HERMANN VON HELMHOLTZ 



the cochlea and sweep over the nerve-endings. The 

 question is, how does the cochlea behave in such cir- 

 cumstances, and will its action explain quality of tone ? 

 Helmholtz attacked the problem both by analysis 

 and by synthesis. In the first place, he was familiar 

 with Ohm's l application in 1843 f Fourier's principles 

 to the decomposition of a sound wave of any type 

 into a number of simple harmonic vibrations, each 

 simple harmonic vibration corresponding to a simple 

 tone such as a tuning fork approximately gives. 

 Fourier's 2 theorem states that any given regular 

 periodic form of vibration can always be produced 

 by the addition of simple vibrations having vibra- 

 tional numbers which are once, twice, three times, 

 etc., as great as the vibrational number of the given 

 motion ; and further, if we know the amplitudes 

 of the simple vibrations and the differences of phase, 

 then any regular periodic motion can be shown to 

 be the sum of a certain number of harmonic vibra- 

 tions ; in other words, the compound wave may be 

 analysed into a set of constituents of definite periods. 

 Applying this to the motion of the air close to the 

 ear, we find that any such motion, corresponding to 

 a musical tone, may be always, but for each case 

 only in a single way, shown to be the sum of simple 

 harmonic motions, corresponding to the partial tones 

 of this compound musical tone. 



1 Poggendorff's Annalen der Physik, t. lix., p. 513 ; t. Ixii., p. i. 

 1 Theorie Analytique de laChaleur. Paris, 1821. 

 I 44 



