Sept 23, 1 875 J 



NATURE 



451 



he deduces from it the explanation of the third property 

 we have mentioned of musical sounds, namely, their 

 quality or character of tone. 



Chladni was perfectly aware of the complex and varied 

 nature of the vibrations producing musical sounds, but he 

 does not seem to have attached any importance to them 

 in this respect ; for he says (p. 48, ed, 1 830) : " Die Verschie- 

 denheit der Schwingungsarten tragt meistens nur wenig 

 zu einer verschiedenen Wirkung des Klanges bei." 



Sir John Herschel (Encycl. Metrop.) appears to have 

 doubted Chladni's assertion, for he hints clearly at the 

 probable influence on the quality of the sound, of the 

 form of the air-wave (which is only the result of the 

 complex vibration) ; and we may probably consider this 

 to be the first hint on record pointing to Helmholtz's 

 discovery. 



Mr. Woolhouse, in an admirable Httle " Essay on 

 Musical Intervals, Harmonics, &c.," 1835, goes further. 

 He says (p. 'j'j^, speaking of the complex vibrations of a 

 string: "The various combinations of these different 

 modes of vibration must have a considerable influence on 

 the musical quality and expression of the musical sound," 

 which is a still nearer anticipation of the later doctrine. 



Still, however, these anticipations were only guesses ; it 

 was reserved for Helmholtz to put the matter in the 

 shape of a scientifically demonstrated fact. He has 

 shown, by the most elaborate and conclusive investiga- 

 tions, that the quality of a musical tone depends chiefly on 

 the number and on the comparative strength of the various 

 harmonical notes of which the tone is compotmded. 



The overtones accompanying a fundamental note may 

 be present in greater or less number, and they may vary 

 considerably in comparative loudness or softness, and it 

 is on the combination of these sources of variation that 

 the quality of the tone will depend — or, to put the expla- 

 nation in another and more scientific shape ; as Xht pitch 

 of a sound depends on the length or the frequency of 

 recurrence of the air-wave, and the loudness on the degree 

 of disturbance of the particles of the air therein ; the 

 quality of tone depends on what is called its internal 

 fonn, or on the varieties of arrangement of expansion and 

 compression of the air contained within one complete 

 periodic cycle of oscillation. 



Some modification in effect is often produced by a 

 sound being accompanied by unmusical noises, such as 

 the escaping of imperfectly used wind in a pipe, the un- 

 skilful scratching of the bow on a violin, the beating of 

 reeds, and so on ; but these are rather impurities than 

 varieties of tone, and may be excluded from considera- 

 tion. 



There are very few natural sounds which are entirely 

 simple, consisting of the fundamental note only. They 

 are best produced artificially by means of the " reson- 

 ators." The nearest approach to them may be found in 

 the larger stopped wood pipes of an organ, an old-fashioned 

 (not a modern) flute, and a tuning-fork after the sharp 

 ring has subsided. The vocal sound of the Italian U 

 (our 00) is also nearly a simple one. These examples will 

 give the idea that simple tones are soft, dull, and entirely 

 devoid of what is called brilliancy. 



The addition of overtones gives this brilliancy and at 

 the same time adds life, richness, and variety. It is to 

 them that we owe entirely the agreeableness and pleasur- 



able effect of musical tones. In proportion as the higher 

 overtones predominate, so will the sound be bright and 

 sparkling, or if in great predominance it will become 

 metallic, thin, and wiry. If, on the other hand, the upper 

 tones are weakened and the lower strengthened, the tone 

 becomes more full, rich, and mellow. All the quahties 

 of tone most esteemed and most useful in music are rich 

 in overtones. 



Helmholtz gives many examples of musical sounds 01 

 different character, which have been analysed according 

 to his method. The tones produced from strings are 

 peculiarly adapted to this purpose, because the vibrations 

 so produced admit not only of mathematical calculation, 

 but of ocular observation, and so give direct means of 

 comparing the new theory with the facts, the result in all 

 cases being most satisfactory and conclusive. The over- 

 tones in strings depend largely on the kind of impulse 

 and the place where it is applied. In an ordinary piano 

 the first six overtones are all audible, the three first 

 strong, the fifth and sixth weaker, but still clear. The 

 seventh and ninth, which are inharmonious, are excluded 

 by striking the string in a peculiar place which does not 

 admit of their generation. To prove the dependence of 

 the quality on the strength of the overtones, Helmholtz 

 has calculated mathematically what the strength of the 

 first six overtones ought to be when produced with 

 hammers of different degrees of hardness, and finds they 

 should be as follows : — 



With a very hard hammer 

 With a medium hammer . 

 With a very soft hammer . 



100 



I 



O 



Now, as everybody who knows anything about pianofortes 

 is aware that the tone is full and rich with a soft hammer, 

 and hard and jangling with a hard one, it will be seen 

 how admirably the mathematical results correspond with 

 the actual ones, and how both confirm the theory. 



Again, it is easily shown, both mathematically and 

 practically, that thin wires will vibrate in short lengths 

 much more easily than thicker and stiffer ones, and will 

 therefore be more liable to produce the higher overtones, 

 and hence the well-known metallic jangling of thin wires. 

 This is the scientific explanation of the improved tone 

 from the use of thicker wires in modern pianos, inasmuch 

 as they admit of a more powerful blow without the pro- 

 duction of the high and unfavourable overtones that 

 would result from such a powerful impulse on a thin 

 string. 



The peculiar tones of the violin Jribe, wind instruments, 

 wood and brass, organ-pipes of various kinds, and so on, 

 are all satisfactorily investigated in this way. 



Helmholtz devotes much attention to the phenomena 

 of vowel sounds, which had been already investigated by 

 Willis and Wheatstone. He has completed their inves. 

 tigations by bringing the vowel sounds within his theory, 

 and his elegant discussion of the subject, and the im- 

 portant results he obtains, are_among the best features of 

 his book. 



All the above results we have mentioned have depended 

 on the analysts of musical sounds. But the author 

 « 



