45° 



NATURE 



\Sept. 23, 1875 



nature of the body with which it is struck or rubbed, to 

 produce the sound. He further adds the suggestion that 

 such irregularities may be due to irregular tremblings of 

 the smaller parts of elastic bodies. 



Sir John Herschel (" Encyclopaedia Metropolitana "), 

 speaking of musical sounds, says • " Of their quality and 

 the molecular agitation on which they depend, we know 

 too little to subject them to any distinct theoretical dis- 

 cussion." 



To put the problem clearly, suppose we have two 

 musical sounds of the same pitch and the same degree of 

 loudness, but of different qualities. To what physical 

 cause is the difference in quality due ? We know that 

 the rapidity and the amplitude of the vibrations is the 

 same in both cases ; what other element of variation can 

 enter into the phenomenon ? Helmholtz is .the first who 

 has given a complete answer to the question. 



It very seldom happens that a musical sound consists 

 of one simple note ; it is generally a compound of many 

 notes combined together. To illustrate this by a simple 

 example, suppose a stretched string, as a vioUn string or 

 pianoforte wire, sounds any particular note. This note, 

 which is called the fundamental one, will be due to the 

 vibrations of the string as a whole, and if we could pre- 

 vent any other kind of vibration this sound would be a 

 simple one. But the string has a natural tendency (for 

 reasons too recondite to enter upon here) to take upon 

 itself other partial vibrations, and thereby to complicate 

 the effect produced. It will divide itself spontaneously 

 into two, three, four, five, six, or more aliquot parts, and 

 each of these parts will set up an independent vibration 

 of its own, giving a new note corresponding to its length. 

 All these will sound together, and thus by the vibration 

 of the string we get not only the fundamental note (which 

 is usually the loudest and most prominent), but its octave, 

 its twelfth, its double octave, its seventeenth, nineteenth, 

 and so on, all heard in addition, and giving a sound which 

 is a compound of them all. All the additional notes above 

 the fundamental have been usually called in England 

 harmonics J Helmholtz calls them overtoftes (obertone). 



We have given a string as a simple example of the 

 mode of generation of a compound sound, ^ but such 

 sounds are produced in many different ways. A com- 

 pound sound, so far as its effect on the ear is concerned, 

 is due to a particular form of air-wave, produced in the 

 instance given by the superposition of different sets of 

 vibrations of the sounding body ; and such a form of 

 wave may be equally well produced by other means, such 

 as a reed ; or it may originate in the air itself, as in a flute. 

 In every case where a given fundamental note is found, 

 there is the same tendency for it to be accompanied by 

 subsidiary fractional vibrations, producing corresponding 

 overtones. 



The phenomenon of compound sounds, as found by har- 

 monics or overtones accompanying fundamental sounds, 

 has been long known. It was mentioned by Mersenne 

 as early as 1636, and has since been noticed by Bernouilli, 

 Young, Rameau, Chladni, Sir John Herschel, Woolhouse, 

 and others ; but there is great difficulty in getting prac- 

 tical musicians, who have not been accustomed to consi- 

 derations of this nature, to admit that what, judging by 

 the practical impression on the ear, seems only a simple 



and single note, can really be one compounded of a gr«at 

 many sounds differing much in p tch, and some abso- 

 lutely discordant. Helmholtz endeavours to combat this 

 prejudice. He shows by several analogous physical and 

 physiological examples that the senses are apt, in the pre- 

 sence of prominent facts, to ignore others which may be 

 less prominent but equally real ; and he reasons that as 

 the fundamental note is almost always stronger than any 

 of the others, the ear is inclined to refer the whole com- 

 bination to that one note, and refuses to take the trouble 

 of separating and identifying the various elements of the 

 sound. 



An example Oi artificial compound sounds, purposely 

 made, is furnished by a large organ. The pipes from 

 which its sounds arise are in themselves but weak, and 

 no multiplication of them would give tones of great power. 

 Hence the long experience of organ builders has led them 

 to form compound sounds by adding to each note pipes 

 speaking its octave, twelfth, fifteenth,- and other " over- 

 tones," the effect of which is, as is well known, to produce 

 sounds of a_ most powerful and penetrating quality. Yet, 

 if these overtones are well proportioned, they give, to an 

 ordinary hearer, only the impression of one single loud 

 sound. 



By a little practice the ear may be educated to dis- 

 tinguish and separate the various notes which make up a 

 compound sound, and when the habit of doing this is 

 acquired, the illusion disappears. But that no proof may 

 be wanting of this important principle, Helmholtz has 

 contrived mechanical means by which any sound may be 

 analysed, like a ray of light or a chemical compound, and 

 its component parts exhibited separately. He has con- 

 trived certain instruments called resonators, each of which 

 will, like a chemical reagent, test the presence of a particu- 

 lar overtone, and by submitting these in succession to the 

 vibrating influence of the compound tone, they at once 

 show whether the sounds they are tuned to are present or 

 absent therein. 



We have dwelt at some length on this phenomenon of 

 the compound nature of musical sounds, because it is in 

 reality the great fact which underlies the whole of Helm- 

 holtz's researches in this volume, and he himself has 

 accordingly taken great pains to demonstrate and explain 

 it, knowing that, although not a new discovery, it was yet 

 far from being generally acknowledged. Indeed, we con- 

 sider the establishment of this fact, so difficult of accepta- 

 tion by practical musicians, and yet so simple and obvious 

 when explained, is one of the most useful and important 

 features of that portion of the complete work now under 

 review. This establishment and explanation he afterwards 

 uses as the basis for most of his researches, namely, the 

 compound nature of musical sounds. 



Such sounds, we have shown, consist, in almost 

 all cases, not of a simple vibration, but of a number 

 of vibrations of different velocities, superposed upon 

 a fundamental one. The whole thus form a com- 

 pound vibration which, though it produces on the inex- 

 perienced ear the effect of a single note, is really, when 

 analysed, a compound of this note with a number of 

 " overtones " harmonically related to it. 



Among the many novel uses Helmholtz makes of this 

 fact, the most important, physically, is the way in which 



