HAKMONY IN MUSIC. 91 



given fundamental tone, is perfectly determinate. They are tones 

 which perform twice, thrice, four times, &c., as many vibrations 

 in a second as the fundamental tone. They are called the upper 

 partials, or harmonic overtones, of the fundamental tone. If 

 this last be c, the series may be written as follows in musical 

 notation, [it being understood that, on account of the tempera- 

 ment of a piano, these are not precisely the fundamental tones of 

 the corresponding strings on that instrument, and that in par- 

 ticular the upper partial, b" b, is necessarily much flatter than the 

 fundamental tone of the corresponding note on the piano]. 



c c' d' c" <!' g" b"b c'" d'" e'" 



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Not only strings, but almost all kinds of musical in- 

 struments, produce waves of sound which are more or less 

 different from those of simple tones, and are therefore 

 capable of being* compounded 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 mathe- 

 matician, and on paying sufficient' attention can distin- 

 guish 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. Experiments 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 sympa- 

 thetic vibration, not merely the little plates with their 

 accompanying nerve-fibres, corresponding to its funda- 

 mental 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 



