we can easily see this oscillate from a to a'. and no -ound will be heard. The reason for this latter fact is that the vibrations are made so slr)\vl\- that the air-particles have SOUND, AND ITS RliL.lTfOX TO MUSIC time to slip out of the way before the onset of the bar. If now tlie free part be made gradually shorter, the vibrations will grow faster, and will linally be so blended together that they are indistinguishable. At a certain point, too, a low t(jne will be heard. This tone arises ivoni the fact that the air-particles no longer have time to avoid the bar as it approaches, and are therefore hit by it at each of its attacks. When the particles next to the bar are thus affected, they are thrown violently against those next to them, which in their turn transmit the impulse to their neighbors. This crowding together of par- ticles, or condensation, as it is called, now passes „, , ' ' i The wave of along rapidly from one series of particles to condensation, another in all directions away from the bar. Hut after the rod has forced together the particles which obstruct its passage, it immediately springs back in the oppo- site direction, leavins^ in its track a s])ace which _,, , o ' 1 he wave oi is rendered practicallv emptv of particles, and rarefaction. which is thus said to be rcrcficd. This wave of rarefaction follows immediately after that of condensation, just described. .Again the rod attacks, and an(jther wave of condensation starts out, succeeded as before Ijv a wave of rarefaction ; and these alternate conditions are repeated, so long as the rod continues to A'iljrate. The manner in which the waves proceed from the sounding object to the ear of the listener is graphicalK- portrayed in Fig. 6. One of the prongs of the tun- ing-fork here rep- resented produces vibrations in ex- actly the same wav as the metal bar which we h a v e taken as our model. In actual computa- Fig. 6. tions, a comi)letc r\ SOUND. .1X1) ITS RliLATlOX TO MUSIC sound-wave is made to consist of the sum of a condensation and a rarefaction. I lence the length of a sound-wave will be equal to the distance from any given point ... ... Action and m a condensation to a similar point in the length of a . p . . . sound-wave. next condensation, or irom a given point m a rarefaction to a similar point in the next rarefaction. It is important to notice that the air-particles, when thus acted ui)on, do not move permanentK- rrom their original ., . i.)ositions. If they were blown alonij 1)\- each The vibration ' - J5 . of air-particles, souud-wave, wc sliould fcci a draught of air with each "sound which reaches us. I kit tlie particles act much as do the blades of wheat when a breeze sweeps over the wheat-tield. driv- ing these aside only temporarily. in the case of the air-parti- cles, however, each performs a complete vibration for each sound - wave, corre- sponding to that of the sounding bod}-. 1 low this motion is accomplished can l)e seen by the use of I lie stand shown in I'lg. 7, invented l)y Alariotte over two hundred years ago. In this, an im])ulse given to one of the balls A travels through the entire line of balls, while each one is stoi)pcd in its course by the push which it transmits to the next. Only the end ball C llics olt to a greater distance, the others l)ccoming motionless. Thus does the sound reach the ear. while the intervening air ])articles return to th.eir original ])laccs unless again set in vibration bv the sounding body. Sound-waves arc also frc- (juentlv compared with the waves which arise Sound-waves ' . , , . , \ • i comnared with whcu a stouc IS drop])ed luto the water. As with water-waves. . . , , . , - •, air-particles, the water-particles i)erh)rm an oscil- n- - - 1 ! )i A )(■ x- )C ! i [ /- 1 y Fig. 7. latin"' lution, returning Pnallv to their normal places. lUit SOCXD. ,1X1) ITS RliLATIOX TO MUSIC 9 F--. 8. 10 SOUND, AND ITS RELATION TO MUSIC while the water-particles have an up and down motion, the air-particles move forward and hack ; and also, while the water-waves move simply along the surface of the water, the sound-waves swell out into the form of a sphere, of which the radius is constantly and rapidly increasing. Under ordinary circumstances sound-waves are impercep- tible to any of the senses except that of hearing. Heavy ,,. ... detonations, however, such as the roll of thunder Visible ' ' Sound-waves. ^j- ^j^g rcport of a cannou, can be felt as well as seen ; and in certain cases sound-waves have become visible. Professor C. \'. Boys, in 1897, succeeded in obtaining a series of kinematograph pictures of the explosion of a hundred and twenty pounds of a nitro-compound, taken at the unusually rapid rate of eighty exposures j^er second. In .-/^ of the first ten of these, shown in Fig. 8, .1 to J, the smoke of the explosion appears rising gradually on the right. In the series B to J the sound-wave, in the form of a light ring, is seen rapidly ex- panding beyond the smoke of the explosion. Professor Boys says, "We stationed ourselves as near as prudence would allow, at a distance of one hundred and tw^enty yards, so that only about one-third of a second elapsed between the detonation and the passage of the shadow. The actual appearance of the ring was that of a strong, black, circular line, opening out with terrific speed from the point of explosion as a center."* In the pictures the black line does not appear, but only the light ring which must have accompanied it. *See articles by Professor Boys in Nature for June 24. lcS97, and by Prof. R. W. Wood, in Popular Science Monthly for August, 1900. SOUND, AND ITS RELATION TO MUSIC 11 SUMMARY Sound is always produced 1)\ the vibratory motion of particles of matter, either in a mass or as individuals. Musical sound, or tone, is produced by regular and periodic vibrations, and non-musical sound by irregular vibrations ; but the lines of demarkation between the two are not sharply drawn, and the musician may employ for special effects many kinds of sound usually classified as noise. Some medium is necessary for the transmission of the sound from its origin to the ear of the auditor. This medium is generally the air, in which the sound travels in waves, each consisting of the sum of a condensation and a rarefaction. In this transmission, the air-particles also move in vibra- tions. The sound-waves form a constantly enlarging sphere; and their motion is generally perceptible only to the sense of hearing. REFERENCE LIST. Helmholtz, Chapters 1 and 2. Zahm, Chapter 1. Tyndall, Chapters 1 and 2. Taylor, Chapter 1. Broadhouse, Chapters 1-4. Harris, Chapters 1 and 2. Catchpool, Chapters 1 and 2. Stone, Introduction, and Chapters 1 and 2. Poynting and Thompson, Chapter 1. Blaserna. Chapters 1 and 2. Barnes, Chapters 1 and 2. Barton, Chapter 1. Lavignac, Chapter 1, A. CHAPTER II \"elocitv, Rkflection, Rkiractiox and Diffraction'. Till- rapidil}- with which sound is transniilied through any medium is dependent upon two factor.-, the one of which is „ tlie dciisitx of the medium, and the other its Factors affectms clasticitx. (Jf the.-c, the former tends to retard, velocity 01 ^°""'^- and the other t<.) accelerate the sound. W c have stated that aU matter i> made up of a vast cjuantitv >mall particles, ihe numher (ji tlvjse present „ ,. . , in a gix'cn hulk of matter is said to con-titiUc its eondition ot '^ ^■^"^■'y- dnistty; and this density hucomes greater or kss according as the number of ])article> increase.- or dimini-hes. A change of condition or locaticm. howe\"er. ma\- attect this numher to ,-i considerable degree. We know. iis cler.-e ( or more rarehed ) than that in the \alle_\- beneath. d'hriju^h this ma-> of particles the sound-wa\es proceed at a rate which, though c.xtremcly ra])id, is \et ea.-il\' aiJprecialde ,. ^ . b\- the .-cn-e>. We have all. when -eaterl in the Light faster than sound. ^^.^y ,,f -^ large concert hall, noterl how the beat^ of the orchestral condtict' ir seemed curiour-l_\" to precede the sound.- which lhe\- e\'okcd.. This illusion ari.-cs froiu the same princi])le wdiich causes ihc lightning;' tia-li to be \"i-iblc some- times many .-cco'Uils before its accompanying cra-h of thunder is audible: namel\-, that li^ht trax-e^- r.iu di .'a-!i_-r tlijin -ound. The \-elocitv of liglit. c^imoule'l ;:t ;.i..iUL l'- M'J'il niiles per flash of light. 71-,]^ f-i^;!- ,^.,,jy iherefoi-e be u-e'l \< < aflxTintage in determining -()iuKl-\'elncit\". Let a cannon be tired at a known distance, and the time which elapses lietwcen the tiash anri the report be recMrded. Evidently, if the entire distance be divided SOUND, AND ITS RliLATlON TO MUSIC 13 by the ascertained number of seconds, the result will be the distance traversed in a single second, which distance is gen- erally used as the unit of measurement. l'\)r purposes of extreme accuracy, however, this exjjeriment nuist be conducted with much more care. Several disturbing factors, the chief ones of which are the wind, the ,, ' ' txperiments tem])erature, and the moisture, are almcjst inva- °'^ ''^'^ •'^^'^• riablv to be reckoned on. The most important of these is the wind, which carries the sound faster when it is moving in the same direction, and retards it when the directions are in opposition. In the first accurate experiments tipon the velocity of sound, made by the French Academy of Sciences in 1738, cannon were fired at three stations visible from the Paris Observatory, but at some distance away, a report taking place at one of the stations every ten minutes. The time-intervals between the flashes and reports were recorded and afterwards a^'eraged. In a similar experiment, in 1822, it was sought still ftu'ther to eliminate the inflttence of the wind by firing cannon alternately at each of two stations about twelve miles apart. The time for the light and sound of each report to reach the opposite station was noted, and the mean between the figure arrived at by each set of observers was finally adopted. In subsequent experiments even more pains were taken to secure exactness, such as the employment of electrical devices to record the arrival of the flashes and reports, in order to elim- inate the slight error arising from the portion of time necessary for the observer to realize and then record the sensation received. The velocity of sound thus determined was found to be 1090 feet per second when the temperature of the air was at the freezing point. This velocitv increased, how- „ , * ' - Resultant ever, with a rising temperature, at the rate of figures, about a foot for each degree Fahrenheit. Consequentlv, at the ordinary temperature, 1120 feet per second may be re- garded as sufficiently accurate for rough calculations ; a speed nearly thirteen times as fast as the fastest express train. 14 SOUXD. .-/.\7) /7.S- RRLATIOX TO MUSIC If the number of seconds between the perception of a Hght and its sound be nuiltipHed by this velocity per second, the Determination ^esult will evidently be the distance of the sound- of a^loundtnr '^^^ object. W'c may thus estimate the distance ^°'^y- of a lightning discharge by counting the number of seconds between the flash and its accom])an}ing peal of thunder, and allowing something less than five seconds to a mile. Uefore the above exi:)eriments had taken place. Sir Isaac Newton (1642-1727) had calculated sound-velocity bv labora- torv methods and had secured hgures about a Verification •1111 by different sixth smaller than those we have given. It was experiments. . . atterward discovered, however, that the sound- wa\-es themselves produced a slight rise in temperature which effected this dift'erence. Other experiments at short distances and of a more complicated character have served to verify- the accepted figures. Father ^lersenne (1588-1648) calculated sound-velocity b_\' noting the time which it took for an echo (page 19) to reach him. and the distance of the reflecting object. Velocity calculated from As the souud must travel to this object and back echoes. . . . ,, ... " . . , again, it tollows that a division ot twice the distance of the object bv the number of seconds recjuired for the echo to return will give the velocit}' per second. It is hardl\- possible, however, to sectire extreme acctiracy by this method. While a variation in temperature i)r<)duces a corresi)onding variation in sound-velocity, it is nevertheless trtie that the velocity remains the same, however much the Effect of , . . , . ^ ^,., varying den- density of the air may nuctuate. 1 he cause ot this phenomenon is that with an increase in the densit}-. there is an exactly proportional increase in the elas- ticity of the air; hence the ratio between the two factor'^ remains constant. As a general rule, too, whatever the pitch or other char- acteristics of the sound, its velocity is the same. If this SOUA'D. AXD ITS RliLATIOX TO MUSIC I J were not true, we should hear sounds at a (lis- ,,,.,• ' Velocity in air tance in varvins: order from that of their pro- "°* affected by '-' i character of duction, and the music from a brass band, for sound, instance, would reach us in inextricable confusion. it has been pretty well proved, however, that extraordinarily l(jud sounds may have an increase of velocity over those of ordinary intensity. An interesting example of this exception was afTorded on one of Parry's arctic voyages, in 1822, when, at a distance of two and a half miles, the order to hre a cannon was heard after the report. In other media the velocity of sound is frequently much dififerent from what it is in air. Experiments made b\- means of long ttiljes and organ pii^es have ])roduced ,, , .^ . " oil t Velocity in the following rates per second in gases, at the sases. freezing point of air, or 0° Centigrade : — Oxygen 1040 feet Hydrogen 4164 feet Carbon dioxide 858 feet Carbon monoxide 1 107 feet Xitrous oxide 859 feet Olertant gas 1030 feet Important experiments as to velocity in water were made by two French physicists in 1827, on the Lake of Geneva. Sta- tioned in boats on opposite sides of the lake, one velocity in of them took charge of the sound-production. I'^^'ds. while the other recorded the results with a stop-watch, listen- ing through an ear trumpet M (Fig '-• ) . held in the water. The source of sound was the bell C struck vj by the hammer B. J The lever which im- -I pelled B simultane- 2i ously ignited a flash Fig. 9. of gunpowder by the Gr 16 SOUND. AND ITS RELATION TO MUSIC torch -1/. It was thus found that the velocity of sound in water at 8.1° C. was 4,707 feet per second, or more than four times what it is in air. Different figures have resulted from experi- ments with other liquids, though the increase of velocitv over that in air is considerable in each case. The reason for this fact is that, although liquids are more dense than air, their elasticity is still greater in proportion. In most of the solids, the same conditions exist. In metals, the velocit}- varies from four to sixteen times its rate in air. ,, , .. . In wood, the velocitv is greater in the direction Velocity m ' . ti ^°''^^' of the fibre than across the rings. In the former direction, it varies in different woods from ten to sixteen times its rate in air. The greatest velocity is found in iron and steel, of the metals, and fir and as])en, of the woods. It should be noted that an augmentation of temperature, which increases the velocity in gases and liquids, has generally the opposite efifect upon the velocity in metals. Wood is an especiallv good conductor of sound. To illus- trate this characteristic, wrap up a music box in several -, thicknesses of felt, a non-conductor of sound, so Experiments with wood. ^]^^^ ^]^Q sound is made as nearly inaudible as possible. If, now, the end of a rod of wood three or four feet long be inserted in the wrappings and rested on the lid of the box while it is playing, the sound-vibrations will be plainlv felt along the rod by the hand, and, on a})plying the ear to the other end of it. the music will be heard with greatly increased intensity. Place a guitar or violin against the free end of the rod, and the vibrations will be tran.-mitted to it, so that the music seems to proceed from this instrument. .\nother instance of the passage of sound through solids is afi'orded b\- the familiar string tcleplioitc. which consists of two cardboard tubes, each ha\ing one end c< 'V- Experiment . . ' , , . , with the string crcd bv a piccc of parclimcnt, tlirouiii'i wnicli telephone. ' . . , . , . pas>es a connectmg strmg. Words wlusjxTcd m one tu])e will be carried to a considerable distance through the string, and will reach the ear of the listener, jilaced at SOUMJ. .IND ITS RliLATIOX TO MUSIC 17 the outer end of the other tube, with almost unchminij-^ed intensity. In free air, sound-vibrations sometimes travel to very great distances. Instances are narrated of occasions when tre- mendous explosions have been heard for from - , , , . • . Travelling tive hundred to seven hundred and nftv miles, power of 1 • 1111 1 1 ■ 1 r • •" sound. it is probable that the earth itself assists m carry- ing these vibrations; l)ut Chladni (1756-1827) tells of hearing the sound from meteors the bursting of which indicated that the\- were a hundred and twenty-five miles in altitude. The amount of air affected bv even slight sounds is sometimes enormous. Darwin speaks of crickets whose stridulations can be heard at night for the distance of a mile. In such a case, it is calculated that from five to ten million tons of matter are affected by the noise produced bv an insect w^hich weighs about a quarter of a pennyweight! But sound rarely travels far without encountering some obstacle ; and we now proceed to investigate what then hap- pens. Sound is found to be subject to the same ^aw of laws as are light and radiant heat, in that it reflection. sufTers partial or total reflection. Let a sound produced at A (Fig. 10) strike the reflecting surface D E 2.t the point B. making with it the angle .'/ B /:. The sound-wave wmU re- bound in the direction of C, and the angle C B D will be equal to the angle . / B E, fol- ^'^' ^°" lowing the law that the angle of incidence is always equal to the angle of reflection. To demonstrate this law, take two long glass or cardboard tubes .1 B. and arrange them as in Fig. 11, with a flat card placed as a reflecting surface at C. Put a „ , ,. I o Demonstration watch in the end of tube .1. covering the open- °f t^^'s law. ing with cloth so that the ticks are muffled. Ijy listening at B, it will be discovered that the ticks are loudest when the 18 SOUND, AND ITS RELATION TO MUSIC law of incidence and reflec- ion is coni])]ied with. Sub- stitute other surfaces for the card, and compare their reflective power. Xote that even a flat, or fish-tail, gas- flame will produce good results. P'g- ''• The sound-wave, meeting a fiat surface, immediately changes its course, and travels as thotigh it came from the opposite tlirection. In h'ig. 12, the wave, striking the Progress of a .^ , ^ sound-wave in surface . / B at right angles, returns as if it had reflection. . . ^, " , \ • , ^^ r ongmated at U ; and the smgle rav O I pro- ceeds towards M, where it is heard as though coming from O' Curved mirrors, like those at .1/ and .1/' ( Mg. 13). have the ])r()pcrt\' of Experiments with curved rCUCCtrng par- mirrors. allel rays of either light or sound to a single point called the focus, nr, converselv. of reflecting |i Fis. n. SOUND. AXD ITS' RRLATIOX TO MUSIC 19 the rays from this focus in parallel lines. If a watch be suspended at the focuo /■ of the mirror .1/ ( h ig. 13), and the l)arallel rays of sound reflected from .1/ be concentrated on the mirror .1/'. the ticking of the watch will be heard distinctly at the focus /'"', sometimes as far as two or three hundred feet from the watch. Sound-reflection explains the familiar i)hcnomenon of the ccJu). Objects having- flat, plane surfaces are best adaj^ted for this reflection; and according to the distance „, •^ Phenomenon from the speaker will thev gi\'e back one or ukm-c °^ '^ '^'^^°- s_\-llal)]es. An oljject distant about 110 feet, for instance, will return one syllable onl\'. while an object distant 220 feet will return two s}'llables. one 330 feet away three syllables, and so on. If these echoes themselves hit other reflecting surfaces, a second echo is produced, and sometimes this process is repeated as long as the vitalitv of the sound la-^ts. The result is a series of reverberations, such as those in the cry])t of the Pantheon at l^aris. Cases are cited where an echo has repeated the same sound as manv -as fortv times. Mountainous regions, notablv the canons of the Rock Mountains, are especially suscei)tible to echoes. In large domes, like those of St. Paul's in London or the Capitol at Washington, the phenomenon of "whispering galleries" is frequently displayed. Conversations ma\- be carried on in these l)v two persons cl()se to the wall on opposite sides of the dome, which are inaudible to others only a short distance away. Idiis effect is generally ascribed to a multiplicity of cross-reflections; although some physicists assert that the sound-wa\-es under these conditions are not reflected, but run along the wall, just as water- wa\'es follow the outline of a l)ank when they strike it at a small angle. When sound-waves are reflected by surfaces onl_\- a few feet away from their origin, the tendency is to produce confusion. If the pulses of densitv e.xacth' or nearlv coin- „ . ,■ ' ... Kenection at cide in sounds thus mo\ing in opposite directions. ^'^°''' distances, the result is an increase in intensity; but if the condensation> of the original sound coincide with the rarefactions of its 20 SOUXD. .IXD ITS RELATIOX TO MUSIC echo, the result is a neutralization of both, and a consequent obliteration of the sound (page 41). Considering, therefore, the manifold j)ossibilities for con- flict of reflections, it is not surprising that the acoustics of . . , concert-halls present ])roblems which have thus Acoustics of ' i concert-halls. fj^j- proved iusoluble. For musical purposes, a certain amount of sound-reflection is necessary in order to ffive life to the tones; but unless this reflection l)e admirably Fig. 14. adjusted, confusion will occur in certain parts of the audi- torium, or a silence co)ie may exist, such as that depicted in, Fig. 14. In halls which have confusing echoes, resort is frequentlv had to deadening draperies, or to wires so stretched as to disperse the conflicting sound-waves. Let us note that the resonance of the reflecting object some- times afi:'ects quite decidedly the quality and power of the ^ echoed sound, and occasionallv also its pitch. Kesonance as a •- ' factor in echo. Discussiou of this phenomenon is reserved for Cha])ter \'I. That a flat gas-llame (page 79) ma_\' also reflect sound is onlv an instance of an effect which may be produced by any gas or even an}- air-current of a temperature Reflecting different from that of the surrounding atmos- power of gases and air-currents, plierc. The rc verbcratiou of thunder is thus rog signals. ' caused not onlv b\- echoing clouds and solid obiects, but also by varying currents of heated air. Tyn- dall proved In- an elaborate series of experiments that air- currents were responsible for the great variation in the SOr.M), .IXD ITS Rl-LATIUX TO MUSIC 21 distances at which tOg-sij^nals could Ijc lieard on different occasions. Sometimes, owing t(j these invisiljle reflectors, the signals could he heard onl\' a short (hstance on a perfectly clear day ; while at other times, when the air was filled with moisture, the distance which the sound traxelled was >uri)ris- ingl\- great. The loudne>s of sounds at night, too, is largely caused hv the ahsence of the air-currenls which are more likel_\- to occur during the da}' time. Speaking trumpets and ear trumpets involve ])ractical appli- cations of the laws of reflection. In the former ( I^lg. 15), the sound in emerging is conx'crted into parallel ^ i- ^ •^ '^ 1 speaking and ra\s. just what part the hell-sha])ed end i)lays ^^r trumpets. in producing this result is not well known. In the ear irtniipct the re\-erse ^'°- ^^- process takes ])lace. since the waves from the outer air hecome reinforced in the tuhe of the instrument, and thus reach the ear in greater vf)lume. Sound, like light, dex'iatcs from its cour-e w-hcn it enters a medium of difl:'ercnt den-ity. This phenomenon is called refraction. In an a])i)aratu> designed hv Sond- .^ - Demonstration haus (1815-18X6), shown in I^g. 16. carhonic- of refraction. acid gas forced into a rul)])er hag J, wdiich is supported in a Ijroad hrass ring ()' gi\es the bag the form of a dou- hle convex lens. We c a n demonstrate the fact that a sound })roduced at .S' comes to a focu< just below B by strewing sand on a membrane at the 22 SOUXD, AXD ITS RELATION TO MUSIC B> ! i ! to]) of the box B, since the sand will dance about under the in- fluence of the sound when the lens is present, but will remain quiet when the lens is removed. 1 he focusing takes place b e c a u s e t h e / ^ sound-waves, on entering the , , '^ denser gas. be- come flattened, and when they emerge the por- tion o f the waves at the edges thus come to precede the interior portion, as in I""ig. 17. hnallv concen- trating at B. When a large object intervenes l^etween a sound and the auditor, the soimd loses in its intensity, and it mav be quenched , , , entirelv. if the object be of sufficient size. The Sound-shadows - •' and diffraction, name of somidshadoic has been applied in this decrease. l)Ut if the o])posing object be small, the sound-waves are bent around it. just as the water-waves dash around a small rock. This phenomenon is called diffraction. In cases of tre- mendous explosions of dynamite, it has been found that windows on all sides of houses in the path of the sound-waves were forced in : a result which is explained by this proj^erty of sound. If we listen to a railroad train as it dashes through tunnels and behind hills, the different grades of the sound- shadows will be apparent. SOUND, AND ITS RELATION TO MUSIC 23 SUMMARY SoiTNH travels in air at the rate of 1090 feet per second vvhen the temperature is at the freezing point, and one foot faster per second for each degree of rise, Fahrenheit. I he velocity is tlie same, whatever he the densitv of the air. Sound-velocitv varies much in its rate in other media. In metals and wocxls it is several times as great as indicated in the ahove figures. Together with light, sound possesses the power of reflection, refraction and diffraction. In reflection, the angle of incidence is always equal to that of reflection. Reflection gives rise to echoes and reverbera- tions. Smooth surfaces and even gases and air-currents are good reflectors. By refraction, sound-w'aves can be driven from their course, and brought to a focus. In diffraction, sound-waves are bent around objects of small size. When the opposing object is sufficiently large, a sound- shadow occurs. REFERENCE LIST. Tyndall, Chapters 1. 5, 7. Zalivi. Chapter 3. Catchfool. Chapters 3, 8. Harris, Chapter 2. Blaserna, Chapter 2. Stone, Chapter 2. Laz'ignac, Chapter 1, B. Poynting ami Tho})ipson, Chaptei* 2'. Barnes. Chapters 10, 11 Barton, Chapter 10. Broadhouse, Chapter 2. Taylor, Chapters 1 and 7. CHAPTER III As we walk along a cc)untry road and flirect our attention toward the various sounds wliich reach our ears, we can. as a general ru;e, draw fairl\- accurate inferences Inferences from .... . ' different as t(j tlieir ongms. We conchide that a shrill. sounds. . . . pipmg note is produced hy a hird i)erched on a near-h\- tree, and that the low. droning sound conie> from a distant waterfall. Another low. hut more rasping sound he- tokens the ])resence of a -aw-nhll : and from its direction and degree of intensit\- we assign it a position clo-e to the water- fall. Since we are immediateU- ccmscious of the acuteness of the bird-note.< as compared with the gra\'itv of the tone of th.e ~, .. waterfall, we distingui-h between the two >ounds ihree properties ' °^ sounds. priiuarily h\- their dilTerence in pitcii. I'-ut Ijefore we can separate the tone of the waterfall from thai of tlie saw-mill, we must note their ditterence in qiialitx. since their pitches are nearl\- alike. h'inall_\\ we conclude that the hirrl is clo-e at hand, hut that the other two objects arc a nhle (.»r mcjre awa_\\ froiu the pro]iortional hniducss with \\hich the indi- vidual >ounds reach us. d"he>e illustrations are cited a> ex- amples of the three ])ropertics of pitch. Icita'ncss and (luality which all >ounds ]xjs>ess. and which we now ])roceed to investigate. Referrmg to b'ig. .^ ' r'agf h\ we recall that the \-ibration> of the metal bar were distinguishable, licfore the\- produced a tone. \\ hen the Itar wa< sutticienih- >hortened Pitch fiependent . . , . on vibration trif the oscillations to gi\'c out a souud. iK.nvever, number, . . ' , . . . the toriuer were ^-o fast that thev ki-t tiieir md;- A'idualit}' : and, a- the bar was further .shortened and the :-ou!id con>e(|ueinl\- rij-e in ])itch, the \ibrati(jns Ijlended together comjdetel} . Similarh'. if a violin strmg be plucked in the SOUND. AND ITS RllLATION TO MUSIC 25 middle, the whir of its vibrations is visible ; but when the string is shortened and the pitch accordingly rises, these vibrations are seen to be much accelerated. From numerous experiments of this character, it has been proved that the pitch of a sound depends on the number of vibrations of the sounding body: if these increase the pitch rises, and if they decrease the pitch falls. To determine the exact number of vibrations which a sounding body makes per second, a number of devices have been employed. The distinguished astronomer . . . Devices for (ialileo (1564-1642) found that in passing a determining the . number of knife-blade over the milled edge of a com a vibrations. . . Savart's Wheel. sound was produced which rose m pitch as the knife moved faster. A machine for measuring sound based upon this princijile was invented by Savart (1791-1841). As shown in V\g. 18, this consists of a cog-wheel B, which can be ro- tated rapidly by means of the wheel ./, connected with B by the l)elt D. Fig. 18. savarfs Wheel. If a Card be placed against the cogs at 7: and the wheel turned slowly, a tap is heard each time that a cog releases the card. With an increase in c[uickness a M)und is heard; and b_\- noting the number of revolutions of B per second and multiplying this by the num- ber of cogs on the wheel, the \'ibrati the top of a hollow chest A .-/. from which wind, Fig. 19. C;i.t;n:iir(l-I.,.itonr's .siren. entering through the tnhe B B. is forced in puffs that are emitted simultaneotisly from all the holes. \vhene\'er these coincide. Tims if there he twelve holes, as in the drawing, e\'identl\- twel\"e of these comhined ])utfs nuist occur at each revoltition of the disk. The holes are cut slant-wise in opjK^ site directions, as sliown in the lower right-hand drawing, which is a section throtigh // // in the ujjper right-hand figure. \'>y this means the stream of air is made to turn the disk, as well as to ])ro(lttce the sotmd-jmffs. A screw thread / moves a meclianism which registers the results on a dial .■: c. When the instruiuent i< set in motion, tlic di^k. revolving SOUND, AND ITS RELATION TO MUSIC 27 slowly at first, gives out a series of detached puffs As these quicken, however, a low sound is heard, which ,, . ,, ' ' ' ' Use of the rapidly rises in pitch. To test the number of s'""^"- vibrations of any other sounding body, therefore, the siren must be made to gi\e out a constant tone, in unison with the one that is tested, just as was the case with Savart's wheel; and the frequency is then announced on the dial. With both of these instruments, however, the difficulty con- , . . . , . , Difficulties in sists m keepmg a given pitch constant, since the connection slightest deviation from this constantlv vitiates the results. Helmholtz partly remedied this defect by using an electric motor to run the siren, in place of the irregular wind supply. A graphic method, which is capable of giving very accurate results, employs a style attached to a tuning-fork, as in Fig. 3 (page 3), except that the tuning-fork is .^^^ ^^ ^^^ made to write its story upon a revolving drum method. T T, shown in Fig. 20. This drum is turned by the shaft A b. After the drum has thus been kept in motion for a Fig. 20. 28 SOUND, AND ITS RELATION TO MUSIC given time, say two seconds, the number of vibrations recorded during this time mav easily be counted. Scheibler (1777-1837) made an instrument called the tonometer, consisting of a series of tuning-forks the vibra- c , -. , , tions of which differ bv a small and eriual bcneibler s - ' tonometer. number, through the compass of an octave. In order to test a given pitch by means of this, it is onl\- neces- sary to compare it with the tuning-fork nearest in unison with it. Koenig afterward constructed on this ])]an a (/rand tonomctre iDik'ersal, which covered the entire range of au ' ' Absolute heard. Prima facie, one possessing this gift p'^*^^- should have other qualities of a musician : although this result does not always follow, just as absolute pitch is not by any means an universal or even a common possession of musicians. Since our system of notation employs the same letters, from A to G inclusive, for each octave, it is necessary to indicate more specificallv which octave is meant when f , ," ... ,.-,.. Distinguishing one ot tliese letters is designated. Scientists names of the octaves. use the signs C_2, C-i, Ci, C,, Cs, C4, C5. Co, C7, &c.. 30 SOrXD. .-IXD ITS KHLATIOX TO MUSIC o f which C ^ is the treble C '^-°^^. and the others are the Cs in both directions from this, at octave distances. A system more commonly cmployerl by musicians, and the one which \ve >hall u>e in our discussi(Mis. designates the scale notes as follows : Two-lined Three-liired D K Still lower octaves are indicated bv adding figures below the capital letter- (C, ^n^' '^""-^ higher ones by adding to those ab(.)ve the small letters ( c"'. c''. c\;c. ). .\> jiitch can be measuredi so accurately, one would expect that the advantages of an uni\-ersal standard would cause the „, immediate a(k)i)ti(in of such aii one for all i)ur- rluctuating ' ^ pitch-standards. |„,^es. I'.ut tlic facts sliow f|uite Contrary con- ditions. a> will be understood b\- consulting the table on the oppo-iite ])age. which indicates some of the fluctuations of the pitch-standard since tlie \"car 1 oOO. .V o\'er the lirst colunm shows tile rise in ])itch fri^m the ideal bjwest in ,-emitones and hundrecltlis of semitones, while tmder (/' in the second colunm are gi\'en the numi)er of \il)rations of a' in the stated cases. Owing chiefl\' to the de.-ii"e of leaders of bands and orchestras to produce ])rilliant etlecl-. the jiitch ha> gradtiallv risen frcim the time of Ilandel and Mozart, so that ncjw singers are com- pelled to render compo>ilion- of that jx'riod more than a semitone lugher than was originalK- iniendcd. to the disad- vantage of boih singer and coni])o>ition. A number of attem])ts ha\-e l)een made in recent \ears to secure uniformitw As the result of -everal con\-entions of piano an}ial /'itch, identical with llie f'rench Diaf^ason >ioniia! SOrXD. AXD ITS RliLATIUX TO MUSIC 31 u X ■f.rr-Z.r.-r- ■ O — 'n — X ■f.'ij'Z ■ s' / t: •/. '- '-^. '^^ [ ^ XX - o c X X t^ OC X vi s £ - - : --- -^J- -r 4 -T -T ir. in 1 , X '— .£ o -r -r -T T -r -r t -^ ir, .o ir. 'J- C ~ 1 "". "-. r ; -> -T I -TOO r--; -^ rW (^ '^ -^' ! V T ' iy-i r^' r^ 32 SOUND, AND ITS RELATION TO MUSIC of 1859, which has a'=435. ^lodern orchestras and mihtary bands, however, generally employ the higher Schcibler Stutt- gart pitch of 1834, by which a has 440 vibrations. Physicists, for the sake of ease in computations, take as pitch-basis the theoretical limit of audibility, giving C =16 vibrations, so that Q^32, C=i64. r=128, and c'=^256 vibrations. From these figures o'=426.6, a standard considerably lower than either of those just cited. In the earlier centuries of the Christian era, when music was almost exckisively vocal, the tones employed were restricted „, . , to fifteen or twenty, arranged diatonically in the The musical .' ' fe> .; compass. middle register (page 94). With the advent of chromatic notes, however, and with the greater latitude which followed the extended use of instruments, the compass rapidly increased until it finally embraced all the tones from the limit of audibilit}- in the direction of grave sounds to those sounds which are so piercingly acute as to be unavailable for artistic purposes. The ])iano now begins with .1 of about 27^> vibrations, and continues to c^' of 4224 vibrations. In the orchestra the lowest note, rendered by the contra-bassoon, is C of about 33 vibrations, while the highest is es in exact proportion as the string is sh(jrtene(l, or, in mathematical terms, the number of vibrations is in inverse proportion to the length of the string. Let us next make the weight P e(|ual to one jjound. and a-ccrtain the viljration number of /' K at this tension. If we then increa>e the weight until this \'ibrati(>n num- cerning the i)er is (loul)ie(l. wc shall tind tl'ic weight cciual to tension. . . . ' • • i tour [)ounds. Likewise t(j trcijle the original sihratidii number requires a weight nf nine pounds, and to qtiadruple it one of sixteen pounds. Therefore, the weight mu>t e(iual in pounds not the number hv which the original \ibrations ha\-c been multi|)lie(I. but the square of that number. Thu- two times the original number C)f \-ibrations is produced 1)\- a weight 2x2 the original one, three times the original vibration number b_\- a weight 3x3 the cjriginal one. and so forth. Hence, coiuerseh- stated, the number of vibrations per second of a string varies directly as the square root of its tension. Again, if the two strings of the sonometer be gi\-en the >ame length and tension, and one is twice as thick as the other, the 3. That con- latter will \ibrate twice a> fast as its companion; cerning the . . ... thickness. and. Ill general. an\' increase m thickness occa- -i(jn.s a corresponding decrease in the vibration number. Thus we ma\- assert that the number of vibrations of a string varies in inverse proportion to its thickness. L'pon these three laws i> ba-ed the con-truction of all stringed instruments. In those like the \'iolin, where the strings ^, , are few and the tension-strain is not great, strings Observance c-i ^ ^ these laws in -^n ^^f ^\^q .same length are u-ed, while their i)itch instrument '^ '^^'''"g- is regulated by their thickness and tension. In the man\'-stringed ])iano and harp, howex'cr. the strain is made more nearlv equal by shortening the strings as the_\- ascend in arulenes.s, as well as b\- diminishing their thickne.ss. Thu- the short tine wire of the high tones is replaced in the lower ones b\- a hea\\- wire several feet in length and further weighted by :i\\ encircling wire-coil. sorxD, jxn its rjslatiun to music 35 'I'lie inslrunicnt maker must also remcml)c'r that the laws of >irings apply strictly only to the ideal string detined b}' physi- cists as '"a perfectly uniform and flexible Idi- ., ,.^ . i . Modifications ment of solid matter >tretched between t\v(j tixed °^ ^^^^^ '^'^^• points." As there are always imjjerfections in actual strings, especialK' in the (lirecti(jn of stiti"ness and lack of tmiformitx, the laws mu>t be somewhat mochtied to suit these existing conditions. 'J"liu>. when a string is divided intcj two e(|ual parts, each of these will be found a trifle flatter than it should be theoretically. ( )ther sounding bodies are subject to laws srimetimes quite different from those regtilating the pitch of strings. With rods, the i)itch rises verv rai)idh' as the vibrating jiart IS shortened, so that the number of vibra- vibrating rods and tubes. tions IS mversely proportional to the square of the length of the vibrating part. 1\ibes are subject to conditions more nearlv like those governing reserved for a following chapter. 36 SOUND, AND ITS RELATION TO MUSIC SUMMARY Sounds differ chiefly in respect to their pitch, loudness and quality. Pitch depends upon the number of vibrations which a sound- ing body performs in a given time. The vibration number per second of a sounding body is calculated in various ways, such as by Savart's wheel, I.atour's siren, the graphic method, and the tonometer. Sounds are audible for something over eleven octaves, or from 16 to 38,000 vibrations per second, although the sense of pitch varies much with different persons. Of these sounds only those of between 16 and 4800 vibrations are used in music. Standards of pitch have varied greatly at different times and for different purposes. Even now there are several standards in use. Pitch is unaffected by wind or loudness, but varies some- what when a sounding object rapidly approaches or recedes from the listener. Instruments are constructed in accordance with the laws of pitch, which have been ascertained with regard to the various kinds of sounding bodies. Those governing strings depend on the length, tension and thickness of the string. REFEREN'CE LIST. HclnihoUz, Chapter 1. Harris, Chapters 4, 9. Taylor, Chapter 2. Zahm, Chapters 2. 4. Lavignac. Chapter 1, A. Stone, Chapter 4. Tyndall. Chapters 2, 3. Broadhouse, Chapters 5. 9, Appendix C. Poynting and Tlionipson, Chapters 3, 6. Barnes, Chapters 5, 3. Barton. Chapters 1. 10. lUascrna, Chapter 4. Catchpool, Chapter 7. Pole, Chapter 3. CHAPTER IV Loudness, Interference, and Resultant Tones That the loudness with which a sound strikes our ears is intimately associated with the degree of energy with which the sounding hodv is vibrating is a matter of com- ^ * - ° . . Relation of mon observation. Pluck a violin string gentlv, intensity to ". amplitude. and the tone which results is weak. Pluck it harder, so that it oscillates violently from side to side, and a strong tone is heard. Again, strike a tuning-fork lightly, and observe the weakness of the tone which it gives out. A harder stroke, imparting added energy to the vibrations, will greatly increase the sound-power. Py a slight modification of the experiment shown in Fig. 3, the relation between the extent of vibration and the strength of tone can plainly be seen. Let the smoked glass be pulled slowly along, after the tuning-fork has been agitated, until, decreasing gradually in loudness, the tone ceases altogether. A narrowing white space on the glass is the re- sult, as exhibited Fig. 23. i" J^ig- -^^- ^^lii^'^i demonstrates that the width of the vibrations gradually diminishes as the tone lessens. The width of vibration is called its amplitude ; and physicists have formulated the law that the strength of the sound varies according to the square of the amplitude. Thus in the case of two tuning-forks ./ and B. of the same pitch, if ./ vibrates with an amplitude of one-fifth of an inch and B with that of one-tenth of an inch, the sound of .1 will be four times as loud as that of B, since it vibrates through twice the distance. It has also been found that sound-vibrations are subject to 37 38 SOUXD. AND ITS RELATION TO MUSIC the law which governs the vihrations of a pendulum, namely. . ,. , that within ordinary limits the number of vi- Amplitude -- and pitch. brations continues the same, whatever be the extent of the swing. Hence, increase or decrease in the amplitud3 of vibration of a sounding body does not affect its pitch, since the number of vibrations remains constant. In free air. the vibrations proceed from the sounding body in the form of an enlarging sphere. [Mathematicians have ^. , determined that the mass of air included within Distance and intensity. ^ yard's radius from the centre of a sphere is only one-fourth of that included within a two yards' radius. and one-ninth of that within a three \ards' radius. Hence. the sound-vibrations in traveling two yards from their origin must spread over four times the territory which they cover in the first yard alone, nine times the latter amount in travelling three yards, sixteen times in travelling four yards, and so on. A person at C, therefore (Fig. 24), twice as far awav as a person at B from the source of sound at . /, will hear the sound onlv one- fourth as loud, since it will have si)read over four times Fig. 24. the space. Stated as a law, then, the intensity of a sound in free air diminishes as the square of the distance of the listener from the sounding body.''' *The difference in meaning between the words intensity and loud- ness sliould l)e noted. Intensify refers to the energy of the sound-vibra- tions — a liliysical, measuralile quantity, while loudness refers to the sensation wiiich the Hstener derives from the auditory nerve after this energy has been communicated to it. Intensity and loudness are there- fore related as cause and effect. souxn, ,ixn its relation to music 39 Actually, however, the ettects of this law are much modified l)y disturbing elements. Striking; other (jhjects, s(jund> are echoed or reinforced ( pa^e VJ ) , and, when the\- ... .' Sound-waves originate near the earth, halt ot the sphere m confined to a .... tube. which the sound-waves tend to travel is e\'idently intercepted h\' the ground. 'Jdie more the territor\- over which the\' are allowed to spread is cfjiitracted h\- such mean-, the less does their intensit\- diminish ; and when they are ccjnlined t(j a tube, thcv ma\- travel for long distances with little loss of iniensit\-. since their f(jrce is expended onlv slightly h\- friction along the walls of the tube and by the amount imparted to these walls. The French physicist Regnault (1810-1S78), in ex])erinients conducted through the Paris sewers, was able to hear a pistol shot distinctlv for a distance of six miles when these sewers were made to act as a soimd-carr}"ing tube. Speaking tubes furnish an illustration of one of the practical uses to which this principle has been put. Since the impact of the air-particles is more direct as the air becomes denser, sound is then carried by them with greater intensity ; and. converselv, as the air becomes t^ •. , • ' • - Density and rarefied, its intensity is lessened. In ver\- ra'-ehed '"tensity, regions, stich as the tops of high mountains, tn^ modihcation of inten^it\' is so decided that the report of a pistol sounds scarcely louder than that of a hre-cracker under or(linar\- ci'"cumstances. As a general rule, sounds are heard with more distinctness at night. This phenomenon is onlv partly accounted for by the absence of confusing noises audible in the „ . , , '~ bounds louder daytime, and is ])robably due in a still larger ^' night, measure to the fact that the air is in a more homogeneous condition at night, since the contlicting heat currents induced b\- the sun (page 20) d() not then exist. A\diy the intensity of a sound is greater in the direction in which the wind is blowing has l)een a matter of considerable si)eculation. I'erliai)s the most i)lausi1)le tlieorv ^^ r ■ ^ ' 11^ Effect of wind i> the one which asserts that, as the air ])l(nvn "P°n intensity, along b\- the wind is retarded b\- friction where it touches tlie 40 SOUND. AND ITS RELATION TO MUSIC earth, the sound-waves are bent downward, striking the listener with greater force. On the other side of the sounding b(jdy the reverse process must take place, since the lower parts of the sound-waxes are less antagonized by the wind than the upper ])arts, and the waves are consequently bent upward, thus becoming weaker near the earth. In Fig. 25 is shown the action J AC Fig. 25. of the wind, which blows in the direction of the arrow, "hend- ing down the sound-wa\es from the vibrating bod\" C in the direction of / and inclining them upward in the opixjsitc direc- tion. Every inter\-ening oljject. such as that at ./ tends to increase the downward slope toward /. Sdund-intensitv is also much affected by the sympathetic vibrations of bodies other than the one by which the sound r> J is produced. This ijhenomenon is discussed in Kesonance and ^ ' intensity. Chapter \'I. Haxing considered the intensity of single sounrls. let us now inquire how this intensit\- i> affected when our original sound- waves come into contact with those arising frrnu Nature of the '. , phenomena of other Si lurccs. A vcrv Striking example ot what interference. , .. " ' . - then hap])ens is atlorded b\' tiie action ot xvalcr- wa\-cs. If we obser\e the ruffled surface of a lake, we ])ercci\c a great x'arietv of wa\'es. the smaller su])erim])osed (.n the larger in the form of ripples, those encountering others in their jiatli ])a-sing over tlieir con\-olutions. but each set of zciTc'cs f'rcscninii its idciififx so hnu/ as its oicray lasts. In SOUND, AND ITS RELATION TO MUSIC 41 the same way the condensations and rarefactions of diflerent sound-waves pass through those of other waves which they encounter, each keeping its distinctive character throughout. Finally, the ear has a wonderful power of selecting out the sound-waves which have periodic vibrations, and the mind, having perceived these varieties of wave-frequencies, proceeds to assign them to their respective causes with a considerable degree of accuracy. Hence, hearing a multitude of sounds at the same time, the hum of bees, the monotone of a waterfall, the rustle of the leaves, the lowing of a cow, the barking of a dog, we are able to distinguish between all of them, and to form judgments as to the character of their origins. \'ery loud sounds may, of course, blot out very soft ones. But even in the case of great disparity in intensity, slight sounds are sometimes perceptible, on account of their dis- tinctive quality. Thus a device for attracting the attention of an individual in the midst of the roar of mill machinery is to produce a light hissing sound between the -teeth. The various results which arise from the meeting of different sound-waves are classed under the head of the phenomena of interference. What happens now, when two sounds encounter which have the same vibration numbers? This phenomenon has already been noticed in connection w^ith sound-reflection . Interference of (page 20). Let us assume that two tunmg-forks sounds of the , . , . , ,. , same pitch. havmg the same pitch are soundmg at a short distance from one another. When their waves meet, one of SOUND AUCMtNTATlON BY CON RESONANCE BOX 42 SOUND. AND ITS RELATION TO MUSIC three results nuist follow : the condensations from the one fork may be added to those from the other and the rarefactions from the one to those from the other, in which case tlie sound is greatly augmented (, I'ig. 2()}; the ctnidensations from one fork may be imposed ujxm the rarefactions from the other RF-SONANCf. BOX Fio. 27. (Fig. 27). in which case thc\- neutralize each other, and the sound is nearh' extinguished; or. as is most frequent, ihc wa\es ma\- meet irregularl}-. at >ome ])oint between those mentioned in the llrst two cases, when the intensit_\- ma} var\- either one wnv or another, according to the point of coniacl. This effect of sound-interference is easil\- demon>trate(l be- holding a >ounding tuning-fork jKirallel to one ear. wliile the other is stopped b\- the linger. If now the fork Interference , , , ' - ". ... . , illustrated by a !)e >Iowlv rotated, tour ])omts will occur m the tuning-fork. " , . , , , . course of a re\'olution \\liere the sound i> ex- tinguished. The reason for these silences is explained when \\e reflect that at each time the ])r()ngs of the fork vibrate ''•._ outward the\- not onl\- form a ';., "' condensation b\- their impact. Init also ]ea\e behind a corropond- ing rarefaction, in the >pace be- tween them, .'^imilarl}-. on their o])j)o-ite swing, thev form a condensation in the central s])ace while a rarefaction is left m tlie outside air. Two sets of vilir:^- " Fi?. 28. / A SOUND, AND ITS RELATION TO MUSIC 43 lions are thus i)roi)agaicd. having the same frequency but f)p]x)site phases; and the waves thus generated meet along the hues extending out from tlie four corners. In I'ig. i(S we are su])i)Ose(l to look down u])on the end> of the ])rong> a />. which xihrate outward and inward as ie])resented In- the arrows. The sound will be strong at r (/ c and /', but will be <|uenche(l along the lines // /; ;' k. where the waves neutralize each other. Metal plates, known as Chladni's plates (page 61 ). tend to divide up. when sounding, into seAcral ecjual sectors, of which those adjacent to each other give out sound- . . . Experiment waxes ot opposite ])hases. that is. one is pro- with metal . plates. ducing condensations while tlie other is pro- ducing rarefactions, and z'icc versa, although their vibration numbers are the same. If a forked tube (' /) /: i Fig. -I ) . cai)])ed bv a membrane on which ,^and i^ s t r e w n . be ]>lace(l with one of its prongs o\-er each oif two alternate sectors A A nr B /;. the san- lentl}- agitated, owing to syni];a- thelic resonance ( ])age 60 ) ; but if the ])rongs be |)laced over adjacent sectors A B. as in the drawing, the sar.;! will remain undi>turbcd. showing that the two sets of \ibra- tions are mutuall_\- destructive. .\gain. if two organ pijjcs of e(|ual dimen>ion- be fed from the same \vind-che>t, they will vibrate in o])po.-ite ])hase.-. and Fig. 29. 44 SOUND. AND ITS RELATION TO MUSIC their sounds, instead of being reinforced, will be nearly ex- tinguished. Organ builders are obliged to guard Experiment ... . ... with organ agaiust this contingcnc}', m constructing their pipes. instruments. Having discussed the results which occur when two equal sounds having the same vibration number come into conflict, let us now consider what happens when these Interference . _. ... , of sounds of two souuds havc different vibration numbers. different pitches. ,, , . ., . _^ , „ Suppose that two sets of vibrations V and h are travelling in the same direction, starting in opposite phases, so that the first vibration of /) is neutralized by that of E. If, now, E be travelling faster than D, it will gradually gain upon D until a condensation pulse of E corresponds with one of D. Still gaining on D, E now i)asses along until the vibra- tions are again in opposite phases, and the sound becomes again inaudible. At this point D will have made an entire vibration more than E, and the sound will ha\-e grown from Fig. 30. zero to a climax and then ha\e diminished to zero again. Fig. 30 illustrates this process. 1 lere D is represented by the dotted line, and E bv the C(Minected line. The opposing phases are at A and B. and the climax of intensity at ( . Such an increase and decrease of sound has Ijeen given the name of a beat; and it is evident that one of these beats must occur whenever one set of sound-waves gains Beats and their frequency, over another by a single vibration. Thus if a sound vibrating 100 times ])cr second travels with one which vibrates 101 times in the same interval, one l)eat per second will result ; if the first sound vibrates 100 times while the SOUND. AND ITS RELATION TO MUSIC 45 second vibrates 102 times, there will he two beats; and so on. (liven the vibration number of one sound, therefore, it is easy to determine that of another wdiich vibrates nearly in unison with it, simply by counting the number of beats per second which they cause wdien sounding together, and adding or sub- tracting these from the vibration number of the first sound, according as the second sound is sharper or flatter. It is on this ])rinciple that the vibration ntmibers of sounds are reckoned from the tonometer (page 28). Tuners of instruments, also, gauge the accuracy of their work by noting the beats. A piano tuner, for instance, adjusts a string so that no beats occur between it and the tuning-fork with which it should be in unison. As there are generally three strings to each tone, the other two strings are then stretched until they make no beats with the initial string, when their unison with it must be perfect. As the difference betw^een the vibration numbers of two sounds increases, the beats quicken until they blend together, The result of J"^^ ^^ ^^^^ spokes bccome iifdistinguishable when quick beats. ^ wheel revolves quickly. The effect of unrest remains up to a certain point, however, voicing itself in w'hat is commonly called a discord l)etween the two tones (page 98). Fig. 31. 46 M)uxp. .i.\/> rr.\ h'li/.ATiox to music l.issajous (1") 1 . ()1 tWo recording beats. . . , . / ,. tuiung-lorks ./ and B , one is kept soundmg 1)\ means of an electric current, while the number of vibrations of the other is regulated by a sliding weight on one of its prongs. By means of a style attached to the end of each fork, the combined \ibrations are recorded on a snioked-'j!-' -s ijlate, Fig. 32. and thrown upon a screen by the lantern at the loj) of the ap])aratus. Dr. Koenig, using a similar device, obtained the results shown in I'ig. 32. SOUND, .'IMP ITS RliLATlON TO MUSIC 47 Beats occasioned by defects in instruments. .Man\- oilier condilit ms I)esi(lc tliosc descriljcd nvdx ,^ive rise to heats. Defects in a musical instrument, causing- its parts to vibrate out of unison, mav ])ro(luce tlieiu : thus ue often hear l)eats in the tone of a hell, owiui^" to the fact thai it divides into .'■■•^■nienls when soundiui^' and that these segnienls have imi)erfections in con- struction which puts them slit^htl\- out of tune with each other. I'lcats are ])ro(luce(l not onl\- l)y the fundamental tones, hut also 1)\- the iip/^cr /^artials or (n'crfoiics which accompany them in most musical sounds ( i)aije 51), when these r, , . 1 -^ Beats from overtones (litter from one another slii^htlv in overtones, 'pitch. Accordini^l}-, the interference of two complex tones may invoh'e a \'ariet}' of beats of dilterent degrees of loudness and (.)f rapidit}'. When we hear two loud tones of ditTerent ])itches sounding together, we are sometimes ccjnscious of the presence of a third lone, lower in pitch than either of them. Tar- „ ,^ i Resultant lini ( 16')2-177(}). the noted violinist, is said to t°""- have first drawn attention to the existence of such t(mes, and in his honor the\- were formerly called l\vt'uu's fours, although lliey arc now generallv known as resultant tones. The follow- ing table shows in black notes the resullant tones j)r(Mluced b\- the chief intervals included within the diatonic scale, repre- sented by white notes on the upi)er staff ( h'ig. 3vV) : — P(t4'I' M«j .'J"! .M, „..■;»' Maj 6'h Min6'J' Fig. 33. Perhaps the reed organ is the best available instrument with which to experiment with resultaiu tones. They are not alwa\-s „ , easiK' i)erceptible ; but if the tone of the same How to hear - ' ' these tones. piteli as the resultaut tone be ])reviously sounded, the latter can be more readil\- detected when its generators are nlaved. 48 SOUND, AND ITS KELATION TO MUSIC What causes these tones is still a matter of controversy. Since the vibration number of a resultant tone was found to „ , , „ , be equal to the difference between the vibration rlelmnoltz s ^ res^uitant*^ uumbcrs of the generating tones, and is there- '°"^^- fore of the same frequency as the beats which they produce, it was at first supposed that the resultant tones were caused l)y these beats. Helmholtz, however, discredited this theory on the ground that the resultant tones and the beats were sometimes heard simultaneously ; and he therefore ad- vanced the theory that when the amplitudes of the vibrations of two sounds are very great these set in motion other sound- waves, different from either of the original ones. From 'this theory he also deduced the existence of what he called sum- mational tones, whose vibration numbers are equal to the sum of those of their generators. What we have described as resultant tones he distinguished as differential tones. Dr. Koenig, however, as the result of manv intricate experi- ments, reverted to the former theory, renaming resultant tones „ „ . , beat-tones. In support of this theorv he not onlv Dr. Koenig s ^ ' theory. ])roved that a tone and the rattle of the vibrations which produces it can sometimes be heard simultaneously, but also showed that many of the phenomena connected with result- ant tones arc explainable only on the hypothesis that they are caused bv the beats. Tt is also a matter of dispute as to whether these tones reallv exist in the outside air or are formed within the cavity of the ear itself, Helmholtz advocating the former view and Dr. Koenig the latter. SOUND, AND ITS RELATION TO MUSIC 49 SUMMARY The loudness of a sound is proportional to the square of the amplitude of its vibrations. X'ariation in this amplitude does not affect the pitch. In free air, sound-intensity is inversely proportional to the square of the distance of the listener from the sounding body. When sound is restricted to the boundaries of a tube, however, it proceeds with little lessening of intensity. Sounds are louder in dense than in rarefied media, and are also generally louder at night. They are intensified in the direction in which wind is blowing, and softened in the con- trary direction. The results which follow when two sets of sound-waves meet are called the phenomena of interference. When two sounds of unison pitch and equal intensity meet, the individual intensity of each may be augmented up to twice what it was at first, or it may be reduced even to complete extinction. If the two sounds are not in unison, undulations in intensity known as beats occur, of which the number per second equals the dift'erence between the vibration numbers of the sounds. X'arious conditions give rise to beats. They are useful for determining exact vibration numbers. Two loud sounds are sometimes accompanied by a resultant tone, the nature of which is disputed by physicists. REFERENCE LIST. HeUnhohz. Chapters 2. 4. 7, 11. Tyndall. Chapters 1, 8, 9. Zahm. Chapters 2, 7. Harris, Chapters 6, 12. 13. Catchpoo!. Chapters 4, 8. Taylor, Chapter 2. Poyntiuy and TJioiiipson, Chapters 1, 10. Stone, Chapters 3, 5. Broadhousc. Chapters 5, 12, 14. Blascrna. Chapters 2, 5. 50 SOUXD. ,1X!) ITS RELATIOX TO MUSIC Meyer. Chapters 8. 13, 14. Bar)ies, Chapters 9. 12. IJartotJ. Chapters 1, 7, Pole, Chapter 3. CKAI'TER V OiJAi.nv TuF. third property of sound, that of quality, enahles us to (Hstinguish helween sounds c\en if they Ije of the same pitch and eciual loudness. In Hstenin"' to an orcliestra, „, , . .. 1 f^ ' Characteristics for instance, we recognize without (ht^cuUy the °^ quality, tones ])ro(hiced b\' the viohns, the tiutes. the oboes and the lruni])ets h\- the characteristic ([uahty of each. W e are alstj able \o (h'aw chstinctions between two instruments of the same species, sax iny of two \iohns that the one is smor)th and pleasant in tone while the other is rough and disagreeable. Again, under the lingers of an artist a violin niav give out niehnlious and thrilling tones, while the same instrument con- stantl}- offends our ears when handled b\- an unskilled amateur. There are thus unlinuted gradations in tone-character: grada- tions which ;ire so analogs 'Us to shades of color that they arc often spoken of bv musicians as -zwictics of f<'iir-color. .*^cientists iuv a long time found luuch difficidt}' in exi)laining the phenomena of soun(l-(|uality. Joseph .^aux'cur ( 1653- 171o). the inventor of the wcn'd "acoustics," and 1 1 , 1 1- Tlieories as to se\eral others advanced the tlieory that quaht\- the nature of is i)roduced b\- the combination of secondarx^ sounds with the chief tone; but no adecjuate de\'elo])ment of this idea was j^resented until 1 lelmholtz brought out his authoritative work, which contained a full and conclusive study of the subject. In this he clearly proved that almost every musical tone consists not only of a principal tone, but also of a number of subordinate tones of lesser intensity. To these secondar\- tones several names such as oz'crtoiics and haiimviics have been given. The latter term was applied bv Sau\eur (mi the theorv that the numerical „ , u . Use of the term relations which their vibrations bore to those of "partiais." the principal tone could alwa\ s be expressed by whole numbers 51 52 SOUND, AXD ITS RELATION TO MUSIC in the series 2, 3, 4 and so on. It has since been discovered, however, that in many instances, notably in connection with rods, bells and plates, these relations are much more complex than was at first suspected. A more comprehensive nomencla- ture, therefore, designates all the tones which combine to produce the total effect from a single sounding body partials. The lowest of these, which is generally also the most promi- nent, is the fundamental, while the others are upper partials. Those whose relations to the fundamental can be expressed in simple whole numbers are called harmonic partials, while the others are called inharmonic partials* Ilelmholtz demonstrated the important law that the char- acter of an individual tone is determined by the number and position of the upper partials and their relative Laws governing the quality of a intensities. Dr. Koenig afterward showed that tone. quality was also affected by the relative po>itions of the condensations and rarefactions of the upper partials. or their dift'erence in phase. It can readily be seen, therefore, that, since a multitude of combinations of the upper partials may occur with ever\- varietv of intensitv and with still other modifications through variations in phase, there is practically no limit to the number of possible gradations in tone-quality. A clever device called a reso- nator ( Fig. 34 ) for detecting and studying upper partials was invented by Ilelmholtz. This u , - ,. . is in the form of a Helmholtz s resonators. lloHoW globc bcSt made of thin brass, having a small aperture h on one side with a pn ijection which can be inserted ^'s- 34. ndmhoitz-- Resonator T;u- reader should be careful not to confuse the terms partials and upper partials. the former name includiny both the u[)j)er partials and tlie fundamental. Thus the fundamental is the first !)artial, the first upper partial is the second partial, the second upper partial is the third partial, and so on. SOUND, AND ITS RELATION TO MUSIC 53 in the ear, while a larger opening a in the opposite side admits the sound-waves from the outer air. In accordance with the I^rinciples of resonance explained in the next chapter, this in- strument has the power of selecting out a single tone to which it is tuned and of reinforcing this tone so that it strikes the ear with greatly increased intensity. By constructing a number of these resonators tuned respectively to the various degrees of the scale, lielmholtz was able to listen for the appearance of upper partials in a given sound and to determine the pitch and intensity of anv one of these by its agreement with the pitch of its sympathetic resonator. In this manner it was discovered that only in a few instances, including mainly the tones prodticed by some tuning-forks and stopped organ pipes, was there an approach to ^^^^^^ ^^ ^ an absolutelv simple tone. Moreover such pure tone produced t^ ' by aaaing tones, while pleasant to hear, quickly become un- paft'a's. interesting. With the addition of simple harmonic partials, character and vitality is imparted to a tone ; while an ad- mixture of remote overtones results in more pungency and incisiveness, frequently accompanied by discordant elements. Unfortunately, the range of tone recognizable by the resonators does not extend to sounds very acute in pitch, so that it is difficult to investigate the character of the highest upper partials. While, therefore, it is comparativelv easy to analyze the simple harmonic partials of a given tone, it is a more difficult task to reconstruct this tone if it contains partials „ , , t How far vowel bcvond the reach of resonators. This fact has rounds can be reproduced made the problem of reproducing the varieties of artificially, vowel sounds hard to solve. lielmholtz. Koenig and others, recognizing that the peculiar characteristics of spoken vowels are caused by certain combinations of upper partials, have made many attempts to mimic these sounds l)y artificial ineans. I'v sounding together tuning-forks of ])itches and strengths corresponding to the ascertained values of the partials, an approach was made in some cases to the original sounds ; but 54 SOIWD. ,l.\D ITS RliLATIOK TO MUSIC owing to the impossibility of providing" for many inharmonic ])artials outside the scope of the resonators, some of these experiments proved less successful, h'ig. 3,^ depicts an elabo- Fig. 35. rate instrument made ])\- Koenig, consisting of ten reinforced tuning-forks which can be ])ut into \ibration 1)\- means of an electric current. The keyboard in front allows the operator to throw (jn an\' combination of the^e forks which he wishes, regulating al>o at will their relati\e intensities. \\x means of this instrument the \'o\vels // (as in boot), o (as in no), and (/ (as in ah] have been reproduced with considerable lidclit} : but onlv a slight suggestion can be gi\cn oi those \'owel sounds which contain complex and actUr ]iartials, such as the sounds of e and /. I'or the investigation of the h.armonic partials the liest medimu is the sfrctchod striiui. some of the laws of which we ha\'e alrcadx' .-studied in L"ha])ter lib I.ct us Production of . . ' ^ ^ partials from agaui rclcr to the sonometer sliown on ])agt' .").■>. strings. Ilavimr tuned one of the strings to bass SOUND. AND ITS RliL. IT/ON TO MUSIC 55 C ^==^ , let us touch a feather to the middle of the string and pluck the string half \va\- between the point touched and one of the ends. We now clearlv hear the second partial. which is the note r ;3'^ -li^^ . just an octave above the tirst partial or fundamental. This new tone is produced by each of the two ecjual i)arts into which the string is di\ided. and each of which, according to the laws of stretched strings (page 33), must be \ibrating twice as fast as the whole string. Where the feather tt)uches the string there is scarcely any motion at all. This point is named a node. At the middle 11 1 1 • 1 Nodes and ot the 'c'Ciifral sc(j)nciits, as thev are called, which ventral seg- . , ' . , . , ' , . ments. occur on either side ot the node, are the points of greatest motion. If the feather be removed from the string the latter will continue to vibrate in halves as long as its momentum lasts. Likewise, damping the string at one-third of its length will divide it into three \entral segments separated bv two nodes; and the third partial thus gi\en out will be ^,, ,. , ' "^ Other partials an ocia\e and a fifth above the fundamental °^ strings. y^^~"^ '^ . Again, the fourth i)artial. made by dividing the string into ([uarters. will Ije one octa\e abo^•e the sec()nd ^rE^ , while the tifth partial, produced by a division into fifths, gives the note a major third abo\e its predecessor ^ . It should be observed that the two ends of the string in each case form two (,)ther nodes, in addition to those enumerated. An interesting ex])erinient is perfcjrmed bv i)lacing a number 56 SOUND, AND ITS RELATION TO MUSIC of small bent pieces of paper or "riders" upon the string before „ . , it is sounded, red ones where the nodes should Experiment ' with "riders." appear and blue ones on the ventral segments. When the string is put into vibration the blue riders will instantly be unhorsed, while the red ones will retain their position. This effect is shown in Fig. 36. Fig. 36. Continuing still further to divide up the string into integral parts, we may form any number of segments and their accom- panving nodes. For j)ractical uses, however, only The "harmonic ."'^.,, . ., ,, ., series" of a icw 01 the harmouic partials need be consid- strinsTSi ered. The brst sixteen of these for the note C are shown in b^ig. 37. The vibration numbers indicated beneath are calculated on the basis of the scientific jntcb. which is somc- 64 128 192 . 6 7 S 9 10 11 12 13 li 15 1» 250 320 3H4 448 512 576 640 704 768 872 8U6 960 1024 The Ilarnionic Series what lower than the international. Note also that the partials indicated by black notes are slightly out of tune with the cor- responding tones in our scale. Let us now inquire what are the motions which a string SOUND, AXI) ITS RliL.-lTlUX TO MUSIC Fig. 38. makes wlien tlie presence of several upper partials causes it to vibrate in a ntunl)er of dilTerent directions at Complex the same time. I-'i','' 38 shows some of the simpler motions of ■^ . strings. of these motions. If the strmg- ./ M B gave out onlv its fundamental, it would assume the uniform curve ./ C B. When, however, the string, besides vibrating as a whole, also di\-idcs up into segments, these must adapt themselves to the fundamental vi- bration, appearing as alternate elevations and depressions along the length of the string. Thus when . /' M' B' vibrates in its entirety and also in halves, the segment on one side moves outward when that on the other >ide moves inward, and vice versa, so that positions like A' C B' are assumed. Again, . /" M" B" , sounding its funda- mental plus the second upper partial, takes positions corre- sponding to the curve A" D D' B" . As other overtones are added, the motions increase in complexity, each partial, how- ever, preserving its individuality. This complexity is, of course, transferred to the resulting sound-waves, in which the various condensations and rarefactions are correspondingly superimposed upon each other. Given upper partials, however, can exist only when condi- tions are favorable for the formation of their nodes and ventral segments. If, for instance, a string be ^ ... '^ f^ Conditions ijlucked at its centre, there must be a maximum ""'^^'' which 1 given partials of viljration at this point and hence it cannot ^^^ occur, become a node. C'onsequentlv all the partials. such as the second, fourth and eighth, which have a node at the centre, are ai)sent. Again, sounding a string at a point where the node of a discordant ]iartial would l)e formed, the tone becomes inorL' agreeable b\- the eliminatitai of such partial. Hence the skilled violinist draws his bow at the most favorable division 58 MJLW'D, .1X1) ITS REL.-ITIOX TO Mi'SIC of the strings, and tlie piano maker care full \- disposes his liainnier strokes to ])ro(luce the hest tonal (|ualit}-. The \'il)rations of Ijodies other than >tring"s are go\-erne(l hy more or less divergent conditions. Turning to the suhject of ^ , r , sciiiiiliiKi rihis. let us first examine the m(*tions Partials of rods fixed at one end. , , ,- ^ ,-, ,^1 fixed at ( mc cud and free at the other. In I'ig. 3'' a rorl thus located oscillates as a whole hetween the ])ositions indicated h_\' the dotted lines p o and p' o. With Fit;. 40. the ad\ent of the second jiarlial the fixed end niu:-t fi)rni a node, hnl the free end, unrestricted in its nioiiiin. heconie- the centre of a \entral segment. T\'v other node niue'-, the rod form> two and one-half ventral segments, with the lir>t node located at one- llfth of the length from the free vud. while each of the entire segments ()ccn])ies two of the remaining four-tifths ( I'ig. 41 ). Succeeding partials would continue to di\ide the rod according to the odd numl)ers. 7, [). 11. Cvc. These upper ])artials ri-e very rapidly in pitch, and are inharmothc in character. Thus the I'lrst up])er partial has ahout 6'. 4 as manv \ibrations as the fundamental, 1 M 1 1 " 1 - / w Relations of while the next has l/'j as man\'. We can verv these partiais as to pitch. readiK- hear the high o\'ertones which ring out as we strike a tuning-fork, but which afterward vanish, leaving the fundamental. A tuning-f(jrk is subject in each of its branches practically to the -ame laws as are rods fixerl at one end. Wdien gi\ing oui its fundamental it \ibrates with a node at ^ ,• , , Partials of the lower extremity of each Ijranch, which corre- tunii^g-forks. >l)onds to the hxed end of the rod. The three segments thus formed \ibrate in unis(jn with one another. Two other nijdes 6i i7i are formed ujion the appearance of the -econd n].per ])artial, and still two more with the third, these ui)])er i)artial> bearing 60 SOrXD. AX/J ITS RliLATIOX TO MUSIC the same relations of 6/4 and 17' j viljrations resi)ectivelv to their fundamental as did the rods before discussed ( see l""ig. 42 j. It shoukl be nuied, however, that the viljrati(jn number> ^■arv somewliat in the case of forks of ditterent .-hapes and materials. Rr)ds with biith end< free, emploxed in instruments like the .vxhif'lioiir and inctalloplioiic. were investigated with great care b\- L'hladni ( 175()-18i7 ), who has received the Vibrations of " ,, ■ - . - i - i ■ ■■ ti rods free at both a])])enatii)n ot tather ot modern acoustic>. the ends. . . . 1111 primarx' motions ot such a rod are seen by liold- ing a -i\-f -liakcn it oscillates between the positiijns shown in ./. big. 43. the points at which it IS held tornung 1 ; ; 1 I " ■ I nodes. Held nearer the ends, it \'il)rates a> tinder B. with three nodes. As its funda- , 1 1 • , Fig. 43. mental, which occurs wdien the two n(jdes abnie arc iM'escnt, a free rod gi\'es (jut a tone ')'4 times as acute as the fundamental of a similar rod tixed at <.ine end. or a tone corre>ponding t(j the tirst upper ])ailial of the latter. The sttcceeding ])artials rise rapidlv in l»itch, bearing al)ijut the sante relations to their fundamental a- those in connection with rods hxed at one end. Longitudinal ^■ibrations mav be ])rriduced in a rod b_\- clamp- ing it in the middle and rubbing one sectitjn lengthwise. If m ivor\- l)all te sus])enrled lyainst o n e end of the rod, a- in bdg. 44, it will be re])elled vig- orou-l_\-. Savart, indeed, founrl that it wa- i^o-.- sibie. b\- thur- rubbing a Lda'is tube with a wetted cloth, t Partials produced when rods vibrate longitudinally. Fig. 44. diatter one end of it bv SOl^ND. .IX!) ITS RliL.lTlOX TO MUSIC 61 the force of its own molecular motion. l^Vee rods \ibratini,^ lonoitiulinallv may be divided into 2, 3, 4, 5 .segments, and so on, the \iljraticjns of which fcjrm harmonic parlials like those of strings. W hen the>e rods are fixed at one end, the tones which they dex'elop are in the order of tlie uneven harmonic partials. 1, 3, 5 and so forth. A curitais instrument devised by Marloxe ( 179.S-1S74) is furnished with rods of wo(k1 or glass which arc pla}'C(l u])()n by rubbing lengthwise with rosined fingers ( h^ig. 45 ) . Chladni conducted a series of interesting experiments while study- ing the motions of * . Chladni's sounding glass or experiments with plates. metal plates. Some of his results ma\' be appreciated bv emplo\"ing a square ])latc tixed to a support in the middle. If fine sand be strewn upon this l)late and the plate lie made to sound b)' drawing a violin bow against one edge, as in Vig. 46, the sand will be vio- lentlv agitated. Tress a finger at the middle of -. >ne side and the sand will colled along the four intersecting nodes thus generated. Tn h^ig. 47, which shows the result of this ex- ])erimenl. the ])lus and minus signs indicate that the aher- Fi„. 46. nate segments are vil)rating in Fig. 45. 62 SOUND, .INI) ITS RELATION TO MUSIC opi^osite phases; that is, that when one segment vil)rates out- ward, tlie (jnes adjacent \ibrate inward. In I'dg. 48 the linger lias l)een ])re>>ed against one corner of the ])late. while in I'ig. 4*^ two other points have also been touched. When the plate i.> di\'i(led as in hdg. 47 the fundamental is sounded, ddie di\dsion .-hown in I'dg. 48 gi\-cs a tone a lifth higher; and + ». - + FiL'. 47. Fig. 48. Fig. 49. more comi)licated divisions result in tones still more acute in pitch. 15y touching the ])late at ^■arious other piMUts a multi- tude of beautiful figures ma\' be evoked, such as those shown in I'dg. 46. W hen the plate is strewn with a very light material, such a-; lycopoditmi powder, the effect of the vibration U]V)n this is e.\actl\- the oi)i)o>ite of what it \\as upon the Effect on light " . ' ' ' powder of vibra- saud, suicc the powdcr collects at the centre oi tion of plates. .,.,,, „,, the segments instead ot along the nodes. I he reason for this fact is that the e-xceedingl}- light particles are drawn int*) the vortices of the minute whirlwinds which are generated b\- the \ibrating ])ortions, and so are heaped uj) upon the--e latter. Compound sand figures liave been i)roduced by ])lacing one plate <)n top of another in >uch a wa\- that \-ibrations of O{)])o- ^, ,, site phases were superimi)osed. Circular platc< Other plate ' ' ' ' figures. (,,- disks also give rise to other interesting sanrl designs, which follow the .-^ame general laws as those govern- ing trunients are ])a>ed are the same as tliose which gcjvern tlie tones of sonorous tubes, which we now ])rocced U) consider. That it is reall\- the air witliin these tubes winch vibr;ite.- and not the solid exterior walls can be easilv shown bv ex])eri- mentini'' with three tubes of exactl\- the same Proof that the . ' . . air in a tube sizc but ot (littcrent materials, ,-uch as glass. '''^'■^"^- 1 11 1 I -11 1 - i' 1 cop])cr, and cardboard. It wnl Ije le. so that the tttbe is tra\"ersed lengthwise four times in the ])a>sage of a single sf;und-wa\-e, (jr, in other wrjrd^, each sound- wave is fcnir times the length of the tube. I'.v Idling the tube with various gases, tones of different pitches are produced. Since, however, their sound-waves are all equal in length, the relati\"e velocit}- of sound in the air and in the-e gases can Ije easil\- calculated. Fig'~T2. At the end d. where there is the greatest alternate conden- sation and rarefaction, there is _\"et the least motion; hence a node is formed across the tube at this ])oint. A Upper partials . , of stopped maximum ot movement mu-t aUvavs take ])lace. i^^^^- , 1 1 1 • 1 •' 1 1 liowever. at the o})en end a. which is thus alwaws the middle of a \'entral segment. \\ hen the air in the tube \ibrates under a more })owcrUil current, the tirst U])per ])ar- tial is formed; and the additional node is a third of the length of the tube from its to]), just as was the case with a rod fixed at one end. In like manner the succeeding partials are formeri b\- rlivisions of the tube according to the odd num- bers, .r .^. 7. and so forth, as shown iii I'^ig. .^.x These r)artials, SOUND, .IXn ITS R/iLATfOX TO MUSIC 65 •; unlike those of rods fixed at one end, are members of the harmonic series of strings ( I'lg. 27). Tubes o['cn at both ends iin'olve conthtions some- what (Hii'ercnt from those just discussed. A pulse of condensation entering such a tul)e ( h^ig. 34) at a. passes through c to b, where it rushes out into the free air, generating at the same time a pulse of rarefaction, which starts back from /.'. Another pulse of rarefaction, how- ever, starts simultaneously upward from a at the same rate ; and the>c two pulses, encountering each other at e with e(|ual force, Icnvc the air at c in a state of rest, or, in other words, form a node there, each of the . , ' A sound-wave ])ulses then rushing by to its destination '" ^" °''^" '"''^• at the end opposite to that from whence it came. Pulses of condensation now start back from each end, meeting at the nodal ])lane c as did the pulses of rarefaction. It is evident, therefore, that a com])lete sound-wave involves the passing of a pulse of condensation from a to /' and a return of a pulse (^f rare- . . Length of a faction from b to a, or, m other words, sound-wave in - 1 , . , , an open tube. a length of twice that ot the tube itself. Inasmuch, however, as the length of a sound-wave in a stop])ed tube was four times the length of the tube, it follows that an open tube must give a fundamental tone an octave higher than that of a stepped tube of the same length, since its sound-wave is only one-half as long. Fig. S3. FiK 66 SOrXD. .IXD ITS RJiL.l'JIOX TO MUSIC With the formation of upper jiarlia!^ in an open lube, both ends of the tul)e. where the l)(Jint^ of maximum minion art- located, will alwa\"s l)e centres of ventral >ey- ments. When there are two no(le>, forming' the secrind partial, an entire segment will C(jnsequently arise in the middle of the tube, and a half segment at each t-nd ; Partials of open tubes. / \ Fig. 56 hence the nodes will ' from each of its end.-. )e a c|uarter of the lengtli of the tube The tone thus gi\en out i.- an octa\e above the fundamental. The third ])artial. >ound:ng an octa\'e and ;•. lifth al)OVL' the tundamcntal, lias node:- one--i.\th of thit len^^tli from the ends and al>o a node in the middle; while the i"i iurih ])artia]. -iiunding two octa\e.N ,ibo\-c the ftmda- meiual. Iia-- nodes one-eighth of the length from each end, \sith two iither< at ecjual di>tance> between. .All the-^e utTect- SOl'Xn. .1X1) ITS- h'HL.ITfOX TO Ml SIC 67 arc shown in Vig. 55. The ii])i)cr ])artials in this case follow the harmonic scries inibrokenly in the snccession i, 3, 4, o and so on. A clear method for showing" the position of the nodes in tubes open at both ends is shown in My. 56, where such a ttil)e is represented 1)\- an o])en organ ])ipe P P, Location of having one of the sides made of glass, if this nodes and sc2f mcnts. pipe be ptit into \ibration and a small strcu'hed mcml)rane in strewn with sand be lowered into it, the sand will dance about where the motion is greatest, but will remain (|uiet when a node is reached. Tubes of which the length is great in proportion to their diameters follow (|uite closely the law suggested above, that the pitch is inversely proportional to the length of the tube. The i)itch may be con- Modificaiions of ° I J ^ theoretical laws. siderably affected, however, by greatlv increasing the diameter. \'ariotts other conditions as to the shape of the tube cause modifications of its the(n-etical laws, and must be taken into consideration by instrument makers. 6S SOUND, AND ITS RELATION TO MUSIC SUMMARY The quality of a tone depends upon the number, position, relative intensity and i)hases oi the secondar}- tones which are mingled in it. The relation of these upper partials, as lhe\' are called, to the fundamental ma}' be expre>sed by sim])le whole numbers, in which case the\- are called harmonic ])ar- tials, or bv fractional numbers, when the\- are called inh.ar- monic partials. Given com])lex tones can be reconstructed only in scj far as the\- contain the sim])Ie harmonic jjartials. In forming their ])artials \'ibrating bodies divide U]) into nodes and ventral segments. The presence of several ])artials causes complicated motions in the \-ibrating body. Strings form their ])artials in an harmonic series, the members of which are related to each other as the successi\e simple whole nimibers. The partials of rods, plates and membranes are generally inharmonic and high-pitched. The\' are formed under various and scjmetimes com])licate(l ccnulitions. Tubes, either stopped at one end or oi)en at both ends, give out musical tones bv the vibrations of the air or gases with which they are filled. While in both cases the harmonic series of partials is produced, in that of stoi)])ed tubes onlv the odd ])artials are possible, while the entire series can occur in tubes (j])en at both ends. l^EI'Kr^F.XCE LIST. Ilelmlioltz. Chapters 5, 6. Tyndall. Chapters 3, 4. 5, 6. Zalnii. Chai)ters 4, 5. 6. 9. I'cyiUiiii/ and I'hoiiipscii. Cliaj^ters 5, 6, 7, 8. Inmics. Chapters 3, (>. 7. 8, Harris. Chapters 8, 9, 10, 11. Taylor. Chapter 4. Bruail house. Chapter 8. Stone. Cha[)ter 5. Laiifpiac. Cliapter 1. A. Barton. Chapter 5. HIascrna. Cliapter 8. f'olc. (Jhai)ter 3. CHAPTER VI Ri'.soxAXci': XoT only do sounding bodies transmit their vibrations to tile surrounding atmosphere, but tlie\- also have the i)o\ver v of setting ui) svmimthetic vibrations in other „, , ■^ i - 1 The phenomena bodies, whether these latter are in direct coiUact °^ resonance, with them or not. I^Vom these conditions man\' interesting results follow which are grouped together under the title of the phoioinciia of rcso)iancc. To understand the nature of these phenomena, we must recall the familiar mechanical law of cumulative impulses. 'Jdie working of this law may be illustrated bv „, , , '^ -' - The law of an old-fashioned swing, well-freighted with chil- cumulative "' o impulses dren. Another child stands behind the swing- illustrated, seat, and when he gives it a slight push it swa\'s gently awav from him, immediately returning in his direction. A second ])ush increases the momentum, which grows still greater as the pushes continue, until the children are flying through the air in long sweeping undulations, to their great delight. Each j)ush, howe\-er, must be given exactly as the swing-seat reaches the point nearest the pusher in order to be eiifective, since otherwise its motion would be retarded or might even be entirely stopped. For another illustration of this law, let a heavy weight such as a cannon ball be suspended from the ceiling by a string, and let a slender thread be attached to the weight. Further r>v gentlv pulling upon this thread at the ])r()per illustration 11 -1 i_- 11 1 1 of the law. intervals the weight may hnally be made to oscillate back and forth over a considerable arc. A more remarkable form of this experiment is performed bv simplv blowing puffs of breath against the weight, which may thus be induced to assume a motion almost as great as before. Similar results follow when a ship is tossed about in the 7(' souxij, AXD iT.-> ri:latiu.\ tu music irouyii of the sea, gaining momentum from the continued imi)ulses of even comijaratix elv small waves. Practical , . . examples of Suldiei"-, wlieii marchuig across a bridge, are the law. ■ '. commanded to break ste]). >ince otherwi-e the results to the structure fronrtbe accumulated momentum might be disa.^trous. We ma\' a])})rcKich the musical ai)plication '>i this law b\ a few e.\i)eriments with ordinar\- pendulums. Let two oi Transference of the>e wliich luu'e tile >ame \"il)ration rate be pendulum , , - , • , i - - , vibrations. -u^jieiuled t roni a bar ot wo.^d. It one ot them -a) When the . . . .,, . . pendulums have be HOW sct lu motioii ii Will commuuicate lt> the same ■, ■ i i i i i vibration rates. Vibration.'- to tile otHLM" thrtjugb the comiiKjii sup- ])orting bar, so that liotli will o.-^cillate alike. I'urther than tlii-, if two clocks whose pendtilums \-il)rate ali)u>st exactl}" in ihe .-ame time be set side by side on a table, the f|tucker of tlieiii will draw U]) the time of the other until the}" mo\'e in iini-( m. In the case of the swing abo\e alluded tc), if the child had gi\"cn a ])U>h at the expiration of e\er\- two o-cillations instead ,, , ,,,, ., ^if each one. the nionK-ntum would ha\e increa>ed (b) When tne pendulums have .^^ before, but iiKjre slowlv. With one pudi to dinerent vibra- - ' tion rates. cacli three o>cillations the iiiolioii would ha\'e auumented still more slowly, and with one ini-h to each f^air I i-cillatii ins the incr(ja>e would have I)een \'erv -low indeed, ."^o, if (tiie of two pendulums attached to ;i common liar \-ibraie- twice ci< slo\vl\- a- the other it will .--et the latter in vibration b\- ;id(ling to il- momentum at e\"er\- -ecoiid >wing : but this el'ect will I'ccur more gradualK' than wa- the ca-e when tlie jieiululum had tile \- one-fourlh that (jf its c^ aii- ])ani' >n ])enduluin. Let u- 111 iw hold in either hand one (^i two tuning- lork- whitdi lia\e exactL' the -ame viliration number. Striking i iiie of the-e and soon alter damping it with the fmger-. we are :ibl(,- 111 hear a faun re-])oii-e coming" from the iither If llie SOl'XD. .IXIJ ITS RliL.lTlOX TO MC.^IC xihratidii numlicrs of tlic two forks were not the same, no such tone would be ])rocluce(i. When llicse are ecjual. how- e\er, the fork originally sounding impinges its ^ ^ & i- & Sympathetic vibrations upon the other through the medium vibrations of , . . ■ . tuning forks. of the air, ju-^l as uie pushes were .i^iven to the -win.i;-, or the ])urf> of lireath struck tlie suspended cannon hah. A inilse of c(jn(len>ation prtjceedin^' from tlie lirst fork hits tlie second, giving it a slight forward momentum. It- return is then facilitated 1)\- coincidence with the rarefacti(jn which ha< folhnved the condensation from the lirst fork. .\nother pul-e of condensation now strike- the second fork, and the whole ])rocess is rei)eated with slightly increased momentum. Thus the motion accumulates, as in the exam])lcs above cited, until the ,-econd fork sings stcadilv with the tirst. Hut a tuning-fork ma}" with equal facilit\- incite s}'mpathetic \ibrations in bodies unlike itself. Let us hold our sounding fork o\er a gla-s iar. as in biij". r7 , tirst ascer- „„ . , ■^ •' ^ Effect of a taining the pitcli of the air-column in the emptv tumng-fork '^ ' ' - upon an air- jar 1)^- ])lo\ving gently acr(jss its mouth. If this column. l)itch is higher than that of the fork it will be necessar\- to iwer n h\- hading,"' which is accoiuplished ])y ])artl\- clo-ing the mouth of the jar with a card or other flat object. If, howex'er. the p'lich f)f the jar i> lower than that of the fork, water may be poured in until their \ibration num- bers coincide. Tlie point at whicli the\- are in uni-or. ma\- be easily determined, since the tone of the li ! fork will become reinforced b}* I' ' the resonance of the air in the jar when the vibration numbers ap- proach each other closely, and this resonance will attain a maximum when they are exactly the same. 72 -OUXJJ, JXD ITS KLLATIOX TO ML' SIC Under the latter condition what takes place is as follows: — When the prong of the fork moves to h (Fig. h7 ) a pulse of „ , ^. c condensation runs down the iar as far as the Explanation of ^ ^ i this effect. water level, whence it rebounds ; and when the prong moves to a a pulse of rarefaction performs the same process, the entire sound-wave thus equaling four times tht distance from the mouth of the jar to the water level, as might be expected in the case of a tulje stopped at one end ( l)age 64). Knowing the vibration rate of the fork we may now calculate what should he the length of the air-column in the jar. If the fork gives 435 vibrations ])er second to a'. for instance, the length of its sound-wave must ecjual the velocity of sound ])er second, or 1120 feet, divided bv 435, and the length of the air-column must conseciuently be aljout seven and one-half inches, which is one-fourth of the result of this division. In the case of a tube open at both (znd^ the air-column is twice as long, or about fifteen inches \\'e may test the accuracy of these conclusions by rolling up a piece of cardboard so that it forms a tube fifteen inches long and an inch in diameter, and holding over one end the sounding fork, when the tone should swell out considerably. I-^xtending or diminishing the length of this tube will reveal the condition of greatest resonance. It was noted that the tone of the fork begins to be rein- forced a little before the point of maximtim resonance i-- „, . , , reached. Idiis result occurs from the fact that The point of reinforcement j]^^, flexible character of the air-column allows or the tuning- ^°^^- it to be more easilv influenced than the more rigid ttming-fork, which required absolute tmison with another sounding bodv before it could be affected by it. Savart devised an apparatus shown in Fig. 58 which vividly illustrates the phenomena of resonance. .V l)ell T /' is mounted on a stand /) V C to which is altached Savart's . , , i t i • i i resonating at B a rcsouating chamber ./. In this chamber device. is a ])iston which pro\'i(les for the regulation of its lens^th. When the bell is sounded 1)\- a \-iolin bow and the SUL'XI), .-IXI) ITS RliL.rnOX TO Mrsic |)i>l(in is moved back and forth the varying degrees of reso- nance are perceived, the niaxiniuni sounchng with great power. Resonating chambers sncli as this are sometimes attached to Fig. 58. tuning-forks to heighten their effects. More often, however, the forks are mounted upon resonating boxes Resonating which are constructed of a size calculated to boxes. insure the best results, and which are left open at one or both ends. I'hus a fork having a vibration rate of 384 requires a box open at one end only, having a length of 7.3 inches, a width of 3.8 inches and a depth of 1.8 inches. A fork thus mounted is shown in l-'ig. 59. 15v ex])erimcnting with two re- ^^ Fig. 59. inforced forks of the same vibration rate some interesting results mav be obtained. l?lacing them a short ... ^ , . , . Experiment distance apart and pouUmg the open ends ot their with reinforced ,111 1 tuning-forks. resonatmg boxes toward eacii other, let us sound one of the forks b\- a violin bow. Immediately the other re- sponds with a strong tone, which continues after the first one is damped with the fingers. If we now release the first fork 74 SOi'XD, .L\'D ITS RliLATIOX TO Mi' SIC and afterward damp the second, the hrst will again sound. having taken its motion from the second; and this proces> of transference may he repeated until the energy (jf the \-ibration- is entirely exhausted. .Again, if one of the forks be put slight]}- c)Ut of tune with the other by attaching a i)iece of sealing wax to one of its prongs, it will still respond, since the \'ibrati(>n- will be transmitted through the resonating boxes, although the response will be much feebler than at first. While we originally placed the unison forks near together, >uch proximitv is not necessary, since if \\'e sepcirate them b\- the length of the room thev affect each (jther Effect of * -. . . distance upon nearK" as ])owertullv as betore. Dr. Kot-mg resonance. ' . . ' . . , . ' made some mterestmg cxpernnenis on tins line with two tuning-forks each ha\'ing a vibration rate of 12S per second, througli the conduit of Saint Mi(-hel, in Pari- \W pointing the o])en ends tif their res(Tnating l)0xes toward each other he was able, upon sounding one of them, to elicit a response from the other at a distance of o\er a mile. \\hene\'er a ljod\' is free t(j \'ii)rate in uni-on wiih a >ouiid ing body in its \'icinitv such s}-m])athelic \'il)rations will be -el U]). If the two strings of the S(jnometer i l-^ig. Conditions -, -, , , • ■" i - , ,' favorable to JJ 1 be tuucd m uuisou and one ot them he resonance. 111, 1 -ii i \\- 1 plucked, the other will re>])on(l. We na\e orteii felt the vibrations of an entire edifice when it acted in -ym])alhy with a deep-toned organ jjipc. A tone siamded on the ])iano mav cause a chandelier ()r a ^\■indow pane to jingle ^•iolentl_\. The writer was once ])laving ujjon the ])iano when, from tlie force of a loud lone to which it re-i)on(led. a large bowl of hea\w ghi'-^ in an adjoining room was shallered. Pig. oO shows a device called a si.iind-iniU . in which mechan- ical use is made of reso- nance. b(jur small cylin- ders each open at one end are atlached lo radiating arms balanced U])on a cen- tral pi\ot so that the_\- re\-ohe freelw When ihe lone to which lhe\- ;ire all The sound- mill. SOiWD. JXD ITS RliLATIOX TO MUSIC /o tuned is sounded the pressitre upon the node at tlie bottom of each causes them to rotate as long as tlie sound continues. Xo motion will he produced unless the actuating tone he absolutely in unison with that to which the cylinders are tuned. 'ihe resonators devised bv 1 lelmholtz have already been described (page ?1). J'^ach of these instruments has the power of selecting oiu one simijle tone to which ,, . . 1 '^ ' Various iorms it responds. Other forms of resonators have °^ resonators, also been invented which mav be adjusted to more than one tone, or which ma\- res])t)n(l to several tones at once. Per- haps the most startling results, however, are produced bv an in>trument of this species which reinforces the murmuring sounds c(jnstantlv tiitting about in the atmosphere, but which are ordinarily imi)erceptible t(_) the ear. ]n the form of a straight trumpet with a])ertures in the sides for changing its resonating ])itch, this mclodia- pho)ic. as it is called i b'ig. 61 ), when adjusted to the ear permits (.)ne to hear a succession of tones which are thus raised frcjm insignificance into power. The singing of the seashell when it is lield to the ear furnishes another ilhislration ^'^- ^'- of the same princijjle. In the case of wind instruments, which are really tuljes t)f \ariotis sizes and shapes either sto]:)ped at one end or open at both ends, the air-columns are set into \-ibra- , , ... Resonance of tion m one ot two wa\"<, the tn"st ot which is bv wind instru- ... .' . , ' ments. directing a stream ot air toward a sharp edge at the mouth of the tube, and the second bv causing a reed annexed to the air chaml)er to \-ibrate. F.xamples of the former method are found in flutes and the flue pipes of the r)rgan. while the latter is exemplified in clarinets, oboes and the reed j^ipes of the organ. The exact manner in which \il)rations are incited in pi])es of the flue or ■"whistle" t\'pe is still a subject of contro\-cr-\-. 76 SOiWD. AXD ITS RELAllUX TO MUSH How flue pipes are made to speak I'iy". ()1 represents a section of an organ pipe of this kind. In tliis tlie air, forced from tlie wind che in a thiii sheet througli tlTc small a])erture c toward the sharp edge at (/. Helinholtz a>>erted that the hissing ncjise made at this point is caused 1)\- a mixture of tone-; to one of wliich the pipe responds by resonance. A later theor\- which has met with mtich a])- I^roval is that the thin layer of air directed across the embrochtire d c acts like a reed and so in\-igorates the air in the large chamber of the pipe. The general and sectional view of a wooden organ ]ii])e in h^ig. 63 and of a metal one in . ^; Fig. 62. I'i-. ^4 Fig. 63. Fig. 64. shows the structure of the.^e and the i)osition of the air-inlets. A reed i)r(j])erh- consists of a thin, narrow stri]) of flexible b -».^ b SOUWD, AND ITS RIlLATIOX TO MUSIC 77 flialcrial, llxcd at one end. Organ reeds, commonly of metal, \il)rate over a rectangular orifice either slightly construction narrower and >h()rler than the free part of the °^ reeds, .•eea itself or just large enough to permit the reed to move within it. In the former case the vihrating reed hits the sides of the orifice and l^^ ^^y - ----- - "--'^^^'"^''^ I^I/'^St;;;^ is called a strikiiuj ^ a%: '. ^ . - " " ' ', reed, while in the latter case it is called a free reed. The top and side views of a free FiR. 65. J • • reed are given m hig'. ()3. The tongue r .c is attached to the metal block a a, ^■ibrating between the positions at j::^, and c._,, B. The air, l)assing' in the direction of the arrows, is emitted in a series of ])uffs similar to those of the siren. Since the resulting- tone is very rich in up]ier partials, some of which produce a strident effect, it is necessar\- for musical i)uri)oses that one of the tones, most often the ftmdamental, should be so reinforced as to overcome the presence of these discordant elements : hence the reed is generallv ttsed in connection with some form of a resonating" tube. Idie fact should be especially noted that the tone of the reed is caused by the puffs of air to which it gives rise, and not by the vibrations of the tongue itself. Examples of the use of both free and striking reeds in organ pipes are pictured in Fig. 66, . / illustrating the former and B the latter. A conical tube such as is .^ , , . Use of reeds in shown at the top of the i)ipe . / is frecjuently ^'^^^'^ '"p^^- superimposed, in various shapes, to modifv the (|ualitv of the tone. I'\)r changing the ]Mtch of the reed a tuning wire, which presses against it, ma\' shorten the vibrating ])art, thus raising the ])itch, or may lengthen it, with the opposite result. In /? the air rises into the large chamber through the tube at the lower end. Passing into the semi-cylindrical tube r r. which is fastened to the block .s- ,9, it sets into vibraticMi the 78 SOUND, AND ITS RI-L.ITION TO MUSIC reed i, which causes the air in the chamber to sound hy sympathetic vihraticMi. bov this latter resuh to occur it is necessary that the air-column in the cham- ber should be at least nearh of the same pitch as the reed itself. Since the reed is of metal and therefore of considerable rij^iditw it forces the air-column to assume its own viljration rate, unless the rates of the two bodies are too much al \ai-iance. In instruments in which the reeds are com- posed of \er\- dexible ma- terials tlie air-columns im- po>e their pilches upon the reeds. A\ hat has thus been said about orijan ])ipes mav be ai)f)lied with \-arious modifications to all kinds of wind instru- ments, consideration of the individual peculiarities of which is rcserx'ed for a special chapter. The nature Resonance in . . ... other instru- of recd actiou in relation to the voice is ot jiar- ments. ticular miportance. Air-columns mav also be set in vil)ration b\- i;as-tiames. C'omnion illuminatin,^^ i^as ma\ be used for this ])ur])ose. but better results follow from the emplo_\'meiU of Indrot^en. In Iml;'. fu lu'droi^'en gas, generated in the bottle on the left, i)asses into the lul)e in the rear and i^ ignited :is it emerges from a small opening in the toj). When a glas-^ tube of the ])roi)er dimensions is i)laced over the tlamc thus ])rocluced ;i clear, musical tone is lieard 66. Singin flames. SOLWD. AM) ITS KliL.lTIOX 10 MUSIC ^) l'"araday (179l-lS()7) (icmonstraled that the gas-flame when soundin.i;' emits a >eries of explosions e(|nal in nunrner to tlie \ihration rale of the air-eolumn in the tul)e. which con>e(jnentl\- resounds to these impulses. Heside their funda- nieiUals. such tubes ma_\' i^i\'e out se\'eral up[)er partials when excited 1)\- the flame. A nuich stronger fundamental tone and a greater number of U})])er partials ma\' be obtained from large cojjper tul)e^ under the influence of singing flame.s Kastner (1S.^2-1SS2) constructed a kind ')f pipe organ in which, when a ke\- was ^'"- ^^■ depressed, two >mall flames were Ijrought together in a pipe sm that a tone was produced. The dex'icc. however. ])roved more curiou> than of practical value. T} ndall and several others investigated the i)henomena of -ensitive flame>. A comiuon "bat-wing"" burner „ '^ Sensitive wheti under ordinar}- ])ressure as>umes the form flakes. at the left of I'ig. AS. and is imaffected bv -ounds. When Fig. 68. 80 SOL'XIJ. .1X1) ITS KliL.lTlOX lU MUSIC the gas pressure is pushed heyond a certain |)oint thx tlame "flares" in the manner depicted in the riglit-lianrl drawing. If now the gas l^e regulated so that the tlame i> just on the point of flaring, the latter Ijecomes >ensiti\'e to certain >t.)tmi'ls. and darts out into a forked ai)i)earance whene\'er these are produced. This flaring n(jrmall\- arises fr(jm a certain aiu(»unt of friction generated Ijy the rush of gas from the l)urner; and when the force of the gas has ncarK reached this ])oint the agitation of the flame ])roduced hv its xibrations in s_\-mpath\- with a sound is sufficient to cause it to lo--e its ecitiilibrium. 1')}- exi)erimenting with different burners .-scientists have succeeded in producing flames of a high degree of -ensitivit}'. T,, , ,., Wdiat is called a steatite burner The steatite burner. gi\-es. uuder nonual conditions, a delicate flame aljotit twcnt\- inches long, of the form on the left in h'ig. (.\). Influenced b>' different sounds this flame a>sumes wirious other sizes and >hapes. .^uch as the one on the right in I'ig. 60. High ujjper ])artials. like thoitive that it respond> even to sotm(l> inaudible to the ear. I'hat it is not the flame itself which is thu- sensitix'e to sottnds but the gas as it escapes from the burner, has been pro\-ed b\" Effect of sound , , . . , . . ', on unignited -ubstitutuig lor tlu' tiamc um^nUcd gas, gas charged with -luoke. Sha])e> similar to those assumed b\- the flame are formed Ijv such gases when res])ond'ng to a iuu>ical tone. .\s nflght be expected from tlie ex])eriment< with i)enduUnus of uneqtial length recorded on „„ pa'a- ro. a tone is able to influence trtect o. reson- ' '^ ance on bodies ^q^ Qj^jy bodics Vibrating to the of multiple -^ ^ vibration rates, same pitch but also those having SOUXD. .'IND ITS RF.L.ITIOX TO MCSJC HI the relation of the simple harmonic upper partials to the sounding body. 'Jhiis a tunini^-fork ma\- induce resonance in a jar whose vibration rate is twice, tlirice, or four times ils own. Jf a lone l)e sung when the dampers are lifted fre)m ihe strings of a piano, not only will the siring wliich gives the same note resound, but also a number of tones re])re- senting higher partials will be clearly heard. Press down the keys representing the chord c' c' g' ^S=-^e^ on the piano and slrike c '^=^isrz^ shar])ly, releasing it immedialeK' afterward. The group of upper strings will be set inlo vibration induced partly by the fundamental of c and partly by ils upper l)ariials. Likewise tones coincident with the upper partials of another tone may cause these to sound. 1 Icjlding down c ^9^^^^^T^^ on the piano, ])hi)- and release a number of tlie ui)q)cr f's. /:"'s and G's. Many of these will now "dSced^by"''*'' be heard vibrating as partials of the original c. resonance. To prove this fact let go of the kev v^diich is Ijcing held down, when bv the consequent fall of its dam])er the sounds will im- mediatelv cease. Certain substances have so complicated a structure that they are a})i)arently capable of reinforcing any sound what- ever. One of these is wood. IMace the end of „, , Wood as a a sounding tuning-fork against the top of a resonator, wooden table, and a great increase in its tone will result. whatc\-er be its rate of vibration. So also the tones of a mtisic box, when the latter is brought inlo contact with a wooden surface, are nmch reinforced. In ihe case of the resonating box above alluded to (page "/}>') the tone of the tuniir-'-fork is intensified not onK- bv the air-column in the box but also by the wood of which the latter is made. W'ithout reinforcement the tone of a string is so slight 82 50 cay;, .IXf) ITS RliLATIOX TO MUSIC as to I;c scarcely perceptible. This fact can be proved Ijy stretching- a strinj/, sus])en(le(l in free air, bv „ ,■ o o' 1 . Sounding- means of an attached weight. When the string boards. is vibrated b_\- a \'iolin bow little or no .sound is heard: but if it be subjected to an e(|ual tension when stretched o\er a boartl a tone of considerable ^■olume results when the string is sounded. 'rhu> the full and rich tones j^roceeding from a piano come in realit_\- from the \-ibrations o\ the .-ounding- board which ha\c been .-^et in motion through s\'mpath\- with the \ibrating >trings. W'c ma}' realize the agitatir>n of the sounding-ljoard in tlie piano l)\- [)lacing a >mall object such as a pencil upon ii. When a tone is produced to which it can respond, the Experiments .... . with sounding- ])encil Will jar (h.-agiccabl\ , nni)elled l)v the boards. .■,..'.. ' ^ . ' ... l)oard with which it is m contact. A tamihar children's tov was at one time maue in the form of small figures or "iJUiJpets"" which when set U])on the >ounding- i)oard waltzed about merril\. and which could ea-ily l)e o\er- tlirown b\' an especialK- hea\\- lone. All f(jrms of stringed instruments recjuire such reinforce- ment. Ihose of the violin t}])e reinforce the string tone both b\- their wooden bodies and aIed witliui tlicm. ill tlic casc of the ijanio, instruments. ,• , , • i , i i" . the soimding-board is re])laced i)\- a >tretched membrane like a drum-head which .also i> ca])able of re-onat- ing to anv tone, ])roducing. liowxwer. a resulting sound ol a duller, le>- elastic qualit}-. Membrane.-, on .account of their extreme >en.-iLi\"it\ to all .-ouikIs. have been m.ade the bases of important ai)i)liances for recorclimj- .and reijroducing sound. An in- Uses of ' n^embranes. staiicc of .-uch use is fouud ill tlic drum.-kiii of the e.ar. which coiucws exterior u])on smoked paper covering a revolving cylinder. Most of these features were retained in the phoiioyrapli invented by ITlison in 1877, but in the latter instrument the style made indentations in a piece of tinfcjil at var\ing depths, so that, when the st}'le was placed back at the beginning of these indentations and caused to retrace them at the same rate as at first, l)oth the style and the membrane a])proximately repeated their former mo- tions, and hence gave out sounds similar to the original ones. The phonograph. mmmmr\ 70. ( )ri.t;inal of the Phonoi^raph. The nature of this historic instrument ma\- be better under- stood bv consulting Mgures 70 and 71, which give a general and sectional \-iew of its original fi)rm. Soimds trax'cl down the fimnel P P through the mouth])iece proper in in focusing 84 SOl-M). .1X1) ITS NJiL.rnoX TO Ml'SIC oil ihc nicniljranc or diaphragin ;; ii fixed in the bar / wliich is ])i\-()te(-l at o and adjusted by the >cre\v c at the to]). Attached to the (haphragni is a small plate, which carries Fig. 71. the style p. Thi= style is not directly in contact with the tinfoil but i)resses on a sprini^- bearing- a small rounded metal point 7 which indents the tinfoil .r on the revolving cylinder JV. As this original machine was \vorked by hand, diffictilt\- was ex- perienced in producing absolute regularitv in the motions, a defect \\hich is remedied in the modern machines bv the use of a mechanical motor. \'arious forms of the i)honograph are now on the lUcirkct, in which the records are made in a wax com])ositi()n from which thev are afterwards reproduced in firmer materials, .^ome machines still emi)lo\- the cylinder form of records, while in others, sometimes termed gramo- phones, the vibrations are recorded upon a revolving liorizontal SOUND. JXI) ITS RliLATIOX TO MUSIC 85 disk in spiral cur\cs wIiIcIt proceed from llie outer edge toward the centre. The implement now used lor cutting the record is different from that which reproduces it. the former consisting of a sapphire point and the latter of a similar point or How the tone a needle of metal or hhre. One of the greatest is reproduced, marvels of science is illustrated in the comhined work of these little tools, the hrst of which ploughs into the wax a reproduc- tion of not only a single sound with its attendant overtones, but frec|uentl\- of manv other accompanying sounds, each with its characteristic quality, and the second of which travels over each minute indentation with fulelit}', transmitting its complex motion to the diaphragm, whence it is conveyed through the air to the ear of the listener. If we could trace out one of the grooves in this record with a microscope, its appearance would be found to resemble that presented by the ruffled surface of a lake seen through a slit in a card. Long indentations made by the fundamental tones would be seen traversed by number- less ripples, each corresponding to an overtone or another fundamental, and each having a dei)th proportional to its intensity. Several instruments have been devised to bring ])honograph indentations into readable form. Professor McKendrick. of Glasgow, constructed a "phonograph recorder" Experiments r 1 1 r 1 • 1 1 11 • '^'*'^ phono- irom the results oi which he was able to csti- graphs. mate the enormous number of x'ibrations involved in even quite simple sounds. In the record of the words 77/r Royal Society of Eilinburgh, for instance, he discovered over 30()0 Fig. 72. Curve of the pronoun A 86 SOUXD. AXD ITS REL.ITIOX Tu ML SIC \ibrations. Vxg. 72 shows a graphic record of the sound of the vowel /, made by lulward S. W lieeler, of ^'ale Uni- versity, as the resuh of similar ex])eriments. The possibili- ties of stich devices in determining the composition of tone> can readily l)e recognized. The tclcpJiDiic also depends for its action up the sounrls impinging u])()n it. In the traiisDuttcr these vil)rations The telephone. i j • • i • i • i ])rt)duce tiuctttations m an electric current which carries them through a wire circuit tn any doired jilace. There they in turn affect the membrane of the rccci\-cr. wliich reproduces them to the ear of the li-tener. [lU'enied b\- ( Jra- hani ]lell in IS"''), the tele])hone was at fir-t of no commercial \alue (in acccnmt of the indistinctness of the rejjrorluctions. lly means of inan\- cle\'er devices which have enonnousK- in- crea-^efl its sen-itivity. however, it has now attained ilie ])0>i- tion of a household neces>it}". .\t lir>l n> < di-tinctiiin was made between the transmitter and tlie receiver. W'liile tlie latter has retained mucli o\ its original form, the tran-^mitter is now fjuite dift'erent. its ethcac\- having lieen greatl\- aug- mented b\- the tise of carl)on. Animal memiirane^ ha\c lieen generallv re])Iaced in br)th ])lK;nograph and, telephone b\- thin di>ks of mica or metal. l'erha])s the mo>t remarkable manifestation- of the ])he- nonicna of roonance. howe\'er, are found in connection with o . ihe human \"oice. \\\ directing the air current Kesonance in ■ the voice. j,-,^^, ^\^^ cavities of the head, mouth and ihri-at. and b\- miidifving the sha])e of the-e ca\'itie-. the -])eaker or -inger is able to ])roduce an infinite numljer (>f moditicatii ais in tonal intensit\- anrl nualitw l-"urther ci 'ii-ideralioii > .{ ihi- important phase of resonance i- re^-erxed f(jr Chapter \ III. SOUND, AND ITS RELATION TO MUSIC 87 SU\mARY. Resoxanci:, or sympathetic vibration, depends upon tlie principle that a nimiber of shght iniptilses properly applied will linally create considerable momentum. A very rigid body, to be aftectcd by the sound coming from another bod\', must be either in perfect unison with this sc^mul or must have a vibration rate which is a simple multiple of that of the sounding body. J^)odies of less rigidity mav respond when they are not absolutely in unison with the sound which strikes them. Instruments called resonators are capable of selecting out special sounds for reinforcement, and may even develop sounds ordinariK- imperce])til)le to the ear. Air-columns in tubes can be made to resound under the influence of ttining-forks, the ""whistle" device, reeds, and gas- flames. Reeds in organ pipes are either striking or free. Sensiti\-e flames are of value for testing the properties of sounds. Sounding-boards and membranes are apparently capable of responding to an\ sound whatever. The former are usefttl in reinforcing the tones of strings, especially those of the piano and of the \-iolin family. Membranes are chiefly employed for recording and reproducing sound. REFEREX'CE LIST. HchiilioUz. Chapter 3. Barton. Cliaplcr (i. Zaiini. Chapters (\ 7. I'yiidall. Cliapters 3, 5, 6. Harris. Chapters 7, 10. Broadhousc. Chapters 6, 10. Poynt'nig and Tlu>}}ipson. Chapters 4, 7, 8, 9. Stoiic. Cha])ter 3, Taylor. Chapter 3. Ba>'uc.':. Cliapters 4. 7, 8. SOUND, AND ITS RELATION TO MUSIC La^ngnac, Chapter 1. Catchpool, Chapter 5. Blascrna, Chapter 3o CHAPTER VII, ScALi':s. L\ti-:k\ ALs and Chords. Having reviewed the chief facts i)ertaining to the nature anelection of tones as has been described is in many 90 SOUND, AND ITS RELATION TO MVSIC respects a purely arbitrary one, resulting in the formation of „ diverse scales among distinct nationalities. Xcv- Common use " of the octave. erthclcss there are a few intervals which are common to nearly all musical s}'stems. \\ hen, for instance, men and women attempt to sing the same tune, it is natural for them to pitch their voices an octave apart ; and so intimate is the relation between these octave tones that the partici- ])ants often believe that thev are singing in unison. For the same reason we speak of a tone as repeated in another octave when the two tones are an octa\'e or a multiple of an octave apart. Hence the characteristics of any scale are alwaxs in- cluded within the compass of an octave, while anv extensions of the scale will arise from the repetition of the same inter- vals in succeeding octaves. The xeJiolc tone or whole step, a])proximatelv one-sixth of an octave, is the general unit of measurement. (Jther inter- ^^. . ^ , \als freciuentlv found are the i)erfect fifth and Other intervals ' - ' in frequent use. perfect fourth. represented in our scale by C-G and C-l\ and measuring rcspectix'elv 3'j and 2'j stcjjs. F,x- cei)t in the case of the inler\'als cited, hovv'ever, there is little uniformit}' in dillerent systems. We mav in general distinguish two classes of scales, the first of which avoids intervals smaller than a whole ste]). „ , while the other .'-ubdivides the >tei) into interx'al-^ 1 wo classes ' of scales. which are sometimes exceedingl\ minute, 'flic chief scale of the first class is the peiitatoiiie or five-note -cale, which embraces three u-hole-slep inter\-als and two interw'ds of a -lep and a half each, tluir- : ^ ( Figures beiieatli refer to >te])s and frac- /r, ^^ \, _o- "- *- -^ tions of ste])s. ) Its effect ma_\- be judged ' ' '- ' "- , , . 1)\- ])la\in"- in >uccL-->ion the 1,'lack ke\s of the 1 he pentatonic . i . .^ • ^"'<^- i)ianofnrtc. ( 'liine-c folk tunes are almo-t in- \arial)l\- t'ounded u])on thi< scale, wliich is re\ered a- the >u])ernaturall_\-sent foundation of mu.-^ic : and although in China twc-Ke dix'isions of the octax'e are recognized in tlieorx', the ])cnt.atonic --rale -till retains its i)re-tige in i)ra'-tical u-ai;c. SOUND. AND ITS RELATION TO MUSIC 91 Japan and other Oriental nations employ a similar scale, while its existence in Scotland is plainly evidenced in popular melo- dies. In our own system the octave is di\ided by semitones or half steps into twelve parts; and from a combination of live whole steps and two half stei)s the major eight-tone di- /■ Use of the atonic scale ^ ' ^".. » "t7" ^E^^ is formed, ^^^^ ^"p- which is the basis of our music. Our harmonic minor scale eni])loys the interval of IVz steps between the sixth and seventh decrees, thus : -V h ~i TT^ " ^' ^"^^ In some scales still t;reater variety is secured by again inserting this interval be- tween successive degrees of the eight-tone scale. Among stronglv imaginative j^eoples there is a tendency toward the use of minute intervals. The ancient Hindoos, for instance, divided the octave into twenty-two ^^^^^^ ^jj^ ])arts, and the Arabs into seventeen, the latter minute intervals, determined in accordance with mathematical princii)les. A multi])licit\- of scales is the general secjuence to so ct)mplicated a system of subdivision. Intervals as small as the (|uarler-step also existed in the scales of the ancient (ireeks. h^our tones arranged within the compass of a ])erfect fourth, seems to have con- • I 1 1 1- , • 1 1 -n ■ ■ 1 '^'^'^ foundation stituted the earnest ( ireek scale. I his received of the Greek the name of tctrachord. or scale of four strings, from the fact that its tones corresponded t(^ the tuning of the four strings of the original lyre. Terpander the Spartan, in the se\enth centur\' \\. C. combined two tetrachords bv a common note, producing a scale which had the com]:)ass of a seventh; and Pythagoras (died about 500 R. C.) increased this to an octave by placing a step between the two tetra- chords. The latter philoso]:)her investigated the vibrations of strings 9Z SOCXD, AND ITS RELATION TO MUSIC by means of the inonoclwrd, a i)riniitive form of the sonom- Theoryof ^^^^ i^'^S- -- ) ■ -I" ^^^^^ ^vav he discovefed that Pythagoras. when the length (jf a stretched string was di- vided in the proportion of two to one, the interval produced by soiniding the two segments together was an octave; that a di\"ision of three to one resulted in a ])erfect fifth; and that one of four to three gave a perfect fourth. lM"om these re- sults he deduced the ])rinciple that "the simpler the ratio of the two parts into which the vibrating string is divided, the more perfect is the consonance of the two sounds," a theory of which llelmholtz was the first to gi\c a logical exi)lanation. J'Mhagoras constructed an eight-note scale by starting with an octave and inserting the inter\'ening tones found b\- pro- The Pythagorean '-Ceding by i)erfect hfths from the lower tone; ^'^^''^- thu< beginning with the octave C'-C he went from the lower C^ by fifths to (/, D, .1. IL and B. lowering the tones outside the original octave to their position within it b_\' octaves, and adding I' . a perfect fotirth abo\c ( '. Two results of this process should be noted. It was dis- ci:)\'ered that the third tone /: was related to (' in the compli- o ,, , cated ratio of -fV, and hence the major third Results of tj -» ' this scale. .^^.^^ cla>sed as a discord, 'fhen also P_\thagoras found that if he extended his circle of fifths as follows: r, G. D. ./, R, B. Ft. Ct. Ct. m..\t. /!:, Bt, the final Bt w;is shar])er by about -W than the nearest C. obtained bv raising the (original (' bv ()Cla\'es. and that when he ])roceeded downward by fifths as follows- C, /•. Ih. Eh, .lb, nb, Cfb, Co, l-b. Boo. Ebb, Abb, /)-b. the final /'bi was flatter than its nearest (" b_\- the -amc amount, 'fliis discrepancy ha> been called the Pythaf/orcan c omnia. With the tetrachord as basis the Cireek^ formulated three classes of scales or modes, 'fhe first or diatonic genus em- braced all possible arrangements of whole and Greek modes. , , - .... ' . ^ , , halt ste]:)s within tlie com])ass ot a tonrth ; the SOUND, AND ITS RELATION TO MUSIC 93 second or chromatic genus combined two half steps witli tlie interval of a step and a half ; while the third or enharmonic genus embraced two quarter steps and an interval of two whole steps. The following illustrations of (Ireek modes in modern nota- tion do not rej)resent their absolute pitches, which varied some- what. Scales were conceived by the Cireeks, in common with most early peoples, as proceeding downwards instead of up- wards as in our musical system. Examples of the three genera : Dialdiiic Enharmonic Most important of these genera was the diatonic, of which seven modes were recognized. Jn each of these the octave compass was completed bv joining two tetra- ' - ,, . Diatonic genus chords together ; and all became hnally mcor- and complete system. porated mto a so-called "complete system, two octaves in length, to each note of which a name was given, taken from the nomenclature of the lyre strings. The result was as follows ; Hypo -Dorian Hypo-Phrygian Hypo-Lydian \ \ \ \ Dorian i i i : Phrygian : I i Lydian ; I Mixo Lydian ' | The complete Greek system. Undoubtedly Greek music played an important part in forming the music of the early Christian church. The latter, at first purelv vocal, consisted of unison melodies. „ ^ ' Gregorian generally not more than an octave in compass and "^odes. based upon scales that were not definitelv formulated for some 94 SOUND, AND ITS RELATION TO MUSIC time. Ultimately, however, these scales were arranged in a series of "chtirch" or "Gregorian modes" supposedly the same as those of the ( ireck diatonic genus, h'our authentic modes were sup])lemente(l by an equal number f)f plagal modes, each of which was a fourth lower than its corresponding authentic. Later on four others were added. Lach mode had two notes of s])ecial importance, the linal or ending note and the doiuinant or reciting note, which are shown in the table of the orii/inal modes formulated in Iwg. 72>. Finals Dominants Fig. 73. The numbers before the scales indicate the following modes: Authentic. Plagal. I. Dorian. II. Hypo-Dorian. 111. Phrygian. I\'. 1 lypo-1'hrygian. \'. L\(lian. \'I. 1 ly])o-I,ydian. \I1. Mixo-l.\(lian. VIII. 1 lv])<,-.Mixo-Dydian. i lalf stejjs arc shown by slurs. olbcrwi,-,c whole -leps prevail, r.v the eleventh centurv all these scales were united in a long SOUND, AND ITS RELATION TO MUSIC 95 scale of about two and a half octaves, extending from G to c" , and divided into seven overlapping scales of six notes each, called lie.vachords. Meanwhile the dance rhythms and secular songs of the l)eople were conforming to scales which were able to give a de- siraJjle sense of linalitv to the verse endings ■ Rise of major oi rlumed stanzas oi poetry. .V tune and its and minor , . ^ , scales. accompanying harmonies were made to revolve around a central tone, to which an ending formula or cadence hnally led. Thus tonality was evolved ; and with it came the dominance of the so-called major and minor scales which eventually superseded the older forms. . This change in attitude, together with the growing complex- ity of music due to the [)Oi)ularity of instruments and the con- seciuent rise of new forms, presented problems „ ,,. ^ '11 Resulting to the theorists of the later fifteenth and the p^-obiems. sixteenth centuries which provoked much controversy, Let us see what these problems were, and how they were dis- posed of. Jt was tirst necessary to establish the proportion of the intervals of the major diatonic scale of eight notes, which came to be regarded as the basis of our musi- , .• r "^ Location of cal s\ stem. This proportion was determined by diatonic tones, adopting the relations discovered in the hrst fifteen harmonic I)artials resulting from the equal subdivisions of a vibrating string, as shown in Fig. 74. From this series we perceive Pit octave 74. that the interval of a whole stc]), first required for constructing the scale, occurs ])etwcen c" and d" . the eighth and ninth par- tials. According to the laws of strings c" must vibrate 96 SOUXD, AND ITS RELATIOX TO MUSIC eight times while d" vibrates nine times ; or, in other words, their ratio of vibration is 9 to 8, represented by the fraction -|. This interval of a whole step is called a major second. Hetween c' and c' is the interval of two whole tones, called a major third; and for reasons similar to those just advanced the ratio may be represented by the fraction ^. From g to c, a perfect fourth, we derive the fraction |- ; from g to c\ a major sixth, the fraction -5, and from c" to b" , a major sev- enth, the fraction ^f-. These results are summed up in Fig. 75, each fraction showing the relation which the note above it bears to the tonic c. Cnison Maj 2"" Mnj S^.d Per 4'h Per5'!i Maj 6'^ M--ij 7'h Per Fig. 75. Other important intervals in\olved in this scale and also derived from the partials of strings are the minor third from ~, . c' to (/'. with th.e rati<) of ---. and the minor The minor •' o ■ third and sixth, gixth, from c' to c" , with the ratio f. The scale thus formed is called the "true"" or "just"" scale, in distinction from the "tempered" scale (page 103 i. \\"e „, ... ,„ note that the major third is simplified to 4 or ,'■ 4. The just - 1 4 !■ 4 ^'^^'^- against the Pythagorean major third of -f^. so that the upper tone (jf the latter is slightly sharper in pitch than that of the "true"" third. From the table, V\g. 74, we can also determine the ratio b(;tween contiguou> >cale notes ])y applying the mathematical T3 . principle that the ratio of the difference be- between twccn two intcrvals is found by dividing the contiguous ■' ^ scale-tones. ratio of the greater by that of the less. The results are as follows : c, D, /-:. F, r;, .-i, b, c. V ^ 9 ' 1 .'j 8 9 8 15 A\"e notice that, while the half steps have the same ratio of SOUND, AND ITS RELATION TO MUSIC 97 yf , the whole steps vary in size, three having the ratio | and two the ratio ^ . The shght difference of g^- between them is called a comma. After the diatonic scale was thus formed the whole steps were subdivided by chromatic or "colored"' tones, so-called be- cause they gave varied shadings to a melody. These, at first used only bv singers to give chromatic , . '. ' . , tones. smoother voice progressions, were atterward adopted by composers, who discovered that they were available not only for melodic purposes but also as a means of changing the tonality, or modulating. To make this key-interchange possible the new tones must have the proper relations to the other tones of the scale in which thev occur. Thus, since the seventh tone ^ ^. , ' Location of B of the scale of C is a major third above the chromatic tones. fifth tone G, the same relation must exist be- tween the fifth and sev- enth tones of the next scale, G ; hence F^ is placed a major third above D. In like manner C5 is placed a major third above A, G< above E, Dt above B, and A* above F^. After locating the flats by a similar process we shall find that corresponding sharp and flat tones such as F- and Gb are not exactly in unison, but that of the two the flat is a comma higher in pitch. We have said that Fig. 76. Holmholtz was the first 9.S SOfXD, AXD ITS RIiL.lTJOX TO MUSIC „,,,,, to answer satisfactorily the ciuestion of what nelmnoltz s - i *"''^"- causes consonance and (hssonance. Vov inves- yating the relations between the tones he invented the double siroi (Fig. 76), which is a comi)lex form of the instrument shown in I'ig. 19. llelmholtz's siren contains two disks which can l)e rotated either individualK- or in unison. In the lower of these four sets of holes number 8, 10. 12, and 18 respectively, while four corresi)()nding sets in the up])er number 9, 12, 15. and 16. . I antl B are ducts through which the \\-ind i> introduced bv pressure from an acoustic bel- lows. Ke}'s at a and /' serve to throw into action an^• desired series of holes. At CD is a clock-work device used to record the number of revolutions of the disks, luich of the latter i,- enclosed in a brass box which forms a resonator for certain tones. In the illustration a part of the lower box has been removed in order to reveal the disk. A crank attachment ai /: serves lo raise or lower the pitch of the tone gix'cn bv the upi)er disk, bv rotating in either direction the cvlinder which encloses it. I'>y emplo}-ing the proper combinations of holes and rota- ting the disks in unison I lelmholtz was able to jiroduce the different vibration ratios involved in the various Experiments . . . . with this mtervals ot the scale: thus bv openmg the series siren. . . , , . , " ,. , . , . ot Sixteen holes in the upper disk and eight m the lower the resulting ratio of | gives the octave, while the two series of eighteen and twelve holes, having the ratio of i;- give the perfect tifth, and so on. The most significant re:-ult of the-e experiments, however, was in connection with tlie >ound-interferences which cause beats (page 44). In the case of the octave and tifth no beats were heard, but with all the other intervals beats were ])resent, var_\"ing in rapidity and intensit\- with the character of the inter\-al. Generall}'. when an\' "true'" interval was put out of tune 1)\- aUering the ])itch of the upper tone an acceleration of the beats followed. Consonance and dissonance, according to I lelmholtz, are determined b\- the nature and frccjuencv of these beats. As t or dissonance is proportion- al to the divergence of the two lines. Thus per- fect consonance appears at c. f. and g, slight dis- sonance is evidenced at the major third and sixth e and a ; while the increasing dissonance reaches a maxi- mum near either c. Lissajous (1822-1880) invented an apparatus in which small mirrors attached to a couple of tuning-forks were s(j „ , . .,, located as to throw upon a screen the combined Graphic illustra- ' tions of beats. niotiou of the forks, with the result that curves were reflected that were simple or complex according as the interval between the forks was consonant or dissonant. In a Fig. 78. similar device invented bv Kocnig. shown in hig. /8. one of two electrically-excited forks liears upr)n its ]M-ong a piece of smoked glass upon which a st}"le on a ])rong of the other fork is made to trace a record as tlic latter fork is mo\'ed along at right angles to the former, .^ome of the results witli forks of warving fref|uencic^ are >ho\vn in I'ig. 7'K uu\<"U forks giving the simple curves of the first example, the octa\-e next shown imparting a twist to the hgures. which are much dis- SOUXD, AXD ITS RELATION TO MUSIC 101 turbed as the octave is put slightly out of tune in the third example. The niajor third and the half step shown in the ^JS^^^^^^M^^^^ Fig. 79. fourth and fifth cxam])les display the expected growth in intricacw A cliord in music results from the combination of three or m(3re tones. Two thirds joined bv a common tone make a triad : and this triad is consonant when not onlv ., ^ . Nature ot the indi\-idual thirds are consonant. Init also the ^'^'^'^^■ fifth ])ro(luce(l b}' their union. Onlv two distinct triads of this nattu"e are i^ossible in our musical sxstem : the major, in which the lower third is major and the upj)er minor, and the viiiiur, in which these positions of the thirds are reversed. In both cases the fifths are ])erfect. Three jiositions of each triad are recognized, according as either note is jjlaced beneath the others. Since, also, the triad tones may be located in dif- ferent octaves and mav be reduplicated at will, there is much possible ^•ariety in their combination. From a studv of the resultant tones Tlclmholtz selected six combinations of the major triad as mo-t jierfect and six as less 102 SOiWD. .IXD ITS RliLATIOX TO MUSIC r, ^. ■ r i)erfeci. Tlu'se are ♦- * 7 i s 9 10 u 12 '^~~ — r a u. k=l (gS M Fi?. 82. Fig. 81. combination of the tones of the minor triad \\a> foimd free from (Hscordant resultant tones, so that the three best ])o-^iti(.)ns are tlvjse of l--ig. 82._ Tlie major and minor triads f(;rm the basis of our harmonic s_\stem. since tliex- are the chief Other chord Hican^ of e>tabh .-^liiui.;- tonaht}- and i'urni-hini;- formations. point- of re])ose. I'.y adding other third.- to tlu'se, t-hords of the sci'Liith. itiiilh. dczcnt/i. and thirtcmth are built up, all oi' ^•ar_\ in,::^' de,^rees of dissonance. Abidern nui-ician- dis])]a\' their skill b\- the continuous u-e of -uch indeterminate chords to \\ea\'e a web of lo.^icalK-dependent l>ut con.-tantly-sliiftini^' harmonies whicli ,-ometimes dela\ .- the con- clusi\e con.-onance until tlie \er\- end oi the composition. l\evertin_^- now to the formatiijn of the .-cale, let u.- con- -idir -ome of the diftlculties whicli aro>e when the "iu.-t" -cale was a])])lied to I^e\-boai"d in>trumen!-. i-'.\-i- denily, in order to modulate from one -cale-ke\' to another it -hould lie ])o-sible to reproduce rxactU' in the cale of C, for instance, the fifths C-G, Ji-B, J'-C. and -i-/: are true. J) is a coiunia too sharp for the true fifth D-.l. and also a ])crfect fifth from n needs an additional tone, T'i.. W ilh each new scale there must he similar adaptations of the inter\al>, so that, in order that there nia\- he tmre- stricted modulation, an instrtmient must ha\e at least seventy- two ke_\ > to each octa\e I Accordingly, many attempts were made to reduce the num- Ijer of ke\s 1)\ slightK' misttming or tcuipcriiuj certain tones and thus identifving them with others of nearl\- „ ^ . ■^ - bystems ot the same ])itch. Two >_\stems based upon this "tempering." princi])le. each -of which emi)lo_\s hut thirteen keys to the octave. es])eciall\- claim our attention. In the first or nicaii-tuiic tcinpenuiiciit, the upper tones of all the hfths in the ascending circle ( ]^age ^)2) are flatted a ciuarter of a comma each, 'fhe ptu'itv of the ,. 1 ' - Mean-tone major thirds is thus ])reserved. so that condititms temperament, result exactl}' the op])osite of those in the scale of I'x'thagoras (page '^2). \vhicli kept the fifths true while mistuning the major thirds. \\\ ttsing this s}'stem t tenijU'rament is -hown > ai 104 SOUND. //A7) ITS RELATION TO MUSIC ! 1 lelmholtz"s diagram. The i)Osilions of tones in just intonation Comparison are indicated bv short verticals on the lower hor- of different . i i- i - i systems. izontal hne ; tliose ot the tones m mean-tone temperament by the dotted verticals; and those of the tones in equal teinj>eranient by the long verticals below. Although recognizing its a\-ailabilil_\- scientists for a long time oi)pose(l the general adoption of e(|ual temperament on account of its mathematical inaccurac}-, regard- Attitudes . . . . . ' , . ' toward equal uig it as suuplv a make-slult until something het- temperament. " ' . . . \ tcr could l)e devised. Musicians general]}, how- ever, from r.ach onward, have hailed it with acclaim, recogniz- ing its enormous jjossibilities in the direction of added musi- cal resources. They have pointed out that scales are chosen cssentiallv for .'esthetic effect, and tliat this elTect should not be fettered b\- mere mathematical con.siderations. Lhi(|ues- tional)ly the o])ening of the door to unrestricted shifting of tonality has been the cause of the wonderful ad\ance in musical ex])rcssion during the ])ast two centuries; and in \'iew of this dcvelo])ment the slight (le\-iation, scarcelv ])erce])tible even to cxi)ert ears, of the e([ually-t negligible. Then, too, the adoption of a standard scale for all musical use> i.^ of great achantage. It lias been suggested that music in its purelv vocal forms or as rendered bv the Advantages . ',,,,, • • of a uniform stnug f|uartet should be kejjt m pist intonation. scale. r. 1 1 1 • 11 out kevljoard instruments are now so closely SOUND. AND ITS RELATION TO MUSIC 105 connected with all other fornis of music production as to make the adoption of an altered intonation for special situations well-nigh impossihle. Orchestral instruments of fixed pitch are accordingly tuned to the ecfually-tempered scale, to which the players of stringed instruments conform without difficulty. Indeed, ahsolute adherence to just intonation is not easy for violinists, who so far violate scientific conclusions as habitually to play a sharp tone, such as f^, higher in pitch than its corresponding flat tone, or G"b. With singers alone, therefore, is just intonation optional; and, owing to the prevalence of ac- companied vocal music, it is doubtful if many take advantage of the privilege. Certainly, until theorists furnish something palpably better, the equally-tempered scale will continue to justify its name by pursuing its way serenely amid the many adverse criticisms with which it has been assailed. 106 SOUND, AND ITS RELATION TO MUSIC SUMMARY. Scales have l^een formed somewhat arbitrarily, although the characteristics of a scale are generally found within the com- l)ass of an octave, and the intervals of a whole step, a perfect fourth and a perfect fifth arc frccjuentlv recognized. V>\ the word interval we mean the ratio Ijctween the vibra- tion numbers of two tt)ncs. The (Ireek s}'stem of diatonic scales was followed out in the earl\ scales of the Christian Church. 'Jdiese latter were iinallv superseded by our major and minor scales, the intervals of which were fixed by theorists in riccordance with the as- sumption that consonance is produced by simple vibration ratios. llelmhultz was the first to ex])lain the reason for this doc- trine b\- showing that consonance and dissonance are dependent on the absence or presence of disagreeable beats. The major and minor triads are the onl\- consonant chords in our musical sx'stem, and therefore llie oiilv ones exi)ressing finality. ldie_\- are emplowd in a \ariet\- of combinations, ot which but few are theoreticalK' ])erfect in their consonain-e. "just" intonation is im])racticable for ke}!)oard instruments because of the impossil)le number of ke\'s re(|uired to ])fe^er\e the purity of all intervals. The svstem of mean-tone tem])era- ment wa-- long ])re\alent, but was fmalb; superseded b}- that of e(|ual tem])erament. KKbKkbA'Cl-: J J ST. I/chiilioit::. I'art? 2 and 3. Ziiluii. ChapttT 10. luirtnu. ( hapter 0. 1 1 arris. ( liapttT'^ 5. 14-17. l!r( ntllimisc. ('ha]>t(.Ts 13. 15. 16. /'<'U\ I'ari^ _' and 3. Lai'it of the way. A number of fmc hairs and the car- wax secreted b\- glands within protect this from the intrusion 84. Transverse section of the car. SOLWD, ,L\'D ITS RliLAl'lOS TO MUSIC 109 of external objects. At the end of the canal, stretched slant- wise and ctu'ving inward, is the thin, elastic membrane known as the drumskiii {V\\^. 84 /J ) . which, like the dia[)hragm of the telei)hone and phonograph, is cjuick to respond to every kind of sotind-wave which impinges upon it. ISehind this membrane is the middle ear or drum cavity, hollowed otit in the thick bony part of the sktdl. On the side of this cavitv opposite the drumskin are „, .,,, ■' 1 i The middle two >o-callcd zcindu-K's, each of which is covered ^^''• also by a membrane. The lower of these, the round zcindozv (Fig. 84 R) is abotit the size of a pin's head, while the upjjer or oral z^'iiido:^' (.I'ig. 84 O) is somewhat larger. In the lower wall of the cavitv is an opening from which the Eustachian tube (Fig. 84 ILT), ly^ inches in length, leads to the back of the throat. Whenever we swallow, this tube is opened, so that the drum cavity is kept in totich with the external air, and thus relieved from undue pressure. We can appreciate the need of this outlet when we experience the sensation of deafness and roaring in the ear which results from the clogging of the tube that sometimes occurs in the progress of a "cold in the head." Three peculiarly-shaped bones called the auditory ossicles (Fig. 84 .10), which have been named from their fancied resemblance to familiar objects, form a chain ^, ■' The auditory of connection between the drumskin and the ossicles, oval window. These are shown more specifically in Fig. 85. The lower part of the hammer is attached di- rectly to the drumskin, pull- ing it slightlv inward, while the upper part articulates with the anvil. This bone in turn is attached on its lower side to the apex of the stirrup, of ^'S- ^^• which the base is fastened to the membrane of the oval win- llammer no SOUXD, AXD ITS RELATIOX TO MUSIC (l(i\v. All these bones together form a kind of lever which re- ])ro(luces ever}- motion of the drtimskin in the membrane of the o\al window, with this diti'erence. however, that in trans- mission the \ibrations are diminished in magnitude but in- creased in force. As the membrane of tlie o\al window is but -j^- to TT^ij the size of the drumskin, this lessening of magnitude bccome> necessar_\-, while the greater force is re- ciuircd to o\-ercome the added density of the medium on the other side of the o\"al window, to which the \'ibrations must next extend. W'e >hould also mention two important muscles Contained in the drum cavitx , which have the ])ower (.)f tight- ening the memljranes respecti\elv of the drumskin and of the o\al window. It i.-- the inner ear, how e\-er, which contains the most im- portant and complicated -ection of the hearing apparattt> ; in- deed, if all the mechanism of the external and General form •in i • • i of the inner uuddle ear Were destro\ed, it nnght \ et he po>- ear. >ible tor a ]ierson to hear, in part at least, bv holding between the teeth >ome such (kwice as that mentioned on page i). which transmits the souikI throttgh the bones of the head. The inner ear occujtie^ a complex l)on_\- ca\'it\- which is >o winding in its cour-e that it i- called the labyrinth. Within the otuer or boiix labyrinth there is a meml)ranou- .■>ack called the nimil'vauous labyrinth, which follows a])])roxi- matel\- the ctnwes i)f the bon\- lal)_\Timli and is onl\- connected ■ 'A'ith the latter where the ner\ e tibre-^ ])a>s between them. Tb.e-e fibres ramif\- over the stu"face <>i the membranous labxriiith, and are excited l)\' minute liair> which ])roject from the delicate inner lining I'f the nieiiibrane, and which are t!uni-el\'es set in motion by ctiiliths. or niiiitite .^r)lid jjarticles like grains of sand. 'rbe.-~e particle-- are lloating in a waterv tlttid called the rinlclyjiif'h. which tills the membraiiotis lab\'- rinth, and the latter is nearl\- surrotmded liy a similar tiuid called the pcrilynij^Ji. Thi-^ perihni]ih is in direct contact with the o\'al window of the middle ear in the 7'estibulc ( b^iir. '^A Tl which form- th* SOUND, JX!) ITS h'l:L.ITIOX TO MCSIC 111 entrance to the inner ear and also the centre of I) 1 • 1 111 1 '^^^ vestibule Its structitre. hranclimg- ui)\var(l and backward and semi-cir- 1 Ml 11 11 1 • cular canals. trcjin the vestibule are tlie three so-called soiii- cii'ciilar canals ( I'iy. 84 SX'), which have live openings into it. These canals are beliexed to be the seat of the sense of e(|uilibriuni, and are therefore not intimateU- concerned with our discussion of the sense of hearing. It is in the cochlea ( I"ig. (S4 C ), situated forward and down- ward from the x'estibule, that sound-percepti(jn i> esi)eciall\- located. This cochlea ( meaning ■'slieU" ) i> .^^^ ■ ■ r •~ Divisions 01 named from its resemblance t(^ a .^naiI-shell. It ^^"^ cochlea. consists in a tube which winds two and one-half time> around a central bonv axis and terminates in a closed tip. A bom' partition called the lamina spiralis projects into the ttibe for about two-thirds of its diameter, the other third being spanneity proportionate to that of the exciting force. \\"hile thus pitch and i)itc)!sify are deter- mined, (jualitx results from the combination of the diverse sound-components. Intermediary agents between these fibres and the auditory nerve which enters at A', b'ig. 84. and which winds it^ way „, thr(.)Ugh the laminar sHralis, are the ori/ans of The organs ^ ' ^/ .' °^ ^°''*'- Corfi. two ranks of fibres at the base of the basilar membrane, N/hich lean over against one another like the rafters of the peaked-roof of a house. Xerve cells sur- round these fibres both on the exterior side and in the canal between. The exceeding delicac\- of the strticture of the cochlea can be estimated when we reflect that its entire coil has a diameter ^. . of but one-ciuarter tube, ■-tretching from front lo back, are the two folds of meml)rane known as the z'ocal cords. These are attached to tlie outer wall^, and are free which act au- tomaticallx'. the xocal cords n.dv be expanded or contracted iu Frontal sinus Vocal cords Fig. 88. Section of the head and Uiroat locating' tlie organs of speech and sonjf, in iudinu the upper resonators. Tlie important ma.xillary sinus cannot well he shown. It i-. found within the nia.xillar.v hone (clicek bone), 'riic inner end of the line marked ,\'i; ,: ■ - a: // r locates it. SOUMD. .I\n ITS RliLATION TO MUSIC 115 a variety of ways, and the "diink of the glottis" may be widened, shortened, or narrowed until it is entirely elosed. In ordinary l)reathing" the vocal cords remain wide apart, so that the air passes between them freely. When, however, t(Mie is desired, the cords are brought together 1 • • 11 1 • 1-1 r 1- 1 Action of SO that the an" is expelled ni a multitude oi little the vocal ,,,, - cords. pults, as With a reed. 1 hese putis generate a tone which, though feeble, is yet sufficient to set the resona- ting cavities into sympathetic vibration. The loudness of the tone is atiected by the amount of l)reath ])ressure on the \ocal cords, and the pitch is determined bv their tension and ])osi- tion relative to each other. We have now to consider the rrsoiiafijuj canities, the sha])e and adjustment of which have so important an eti'cct on the (|U<'i!it\' and ouantit\- of tone. Reference to b^ig. oo Mi , , ■ • • - 1 1 .The epiglottis (SN Will make the ])osilions ot these clear. At and the .,.,., pharynx. the t(^]) of the lar_\-nx is a lid or cf'ujlottis. which closes it in the act of swallowing and also aids in deyeloi)ing tlie generated tone. Xext ccnnes the cavity at the l)ack of the mouth called the pharxii.v. which nia\- be changed materially in sha])C b}- muscular action, and the walls of which come together when swallowing takes place. If the phar\"nx is kept as far t)\)(.'u as i)ossible its "esonance greath' enriches the v(x~al tone. Into it o])en the two luistachian tubes connecting with the ears (])age 10<)). Two ])assages from the ])harynx lead the one into the iiioiitit rarity and the other into the tiasa! canities. The soft palofc terminating in a pendulous tip called the iiziila. „, ,, >^ 1 1 Tile soft which can readily be seen hanging down in the pa'^te. back of the mouth, regulates the size of these openings. If the soft palate be forced backward until the ])assage to the nasal cavities is closed, vibrations arc ccmimunicated to the latter onK- through the i)alate, so that a muffled "nasal twang" results. When, however, the palate is allowed to hang frceh'. with only such changes in ])osition as are necessar\- to keep the cavities in tune with the generated tone, resonance i< un- 116 SOUXD. AXD ITS RRLATIOX TO MUSIC restricted and the tone vibrates through the cavities of the nose and head. The roof of the mouth, or hard palate, with the soft palate behind it form the floor of the two nasal cavities. These are „, , separated bv the bonv i)artition v.'hich forms the The nasal ' - - i '^^^'*'^^- bridge of the nose, and into each one project three spongy bones which serve to increase the surface area. This surface is lined throughout with mucotis membrane cov- ered with continually moving hairs or cilia, hv means of which the air entering the nostrils is ])uritied, tempered and moistened before proceeding to the lungs. A number of air-chambers or sinuses are hollowed out in the bones beside, above and behind the nasal cavities. As these „, . possess passages of communication with each The sinuses ' i & of the head. other and with the nasal cavities, thev form valuable adjuncts to tlie resonating resources. Since the nasal and head cavities cannot be changed in form, their resonating powers will be determined by their natural size and shape and their freedom from obstructions. While the nasal and head cavities are the chief factors in producing strength and purity of tone, the mouth cavity and its adjacent parts have as their distinct function the The mouth. , . , . . , modifications ot the tone m articulation. A dome- shaped roof consisting of the hard palate surmounts the mouth, bounded in front and on either side bv a row of teeth which furnish resistance to the tongue and lips in forming consonants. The free lower jaw, furnished wdth a correlative row of teeth, renders mobile the tongue, which is attached to it directly by muscles and indirectly by the Iiyoid or tongue hone. Evidently a relaxed lower jaw and flat tongue favor resonance by enlarging the mouth cavity. During articulation there is a constant muscular interi)lav between the tongue and the teeth, which by their varied posi- tions modifv or interrupt the tone to produce Articulation. . . ' ^. i • i most of the ettects which we translate into words. Changes in the shape of the mouth cavity as a whole are SOUND, AND ITS RELATION TO MUSIC 117 responsible for the tone-cjualities known as vozvcl sounds. Experiments have proved that each vowel has a jj^^yre of normal pitch Avhicli is. moreover, the same for ^^^ vowels, all voices. That of oo is the lowest and that of ee the highest, the others ranging between these limits, with ah occupying a middle position. I'^ach vowel-characteristic may. however, be extended u]) and down from its normal pitch, although cer- tain ])itches are more favorable than others. Oo and oh, for instance, are more easily sung at a low pitch and ai and ee at a high one, while ah lends itself readily to the entire compass. A'owel-qualit\- is modified in a variety of ways by conso- )iaiits, which are reallv forms of obstruction to the simple \()wel sounds. IJesides the tongue and lips, the .. , , •^ i ' Nature of organs of articulation, by which these oljstruc- consonants, tions are effected, include the teeth and the hard and soft palates, while the facial muscles may also be called into play as an aid in the process. .According to a classification that is useful for singers the consonants may be grouped as follows: 1. the explosives, such as p, t, f, %', in which the obstruction is complete; 2. the semi-explosives, such as b, d, and hard and soft g, in which the obstruction is only partial; 3. the pennanents, like /. ;;f. and n, of which the sound can be prolonged indefinitely. The aspirate sotmd of h is formed bv allowing the breath to flow through the glottis before the tone is ])roduced. Another classification grotips the consonants according to the place in which thev are i)roduced : for instance, m, h, p, made with the lips, are termed labials; f, d. and r 1 1 -1 -1 Labials, 11, lormed b\' pressing the tongue against the dentals and 1 7 7 1-1 I 11 gutterals. teeth are dentals: and those like k and hard g. made in the back of the mouth, are gutterals. These conso- nant sounds are also used in a number of combinations. There is no considerable difference in the formation of tone for the si)eaking and singing voice. In the o u j ' <^ .~> <-> Speech and former, since distinctness of utterance is the ®°"^- 118 SOUND, AND ITS RELATION TO MUSIC ]jrime requisite, the tone-compass is narrow and the tone un- steady, wliile in the hitter definite pitches are assumed through- out the natural voice compass. ■■S])eecli may he called the prose, and song the poetry of vocalization."'* Singers often make the mistake of unduly modifying vowels and clipping consonants in order to produce puritv of tone, thus defeating the primarv ohjcct of song, which is to give a fuller expression to the meaning of the text. ISesides the sounds of vowels and consonants, all kinds of tone-cjualities, hoth good and had, are possihle to the \oice. ^ , . , Trcjfessional imitators, indeed, are ahle to pro- Graphic vocal ' i '^°"^^- duce a recognizable vocal suggestion of almost any sound whatever. Some attempts have been made to se- cure gra])hic representations of vocal tones, so that practical means iiKn- Ije ])rovided for measuring their degree of con- formity to a given standard. Mrs. Watts Hughes, of T.ond(jn, published a pam])hlet in 1891 recording various ex])erinients with an instrument which she calls the Hid',l- are formed, such as those shown in b'ig-. S9. 90 and 91. Recently, also. by a similar device in whicli ihe vil)rations of a rubber dislx are reflected by an attached mirror upon a rai)idl\"-mo\-inL.' sensiti\'e i)late. Dr. AFirage. o,f T^iris, claims to have secured Fig. 89. Dai.sy fonn 99V/.-/. -'■Rosonanre in Siii.uiiiL; and Spcakins. SOL'XD, .1X1) ITS RliL.lTIOX TO MUSIC 119 photographs of the \oicc wliich show marked distinction- he- twecn true and fal>e intonation. All the tones ])rodttcc(l b}' the human voice cover nearl\- four octaves, although ^ , ' ^ Range of these limits have ''°'"^- been considerably extended bv exceptional singers. Average voices have a range of somewhat less than an octave and a half, c- nn ^- *• ;in(l in men this compas- i- h in. 90. i-ctn toriii I about an octave below that in women. The latter fact is dtie partly to the difference in the f(M-mation of the resonance chamber^ and ])artl\' to tin di- Fi£ 91. Shell form. \-crsit}- in the thickness and extent of the vocal cord.-, ih' -e < if men a\'eraging three-quarters of an inch and those of \v> nncn 120 SOiWD, AXD ITS RELATIOX TO MUSIC a half inch in length. \'oices are classified chietlv according to their quality, so that singers whose hest tt)nes are high in pitch rank as sopranos or tenors, those who excel in the mid- dle tones are called mezzo-sopranos or haritones. while the low voices are classed as altos or hasses. \'oices of extreme range are rare, for the average human voice is of middle range. Fig. 92 shows the normal limits of the various kinds of voices. COMPASS OF THE SIXGLNG VOICE Tenore •■ Tenore Barit ->ne Bas^o ' " Ba s^(> Primo Secondd Cantanle I'rot und Fig. 92. Compass of the singintr voice. SOUND. AND ITS RELATION TO MUSIC 121 SUMMARY. The ear has three sections, of which the outer comprises the lobe and the auditory ca)ial, lea(hng to the drumskin. Sounds are transferred from the drumskin in die middle ear by means of the three auditory ossicles to the oval windoz<.'. which cl()>es the entrance to the inner ear. In the latter the hon\ labyrinth is hlled with a watery fluid containing the incDi- bra)ious labyrintli, and by a complicated arrangement in the cochlea, sound is communicated to the auditory nerve, which conveys it to the brain. There are four factors in the voice. The first of these is the lungs, which as motor furnish the breath supply that sets into motion the second factor or vibrator, consisting of the vocal cords. The tone which they produce is greatly magnified and altered in quality by a number of resonance chambers, which form the third factor. Tone emerges from these as vowel sound, which mav be more or less obstructed by the consonant sounds originated by the fourth factor, namely, the organs of articulation. Individual voices differ markedly in quality and compass. REFERENCE LIST. The Ear. Helmholtc. Chapter 4. Tyndall. Chapter 9. Barton. Chapter 6. CatcJipool. Chapter 7. Harris. Chapter 3. LaTignac. Chapter 1, C. The Voice. Hehnliolic. Chapter 5. Broadhousc. Chapter 10. Barton. Chapter 8. Laz'igiiac, Chapter 2, A. The following books on singing have valuable data concerning acoustics : 12Z SOUND, AND ITS RELATION TO MUSIC Fillebrown, "Resonance in Singing and Speaking." (Oliver Ditson Company, 1911.) Curtis. "Voice P)uilding and Tone Placing." (D. Appleton and Company, 1909. ) Brox^'uc and Belntkc. "Voice, Song and Speech." ( G. Putnam's Sons, 1883.) Standard medical works, like Gray's Anatomy and Waller's Physi- ology may be consulted for more minute details concerning both organs. CHAPTER IX. AlUSKAl. I NSIRL'MKNTS. While the voice, most marvelous of all instruments, has been the common property of ail men in all ages and climes, artiticial instruments have taken on so endless a r r 1 I r 1 Variety in vanetv oi lorms that a mere catalogue or them the construction 1 i' -11 1 AT- 1 11 °^ instruments. would lill a large vokmie. W e shall content ottr- selves, therefore, with examining the most important of those of the present day, and with studying simply the acoustic peculiarities of these, leaving to specialized works the treat- ment of mintite details of their construction and technic. i'^or the most part, instriuncnts lune asstmied their hnal sha])es as the restilt of many experiments, in which scientific theories have played but a small part. When viewed in the light of acoustic laws, however, thev have almost always been fotmd to conform to these laws and to furnish interesting examples of their practical a[)plication. One kind of instrtmient is distingtiished from another by the Diatcrials of which it is made, its form, compass, sustaining power, decjrccs of possible iiitensitw and csijcci- „, , . . ' ./ .' i . 1 Lnaractenstics ally its quality. Again, some instruments are °^ instruments, restricted to the production of one tone at a time, while on others, like tlie violin antl 'piano, tonal combinations are pos- sible. As with the x'oice, each instrument must have a motor for exciting it into action, a ribrator generall\- accom})anied by a resonator, and a meclianism for re(/ulatinity, instruments are readilv divisible into a few well-defmed ty])es. Foremost among these, on ac- count of their wide range, facile manii)ulation „ •^ i Types of and general availabilitv, stand the instruments instruments: " - those with icith stretched strings. Let us first discuss those strings. 123 124 SOUND, AND ITS RELATION TO MUSIC of this class in which the strings are plucked, either by the fingers or by a device called a picctrnm. A weak-toned instrument chielly used for accompaniments is the (jiiitar. This has six 'strings, the three upper of catgut The guitar. and the others of silk wound with silver wire. ■♦*- tuned thus: .V"' *> ^ Its notes are always written an octave higher than played. The strings are plucked by fingers of the right hand while those of the left varv the scale-notes by press- ing the strings against metal bars or frets which cross the neck at the proper intervals. Upper partials or '"harmonics" can be played bv touching the strings lightly, instead of press- ing them upon the frets, at one of their nodal points. The guitar often accompanies the maiidolin. a pear-^haped instrument also fretted and having eight strings tuned in The mandolin. uuison pairs to the same tones as those of the violin, thus: ^^^S^ A ])lcctruin of horn or tortoise-shell rsrr held in the right hand excites the strings. While, as with all stringed instruments, the inferior limit of the ctep throughout the comitas-. the tuning may be "set"' for an\- major or miuiu- scale other than the origin.al one. Running [passages in broken chords, called arpcijgins SOUND, AND ITS RELATION TO MUSIC 125 from the instrument itself, are characteristic of the harp. By touching a string lightly in the middle with the palm of the hand and pktcking it with the hrst two fingers of the same hand, clear and beautiful harmonics are evoked. In the case of the guitar and mandolin the natural tone of the strings is strengthened by sympathetic vibration of the bodv of the instrument and the air within it, ~, . ' Their while with the harp a similar effect is gained resonators. by the sound-box on which it stands, and which acts as a resonator. Instruments with struck strings have as their chief repre- sentative the hard-worked pianoforte. Eighty-eight strings of different pitches, of which all but the verv lowest 1111 1 111 ' 1 '^^^ pianoforte. are doubled and many are trebled, extend at semitone distances over a compass of 7ji octaves, from .-in to c^'. Their t(jnes are reinforced bv a thin, flat sounding-board. ]"\dt-covered hammers are driven against the strings by a key mechanism, to induce vibration, and by the clastic covering and rounded ends of these hammers the metallic overtones are suppressed which are produced when a hard object strikes a string at a single point. By making each hammer attack its string at ^/7 or V^^ '■'^ its length from the end, other disagree- able upper partials are avoided (page 58). The soft pedal, bv moving the action along in the "grand'' j)iano. causes each of the hammers to strike on one less string than it does normallv. Svmpathetic vibrations in ^ ,., i Quality the string thus left free give a peculiarly delicate °^ ^°"^- flavor to the tone; otherwise the ])iano tone is susceptible of little variation in quality. Its availabilitv as a hcnisehold in- strument, its power of suggesting harmonically all forms of music, its usefulness for accompaniments and its large reper- torv of important solo compositions account for the wide pop- ularity and influence of the ]iiano. All the in>truments thus far studied give tones of an cx- piosiir character, since the vibrations of the strings rapidly die awav after their first impttlse : hence the performer has no 126 SOUND. AND ITS RELATION TO MUSIC Means of stopping vibrations. direct power of sustaining a tone and can only suggest this imitatively. as by rapidly repeating the given impulse. Since the harp and pian(_> tones, although greatly weakened. }et continue for some time after the strings have been excited, means for stopping the vibrations must be provided to prevent confusion of sounds. The hari)ist accomplishes this result Ijy laxing the ])alms of his hands on the strings immediately after thev are sounded; while, in the piano, dampers connected with the individual ke}-s descend upon the strings when the keys are released, except when all these dampers are suspended by the mechanism of the so-called "loud pedal." Althotigh the office of this ])edal i< thtis primarih- to allow a tone to continue, its use also results in the reinforcement c^f a given tone by the partials of other strings in unison with it. Of all manufactured instruments those j^ilayed with a Ijow allow the performer the most absolute command over the tone which he producer. Hence in the develo])ment of the orchestra the '"strings." as they are po])ularly called, soon took lirst place, resolv- ing themselves into the four forms which are em])lo\ed at ]M-escnt. the liolin. viola. z'ioUmccUo and double bass. Considering first the ^'iolin. as the most imjxirtant member nt thi< famih- ( Fig. *\3 ) we The violin. - , ', • , tind tliat It n;i^ t(un- strings, the three tij^per of ])lain gut and the lowest wound with fmc wire. Tliev arc tuned thus : Fig. 93. violin. Lt'iicth . 2 'i in.: ltn,trtli of how. 29i in Bowed instruments SOUND, AND ITS RELATION TO MUSIC 127 Brilliant and ethereal tones are produced from the highest string, the others diminishing in vividness, and the lowest having a rich and sombre (juality. X'ibrations are induced by the rosined horse-hairs of the bow, and are communicated through the bridge to the resonating body of the instrument. The air within this also serves as a resonator, as may be proved by blowing across one of the two vents called "F holes." Many violins are found to possess special resonance for one or two tones, although this property is not considered desirable. Diilerent scale-tones are obtained, as on the guitar and mandolin, by pressing the strings upon the finger-board with the lingers of the left hand ; but in the case of ,.,.,, . . Its fingering. the violm the absence of frets at once makes greater demands upon the musical sense of the perfornrer and at the same time opens greater possibilities in the direction of sliding from one tone to another or slightly varying the pitch of a tone. The latter effect is used in the vibrato, made by oscillating the finger to and fro on the string. The normal range of the violin is about Zy2 octaves, extend- ing to r". This range may be pushed somewhat further by the use of harmonics, wdiich result from touching , . .... , ^ . . Its compass. the strmg at nodel pomts mstead of pressmg it down. Several conditions contribute toward the quality of the violin tone. Purity is favored by 'drawing the bow straight across the string, since lengthwise vibrations, ^^^^g, otherwise excited, introduce "scratchy'' elements, possibilities. In light passages the bow is held obliquely, so that only the hairs on one edge touch the strings, while in forte passages the tone is increased by bringing more of the hairs to bear upon them. The speed and pressure of the bow are also determining factors, as is its location on the string. Bowing near the bridge produces brilliant overtones, while the quality grows softer and more flute-like as the finger-board is ap- proached. Ordinarily a position about an inch from the 128 SOUND, AND ITS RELATION TO MUSIC bridge gives the best results. Roughness of the bow or im- l^erfections in the structure of the vioHn may seriously impair the quality of tone. Even an e.xpert violinist cannot produce satisfactorv results from a poor instrument. On the other hand, a violin made skillfully of hne materials, such as well- seasoned woods and enduring varnish, should continually im- prove with proper usage, as its resonance becomes more perfect. V>y affixing a small notched clamp of metal, called a mute. to the bridge, the vibrations are impeded and a soft, veiled quality is imparted to the tone. It is important that the constituents of all the violin-strings should be alike, so that no part of one is ditlerent from a cor- responding part of another, since the lingering Variations in 111- 111 structure of for wholc and halt steps would otlierwise varv on strings. ,. . . " ditterent strmgs. So l"ng as all the strmgs ahke become thinner where the bow is drawn across them, for in- stance, the relative distances remain constant, but if a string breaks and a new one is inserted which is not worn as are the others, difficultv will be found in ])la}'ing in tune. Hence skilled performers often rei:»lacc the whole set of strings when one of them breaks. Single tones are made possible bv the rounded form of the bridge. Two strings side b\- side may be sounded together. but when three or four tones are to l)e combined Special effects. ... arpeggiatmg is necessary. A tone may be sus- tained for anv amount of time, and may be increased or diminished in power while sounding. Man}- kinds of Icf/atc and staccato can be produced, while there are special effects like the tremolo or >hivering of the bow on the strings and the saltaudo or jumping bow. In the l'i.z.::icato the violinist plucks the string- with his fingers. Most of what has been said regarding the violin ap])lic^ alsr) to the other orchestral stringed instruments. Headed b_\ the i\ry opening or closing six smaller holes, of which the player manipulates three with the hand, the length Fig. 96. Boehm Flute. Length, 26i in. ^£ ^y^Q air-col- umn is changed and the tones of the diatonic scale are formed. Other holes, closed by valves, may be opened to obtain chro- matic notes. Starting at c' the range extends upward to about tib'^ Por the lowest octave the fundamental tones are used ; but to sound tones in the second octave it is necessarv to ,. Its registers "overblow" the instrument, so that the first upper ^"'^ quality, partials are heard instead of the fundamentals. Still higher partials are evoked through the rest of the compass. While the form of the flute would naturally give rise to the entire series of upper partials, the friction of the air along the sides of the narrow bore destro} s most of them, so that in the lower octave or "register" the tone is sonorous but somewhat hollow, the middle register is sweet and melodious, and the highest register is more brilliant and 1)ird-like. Formerly made of wood, flutes are now constructed also of metal. Most agile of all wind instruments, they are at home in all kinds of running ])assages and in quicklv re- 1 (.1 1 1 '" !•• -i^M -1 ' 1 Its possibilities. peated or double-tongued notes. W hue used in the orchestra to give brilliancy by reinforcing the tones of other instruments, the flute also renders solo melodies or runs with much charm. A small flute called the piccolo (Fig. ""'"V having a compass 132 SOUND. AND ITS RELATION TO MUSIC The piccolo. Fig. 97. Piccolo. L^iiKth 12Hii an octave higher than the instrument ju.st de.scribed, is the only other member of this family which has orchestral significance. Its clear and sharp middle register is useful for special effects, such as the E^ ^ U-^l ^g^ ^^i^ whistling of the wind or the rustling of leaves. Next among the wood-wind comes the oboe family. This has four principal members, all conical in form, enlarging graduallv from the mouth-piece to the other end. Characteristics ^ ,.,.',, , , ,,,, . ,. . . , . of the oboe which IS Ijeil-shaped. i heir most distinguishing characteristic, however, is the doul^le reed which acts as the motor and which consists of two thin sli])s of cane ])laced nearly in contact and attached by silk to a small brass tube that is inserted in the end oi the wooden part of the instrument. The i)la}er, hfjlding this reed in his mouth, breathes genll\- into it. pro- ducing vibrations which cause the air in the main tuljc to sound. Regulated in length by holes and ke\s ar- ranged on the same ])rinciple as those of the flute. the air-column gives out tones of different ])itche.s. forcing the flexible reed to conform to its vibrations (page 78). .V penetrating c|uality results from the emphasis of high upper partials in the full harmonic series that is ])resent. The ohoc proper (Fig. 98) is the treble mcml)er nf this family, having a normal range from hh U) (/'". When the flnner holes are opened in the The oboe. ' . , - tx ])roper succession tlie scale ot 1) major is sounded. r)ther tones are produced by u.-^ing the keys. Three registers are formerl as in the ca-c of tlie ^-s- ^^■ flute and of these the middle is the most agreeable. i,e:;-tii, since tiie lower is harsh and tlie up])er piercing. Its -■*-^ '" dominant character makes the and A are used more often than the one in C, the lirst sound- ing B^ and the second ./ when the written (' is i)layed. and the other tones maintaining the same relative distances. liesides ])ossessing exceptional beatit}- of tone-quality, the clarinet is able to graduate the inlensitv of its tone more than anv other wir.d instrument, because of its wide _, .,_.,. . Possibilities range and ])ossibilities of ])assage work it is used of the clarinet. in military bands in ])lace of the violin. Again, its sustaining power is exhibited in rich and ])oetic melodic work. Passing over the alto clariiief or basset horn, not often now used in the orchestra, we come to the bass clarinet, shaped 136 SOUND, AND ITS RELATION TO MUSIC The basset horn and bass clarinet. Saxophones. like the ordinary clar- inet but with a crook to the mouthpiece and the lower end bent so that the bell points upward (Fig. 104). Sev- eral of these instruments are in use, of pitches corresponding to those of the clarinets, lait an octave be- low them. Their rich and telling tones sometimes assert the bass of the harnion}- and sometimes appear in singing melodies. Saxophones are employed chiefly in military bands. While they have a single reed, they ditler from clarinets in that their tubes are conical. On account of their shape the\- are gen- erallv classed among the wood- wind, although they are made of brass. Brass instnoiiciits ditter from the wood-wind chiefl}- in the man- ner in which their vibrations are ^^'' excited. Each consists of a conical tube ending )\- a metal mouthpiece. \'ibrations are excited in the latter l)y the li])s of the pla}'er, and are thence transmitted to the air in the tubing. Acting as membranous reeds, the li])s ])riMlucc 1)\' their ])roper adjustment or cuibrocluirc the \-arious tcnos of the harmonic series. generalK- ol)taining the fundamental either not at all or \\'ith difticult}'. When the mouthpiece is funnel-shaped and the tube \'er\- long in ])roportion to its diameter, the production of tlie higher partials is favcircd. .^uch condition- exist in the "natural" Jioni. of which the tubing, coiled Fig. 104. clarinet. Lentrth, 3 ft. ? in. Characteristics . , ,, of brass ui a bcll and ca])]K'd instruments. The natural horn. SOU.WD, AND ITS RELATION TO MUSIC 137 up for convenience, is from 9 to 12 feet in length. With the "natural" horn, employed by the classic masters, it is im- possible without altering the length of the tube to play the harmonics in more than one key, although an}- tone may be dropped a half step in pitch by thrusting the hand into the bell and thus producing ■"stopped" tones, muffled in quality. Normally tuned in C, the natural horn is made to sound in other scales when its tube is lengthened bv the insertion of metal "crooks." Like the clarinet it then becomes a trans- posing instrument, since its music is still written in C. although sounding in a ditferent key. F'.ach note of the horn in F, for instance, sounds a fifth lower than written. The horns in F, E and E^ are the most common. In the modern orchestra the I'ak'c horn, popularly known as the FrcncJi horn (Fig. 105), is generally employed in place of the natural horn. ^^^ ^^^^^ It was first em- ^°''"- ployed by Halevy in La Juivc, 1835, and* Schumann was the first German composer to vise it. Bv the use of three pistons which, when pressed down singly or in combination, change the pitch anywhere from one to s' semitones the trouble of insert- ing different crooks is obvi:,ted. Thus the player is able to obtain the full chromatic scale without difficulty. On the valve horn in F, for instance, all the tones from Bi to c" derived from the fourth to the twelfth partials, can be played, while the second and third partials are also possible. Horns are used in pairs in the orchestra, half the players taking the higher notes and the others the lower; since on account of difficulties Fig. 105. Valve-horn. I.en^rth, 22\ in. 138 SOUND, AND ITS RELATION TO MUSIC The trumpet. in adjusting; the lips players j^refer to specialize in certain l)arts of the scale. I'he mellow yet sonorous tones of the horn are sometimes used in lively ])assages, such as hunting fan- fares, but are still more effective in solo melodies of a sus- tained character. A kindred brass instrument is the trumpet, which differs from the horn in that its tube is but half as long and is bent dift'erently. The diameter of the tube is but }i of an inch from the mouth])iece until it ap- ])roaches tlie l)cll. when it widens out. The mouthpiece is shai)ed hemispherically, like a cup. I'.y the trumjjet in C the full series of upper ])arti.als as far as the twelfth is ob- tainable, w bile those in other keys ^.__. ,., .,, , . •^ b:o. 106. Valve-tniiiipet. are made ])ossible i.enjjth, 22!: in. by the addition of crooks, in which case the written music is transposed. \'al\-e-trtmii)ets ( I'ig. 106) are now generally used in place of the original "naturar" instruments, with the ])reference gi\'en to those in />'' and . /. The ])ractical range is from c to about b'^" . The louder tones of the trumpet have a ringing (|uality that easily dominates the full orchestra; while the clearness and ptu'itv of its soft tones arc em])loyed for distant or mystical effects. All the otlier brass instruments have cup-shaped mouth- ])ieces, and tubes of which the bore is of greater diameter „, , . ^. than that of the horn or the trumpet. The Characteristic ' of the other effect of this Condition is to i)ro(luce tones of brass instru- ' ™^""- a full and round qualitx- but lacking the bril- liancy gi\-en b\- the high upper partials. As a sub'^titute for the trum])ct the cornet is frecjuently used on account of the facilit\- \vith which it can be played, exceeding that of an\- other bra-^s instrument. Of the B'f> The cornet. " . cornet the tube is but 4' j feet long, so that its Its quality. SOUND, AMJ ITS RILLATIOK TO ML'SIC 139 pitch is an octave liii^lier than that of the corres])ouding trumpet. In most other resjiccts llie two instruments are similarly constructed; l)Ut as onl\- the lower partials are ol)tain- ahlc on the cornet its tone is far less commanding;' and sensitive in (luality. In the trombone ( I'ig. 107) very perfect intonation is made ])ossil)le 1)\' a long' sliding section of tuhe wl'iich fits closely into the original tul)e of the instrument, and is . , . Tlie trombone. ])erlectl\- under the control ol the jjertormer. When this slide is closed the instrument is said to he in the first position, in which case the fundamental and seven ])artials Fig. 107. Trombone. I.cTiKth, clcsed, 3 ft. 9 in. can be obtained. I'.y pulling out the slide, six other positions are produced, each sounding tones a half step lower than the previous one, although the fundamental is not obtainable in the lower positions, b'videntlv the same tone can frequently be produced in difi'erent registers. The notes are sounded as w ritten. Of several sizes in which trombones are made the tenor trombone in B'^ is now most common, sometimes supplemented l)y the bass trombone. 1'he normal compass of the former is from /: to d" and of the latter from B to /'. Idie trombone tone is rich, even and sonorous. Three trombones freciucntlv form a c|uartcl with the bass tuba (I'^ig. 108), to produce a soul-stirring combination that resounds above the entire orchestra. The latterBBBBi^lBBi , . , ^ . . . The bass tuba mammoth instrument has four pistons, giving a and the , . ,, 7 L/ T 1 ^ ophicleide. chromatic range from /• to bo . It has now sup-| Kinds in use. 140 SOUXD, .IXD ITS KELATIOX TO MUSIC planted the savage Ophidcide, which was hngerecl Ijv holes in the sides. We ha\e now to si)eak of those wind instruments which T-, . are ijlaved bv a I he narmon- i - ium, American kev-board nicchan- organ and concertina. j^,-,-,_ J^^^^ impor- tant types are the harmGnium, .Imcrican rccd onjau anrl con- ccrti)ia. All of these have as vibrators free reeds (page 77). which are somewhat strident in tone, since this is not reinforced by pi[)es. In the harmonium the air is forced from the bellows through the reeds, and in the American organ it is sucked through the reeds into the bel- lows. Concertinas are furnished with fourteen notes to the oc- tave, having separate reeds for Dt and 7:5. and for (/:; and Ai. The most elaburate of all wind instrumcnt>. anrl one caj^able of prrulucing an infinite ^■arietv of ettects throughout its entire „, . compass, is the pit'C orqaii. Its ti»ne> are ob- The pipe ' ' ' ■' •^■■s^"- taincd from a multitude of both flue and reed pif)es, the latter having either free or beating reeds i page 77 i, and all \aricrl in qualit\- by (Htl"erence< in s]ia])c and materials. .A row oi ])i])es of an\- gi\'cn r]ualitv i-^ made read}- ii>r action b\- drawing out the pr('])er "sto]/" : and when a key i< de- pressed a valve is opened in the corre-^ponrling pi]:)e. thus allowing the wind to enter which cau-cs the i)!pe to "speak."" Stops are also of ditterent ])itcbe-. Tho^e called cii/ht-fnnt stops, from the tlicoretical length, of their lowest ])i])e, gix'C the pianoforte pilch, while those of ,-ixteen feet give an octave lower, those of four feet an octaxc higher, and -o on. Thus the range e.xtends to the limits of auflibilit\- in either direction, Fig. 108. Bas> Tuba I^enyth, 3 ft. .^ in. SO('XI). .INI) ITS RliL.rnOX' TO Mr SIC 141 although ihc kc\hoards or manuals each cover only hve (jc- taves. These manuals vary in nuniher froiu one to tour, and are supplemented h}' a row ui pedal keys 2|j octaves in extent, ])laye(l hy the feet, luich manual is a complete organ in itself, although comhinations of the manuals among them- selves and with the pedals are made jjossihle. Thtis the organ is not properlv one instrument hut a group of instruments, placed within the power of a single performer 1)\- intricate mechanisms that govern wind sup])ly, stop and ke_\' action and combinational devices. \W the develo])ment of its limitless resoiu'ces and the linal ai)plication of electricity to sectire its connections the organ has become a monument to the mechani- cal genius of man. h'inally in c)ur catalogue come the percussion instniinents, which, although generally productive of mere sound rather than tone, are vet often necessarv for the em- Percussion , . . , , ■ , , .' - ,. instruments: ])nasis ot rliythm and for the cappmg ot a chmax. drums. The most musical of these are the kcftle-dntms or timpani, of which at least two are fotmd in the orchestra (Fig. 109). l'",ach consists of a large and hollow brass ]iemis])herc across which is stretched a membrane that can be tuned through the compass of a fifth Ijy keys at the sides. b^elt hammers in]- pinging upon this membrane produce a well-defined tone, which can thus em])hasize im- l)ortant points in tlic comp.osi- tion>. The hass dritni and snare drum are onl_\- occasionally employed in the orchestra, and have no definite tone. Metallic instruments of percussion are represented in tlie orchestra by \ariou< kinds of bells, the triam/le. cymbals, and Fig. 109. Kettle-drum. Diameter of head, 2il ill. and 27 142 SOUND. AND ITS RhL.iriON TO MUSIC Metallic U^^fif/^- Many sensational devices are employed instruments. 1,^ niotlem comjjosers tor special illustrative eliects. These, however, can scarcely be classed among- musical instruments. The following table shows the compass of the princi-pal instruments of the sym])honv orchestra of to-day. it gives the actual ])itch of the instruments with the usual range for orchestral purposes. In solo work the range is more extended. COMl'ASS OF THF. INSTRUMKXT.S OF TIIP: OKCHKSTRA (Showiiii; ihe actual pitch and the ranj,'i- for orchcstralpurpost-s) Strings Fig. no. In the development of the modern orchestra there has l)cen a constant advance in the knowledge of how to combine instruments most elTectivel}-. of the best i)r()portions in which to emi)l()y them, and of the UK^st etlective means of utilizing thcii- indix'idual cliaracteristics. Thus the orchestra has be- come a mammoth instrument which is ca])ablc of giving SOUND. AND ITS RELATION TO MUSIC 143 expression to every shade of musical feeling, and which, moreover, when combined with voices by a genius like Wagner, apparently attains the acme of intensity in the utterance of emotion. 144 SOUXD, AXD ITS RELATIOX TO MUSIC SUMMARY Let us close with a restatement oston Symphony (Jrchestra ( 1911 ). With the conductor, the band of perform- ers in this organizati(jn at present numbers exactly one hundred. I. Stringed ixstiuments ; Plucked : *Guitar. ^Mandolin, Harp (I). Struck: ^Pianoforte. Bozi'cd : \'ioIin ( U) first, 14 second), \'iola (10). Violoncello (10), Double Bass (8). II. Wind ixstki-MEXts: U'ood-i^iiid : I-'lute (4). Piccolo, Oboe (3). English Horn (1), Bassoon (3), Contra- Bassoon (2)^ Clarinet (3), Bass-Clarinet (1), *Sa\2, 97 Circle of fifths. 92 Clarinet, 75, 134-136 Clouds, echoing, 20 Cochlea, lll-li3 Comma in music, 92, 97, 103 Concertina. 140 Condensation, waves of. 7, 19, 41-44. 52, 57, 64, 65, 71, 72 Consonance, 98-102 Consonants, 117, 118 Contra-bassoon. 32, 134 Cornet, 138, 139 Cymbals. 141 Darwin, 17 Density, 12 and velocity, 14-17 in reflection, 19 and intensity, 39 Diatonic scales, 91, 95-97 Diffraction. 22 Discords, 45 Dissonance. 98-103 Double bass, 126, 128-130 Drum cavity (of ear). 109 Drumskin (of ear), 82, 109, 110, 113 Ear, 6, 48, 82. 108-113 Ear trumpet, 21 Earth, as sound transmitter, 17 friction of wind on, 40 Echo, 14, 19, 20, 39 Edison. ^2 Eidojihone. 118 Elasticity. 3, 12 English horn, 133 Epiglottis, 114. 115 Equal temperament, 103-105 Eustachian tubes, 109, 113. 115 Explosions, sound from, 10 of meteors, 17 sound-diffraction from, 22 Faraday. 79 Flames, sound from, 78-80 Flute, 51, 75, 131, 132 Focus of sound, 18, 19, 22 Fog-signals, 21 F)-ench Diapason Xormal, 30, 31 Galileo. 25 Gas-flame, reflection from. 18. 20 Gases, sound from. 2, 63, 64. 78-80 as sound-medium. 6 velocity in. 15. 16 refraction through, 21, 22 Glottis, 114, 115. 117 Gongs. 142 Gramophone. 84. 85 Graphic vibrations, 27, 28 148 INDEX Greek modes. 91-94 (jrei^orian modes, 93-95 Guitar, 10, 124, 125 Halcvy. 137 Halls, acoustics of. 20 Handel. 30 Harmonics. 51, 52, 124, 125, 127, 129, 137 Harmonic series. 56, 65, 67, 136 Harmonium. 140 Harp, 34, 124-126 Head, cavities of the, 86, 114, 116 Heat, retiection of, 17 currents, 20. 39 Hchul-oltz. 1. 27. 2i^. 48, 51, 53, 75, 76. 97-99. 101. 104 Ilciiioiiy. 63 Hexachordal scales. 95 Hindoo scales. 91 Horn, "natural." 136. 137 \alve or French. 137. 138 Hughes. Mrs. Watts, 118 Incidence, law of. 17, 18 Inharmonic partials. 52. 54. 59, 63 Insects, sound produced by, 17 Instruments, 4. 5, 33-35. 45, 47. 51, 123 stringed. 23. 82. 123-130 wind. 63. 64. 75-78. 130-141 keyboard, 54. 102-104, 125, 140, "Ml I)crcussion. 5. 63. 141. 142 Intensity, see loudness Interference, 40-48. 98 International pitch. 30. 31. 56 Interxals in music, 89-106 Impulses, law of cumulative, 69- 71 Jaf)anese scales, 91 Ju^t intonatir)n. 96. 102-105 Kiistncr. 79 Kettle-flrums, 141 Kevborird instrument^, 54, 102- " 104. 125. 140, 141 Kocuui. Dr.. ], 28. 46, 48, 52-54. 74, 100 r.ab\-rinth i'"f ear), 110 l.arvnx, 114 Light, and sound, 12, 13 retiection of, 17 Lissajous, 46, 100 Liquids, sound in, 16 Lobe (of ear >. 108 Loudness of sound, in reflection, 19 degrees of. 24 at night, 21. 39 and wind. 39 laws of. 37-39 and qualitv. 51-54 of voice. 86. 115. 116 of instruments. 123-142 in ear, 112 Lungs. 113. 116 Mandolin, 124, 125 Mariottc, 8 Marloyc. 61 McKendrick. Prof.. 85 Mean-tone temperament, 103, 104 Membranes, 21. 43, 63, 67, 82-86, lis. 141 in ear. 109-112 in head. 116 I\Iersen)ie. 14 Melndiaphone, 75 Melodic progressions, 89 Metallophone, 60 Metals as soimd-confluctors. 16 Miraf/e. /};-,. 118 Mirrors as sound-reilectors, 18, 19 Modes, see scales Modulation. 97. 102-104 Moisture, its effect on soinid, 13, 21 Monochord. 33. 92 Mouth, 86. 114, 117 Mocart. 30 Musical and non-musical sounds, 4 Music-box. 16. 81 Xasal ca\-ities, 114-116 Xeietou. .Sir I sane. 14 Nodes, 55-68, 75. 124, 127 Xoi^e distingiu'shed from tone, 4. 5 Notation, names of octaves, 29,30 O],oe, 51. 75. 132-134 Dphiclcide, 140 Orchestra, 51, 105. 142-145 Or.fran, see pipe organ and reed organ IXDEX 149 Organ pipes, 43, 44, 67, 74, 78, 140 Origin of sound, 1-5 Oscillations, of bar, 6 of water-particles, 8 of pendulums, 69, 70 Overtones, see partials Palate, hard and soft, 114-117 Partials, 47, 51-().S, 77, 79-81, 85, 95, 96, 99 of instruments, 124-139 Pendulums, experiments with, 70, 80 Pentatonic scale, 90, 91 Percussion instrume".ts, 5, 63, 141, 142 Pharyn.x, 114, 115 Phase, of sound-waves, 52, 62 Phonautograph, 83 Phonograph, 82-86 Phvsical basis of sound, 1 Pianoforte, 29, 30, 32. 34. 45, 58, 74. 81, 82, 99, 123, 125, 126 Piccolo, 32, 131, 132 Pipe organ, 30. 44, 10^3, 140, 141 of singing flames, 79 Pitch, 14, 20, 24-36, 41, 47. 51, 53, 56. 60, 62, 67. 71, 77. 78, 80 in the ear, 112 of scale-tones, 89-106 of voice, 115, 117, 118, 120 of instruments, 123-142 Plates, metal. 43, 52, 61-63 Power of sound affected by res- onance, 20 Pulsation atid music, 5 Pythagoras, 1, 33, 91, 92. 96, 103 Quality, 20, 24, 51-68, 77 in phonograph, 85 in ear, 112 of voice, 86. 115-121 of instruments. 123-142 Rarefaction, waves of, 7, 19. 41- 44, 52. 57. (4. 65, 71. 72 Raritv of air and sound-intensitv. 39 Receiver, of telenhotie. 86 Reeds, 76-78, 115, 132-136, 140 Reed organ, 47. 140 Reflection of sound. 17-21. 41 Refraction of sound, 21, 22 Regiiaiilt, 39 Resonance, 20^ 40, 69-88 in voice, 115-12i in instruments, 123-143 Resonators, 52-54. 72-75, 81, 98 113-120, 123, 125, 127 Resultant tones, 47, 48, 99, 102 Rhythm, 5 Rods, sounding, 6, 7, 35, 52, 58-61, 65 Sand figures, 62 S a live It r. Joseph, 51 Sa-cvrt. 25, 60, 72 Saxophones, 134, 136 Scale.-,, 30. 47. 89-97, 102-107 Scheibler. 28 Scheibler Stuttgart pitch, 31, 32 Schionanii, 137 Scientific pitch, 32, 56 Scotland, pentatonic scale in, 91 Seasliell. singing of. 75 Sensations of tone. The. 1 Silence zone, 20 Shi.gers, 30, 97. 105, 117. 118. 120 Sinuses (of head). 114. 116 Siren. 5, 25-27. 97-99 Snare drum. 141 Solids, as sound-transmitters, 6 velocity of soinid in, 16 echoes from, 20 Sondhaus. 21 Sonometer. 33. 54. 55. 74. 92 Sounding boards. 82, 125 Sound-mill. 74. 75 Sound-shadows. 22 Speaking trumpets. 21 Speaking tubes. 39 Standards of pitch. 30-32 Steatite burner. 80 Stringed instruments. 33. 82. 123- 130 Strings, stretched. 1. 16. 33-35. 45. 54-58. 81. 82. 92 String telephone. 16 Susceptibilitv of individuals to pitch. 29 Sympathetic vibration, see reson- 0)1 ce Tarfiiii's tones. tones Telephone. 82, 86 string. 16 see resultant 150 INDEX Temperature, its effect on sound- velocity, 13 l)ro(luctive of reflection, 20 Tempered scales, 96, 103-105 Tension of strings, law of, 34 Tcrpaiidcr, 91 Thickness of strings, law of, 34 Throat, 80, 114 Thunder storms, 14, 20 Tonality, 95, 97, 102, 104 Tones, nature of, 4 production of, 7 deafness toward, 29 relations of, 33 summational, differential and beat tones, 48 (jualitv of, 51-53 Tongue, 114, 116, 117 -bone. 11() Tonometer, 28, 45 Transmitter (of telephone), 86 Transmission ol sound, 5-11, 63. 74, 108, 110, 136 Transi)()sing instruments, 135, 137, 138 Triads, 101. 102 Triangle, 141 Troml)()nes. 139 Trumpets, 51, 138. 139 speaking and ear, 21 Tuba, bass. 139. 140 Tubes, sonorous, 21, 35. 39 60, 61, 64-67. 72. 75. 77-79. 134 Tuning-forks. 2, 3, 7, 27-29. 37, 41-43. 45, 46. 53, 54, 59-60, 70-74. 81, 100 Tyuciall. 1, 20, 79 / 'an dcr iiJicyn, ()3 \'elocity of sound, 12-17, 64. 72 Ventral segments. 55-66 Vestibule (of ear), 110. 111. 113 Vibrations r)f sound, nature of, 2-6. 8 fra\cling ])ower, 17 frecincncv, 24-28 limits of audible. 28-29 standard rate. 30-32 of strings. 33-35. 54-58 of rods, 35. 58-61 of plates, bells and membranes. 61-63 of tubes, 35, 64-67 of reeds, 77, 78 loudness and, 37 interference of, 40-48 relations of, 51, 52 in phonograph and telephone, 82-86 in ear, 108, 110-113 of vocal cords, 115 of violin, 127 means for stopping, 126 Viola, 126, 128-130 Violin. 4, 1(), 24, 25, 34, 37. 51, 57. 82, 105, 126-128, 130, 135 Violoncello, 12(). 128-130. 133 Vocal cords, 113-115, 119 Voice. 4. 7\<. 8(., 108. 113-123 Vowel sounds, i3, o4, 117, 118 Way Iter. 143 Water. velocit\' of sound in, 15, 16 Waves of sound, 7. 8, 10 velocity of, 12-17 alTected in \arious ways. 17-22, 31. 33. 38-40 interference of. 40-48 in resonators. 53 from vibrating strings, 57 in tubes, 64-()7. 71. 71 from tuning- l"i irks. 70-74 from reeds. 77 in ear. 112, 113 Waves of water, 8, 19. 40 Whcch-r. liih.'urd S.. 86 Whispering galleries. 19 Whistle. for measm-ing acute sotuuls, 29 of engine, 33 A\ iiul, its effect on soimd-veloc- iiy. 13 on pitch. 31 Wind-chest, 43. 44. 76 Wind instruments, ()3 64, 7S-7?', 130-141 Windows (of ear). 109. 111. 113 Windpipe. 114 Woofl. as sound-conductor. 16 as resonator. 81, 82 X\-lophone, 60 FEB 141957