80 ON THE PHYSIOLOGICAL CAUSES OF 



series may be written as follows in musical notation [it being- 

 understood that, on account of the temperament of a piano, these are 

 not precisely the fundamental tones of the 'corresponding strings on 

 that instrument, and that in particular the upper partial, V b , is 

 necessarily much flatter than the fundamental tone of the correspond- 

 ing note on the piano]. 



. ba.3- & : " 



Not only strings, but almost all kinds of musical instruments, 

 produce waves of sound which are more or less different from 

 those of simple tones, and are therefore capable of being com- 

 pounded out of a greater or less number of simple waves. The 

 ear analyses them all by means of Fourier's theorem better than 

 the best mathematician, and on paying sufficient attention can 

 distinguish the separate simple tones due to the corresponding 

 simple waves. This corresponds precisely to our theory of the 

 sympathetic vibration of the organs described by Corti. Ex- 

 periments with the piano, as well as the mathematical theory of 

 sympathetic vibrations, show that any upper partials which may 

 be present will also produce sympathetic vibrations. It follows, 

 therefore, that in the cochlea of the ear every external tone 

 will set in sympathetic vibration, not merely the little plates 

 with their accompanying nerve-fibres, corresponding to its 

 fundamental tone, but also those corresponding to all the upper 

 partials. and that consequently the latter must be heard as 

 well as the former. 



Hence a simple tone is one excited by a succession of simple 

 wave-forms. All other wave-forms, such as those produced by 

 the greater number of musical instruments, excite sensations of 

 a variety of simple tones. 



Consequently, all the tones of musical instruments must in 

 strict language, so far as the sensation of musical tone is 

 concerned, be regarded as chords with a predominant funda- 

 mental tone. 



