NATURE 



449 



THURSDAY, SEPTEMBER 23, 1875 



HELMHOLTZ ON TONE 



On the Sensations of Tone as a Physiological Basis for 

 the Theory of Music. By Hermann F. Helmholtz, 

 M.D. Translated with the author's sanction by Alex. 

 J. Ellis, F.R.S., «S:c. (London : Longmans and Co., 

 1875.) 



IN the general advance of scientific knowledge which 

 has taken place during the last half-century, the 

 science of acoustics has hardly received its fair share of 

 attention. Founded on principles originated by the 

 ancients, and afterwards extended by Galileo, Newton, 

 Taylor, Sauveur, Bernouilli, Euler, Smith, Young, and 

 others, the first great and complete work on it was 

 "Die Akustik," of Chladni, published in Germany in 

 i8o2, but which is chiefly known by its French trans- 

 lation. 



It acquired a high and wide reputation, and it has ever 

 since been a standard authority on the subject. Sir John 

 Herschel's celebrated treatise on Sound in the " Encyclo- 

 paedia Metropolitana," carried the theoretical views of the 

 science much farther, and so supplied what was deficient 

 in Chladni's more practical work ; but nothing of im- 

 portance has been added to our knowledge of the science 

 from Chladni's time till about fifteen years ago. 



It was then known that one of the most eminent physi- 

 cists and physiologists of Germany, Herr Helmholtz, 

 Professor of Physiology at Heidelberg, had been devoting 

 considerable attention to the science of acoustics, and, if 

 we recollect aright, some of his discoveries were brought 

 forward by himself in lectures at our Royal Institution. 

 In 1863 appeared a work by him, entitled " Die Lehre von 

 den Tonempfindungen als physiologische Grundlage fur 

 die Theorie der Musik," the result of eight years' investi- 

 gations in acoustical science. This work not only gave 

 much new information on acoustical subjects generally, 

 derived almost entirely from the author's own long-con- 

 tinued investigations ; but it published new and most 

 important discoveries as to the nature of musical sounds, 

 and valuable reflections on the bearing of these discoveries 

 on the theory of music generally. The work met with 

 high and universal appreciation among those who could 

 understand it ; it went through three editions in Ger- 

 many, and was translated into French, which gave it a 

 much wider circulation. Helmholtz's book has been fol- 

 lowed by two popular works in English, namely, " Lec- 

 tures on Sound,' by Prof. Tyndall (1867), and "Sound 

 and Music," by Mr. Scdley Taylor (1873), the chief object 

 of both being to expound Helmholtz's discoveries and 

 doctrines to English readers. We have now, however, a 

 translation into English of^the entirework, as mentioned 

 at the head of our article. 



In attempting to give some idea of the book, it is neces- 

 sary to premise that it treats of two distinct kinds of 

 subjects, physical and musical. In addition to being a 

 profound and practised physicist, the author has clearly 

 devoted much attention to the study of music, both theo- 

 retically and practically, and he has endeavoured to apply 

 his physical discoveries and theories to the elucidation of 

 many points connected with the art which he has found 

 Vol. XII.— No. 308 



obscure. We may therefore divide our notice into these 

 two heads. 



In regard to the physical part of the subject, Helm- 

 holtz's work owes its greatest interest and its greatest 

 fame to the entirely new light he has thrown on the nature 

 of musical sounds, and the complete way in which he has 

 explained and accounted for phenomena in regard to 

 them which were previously very obscure. 



A little attention will lead anyone possessing an ordi- 

 narily susceptible ear to the perception that a musical 

 sound has three properties, each of which may be subject 

 to a wide range of variation. These are : (i) its pitchy 

 or its degree of acuteness or gravity in the musical scale ; 

 (2) its strength^ or degree of loudness or softness j (3) the 

 quality, or character of tone. 



The question then naturally arises to what physical 

 circumstances these three peculiarities are due. In regard 

 to the two first there has been no great difficulty. It has 

 been long known that the pitch of a musical sound de- 

 pends on the rapidity of the vibrations which cause it, for 

 according as the vibrations succeed each other more or 

 less rapidly, the note produces sounds to us more acute 

 or more grave, or, in other words, its pitch is higher or 

 lower. 



The strength, or degree of loudness or softness of a 

 musical sound, has been also known to depend on the 

 amplitude or extent of the vibrations, a larger amplitude 

 giving a louder sound, and vice versd. 



The third property of musical sounds is their quality 

 or peculiar character of tone. A violin, for example, 

 gives a tone of a different quality from that of a clarionet, 

 an oboe, a flute, or a trumpet, which all again differ from 

 each other. The varieties of quality of tone that may be 

 obtained are almost infinite ; we not only possess an im- 

 mense variety of musical instruments and means of pro- 

 ducing musical sounds, all which have their individual 

 qualities of tone, but even on the same instrument the 

 same note may often be given several different varieties 

 of character, independent of the mere loudness or soft- 

 ness. And that these infinite varieties are really objective 

 physical differences, and not merely subjective or ideal, 

 is proved by the facility with which educated ears can 

 identify and distinguish between them, even sometimes to 

 the minutest shades of difference. The stringed tribe of 

 instruments, and still more the human voice, furnish 

 ample examples of this. 



The tone of a particular violin,' or~of a 'particular]" violin 

 player, can be identified by a connoisseur among a 

 hundred, and we all know that the varieties of quality of 

 the human voice, even in the same register, are as easily 

 recognised by the ear as the varieties of physiognomy are 

 by the eye. And even in the same voice, the numerous 

 varieties of vowel sounds producible are, when examined 

 carefully, only varieties in quality of tone. 



The nature of this property of sounds has hitherto been 

 very obscure. Chladni, the great expounder of acoustical 

 science in the early part of this century, says :— " Every 

 real musical sound is capable of different modifications, 

 whose nature is as yet entirely unknown, but which 

 probably consist of some mixture of what is simply 

 noise." He then explains at some length that this may 

 arise either from peculiarities in the structure of the 

 sounding body as regards material, &c., or from the 



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