HARMONY IN MUSIC. 77 



A. lias flat crests and flat hollows, D has pointed crests and 

 pointed hollows. 



These extremely simple examples will suffice to give a conception 

 of the great multiplicity of forms resulting from this method of com- 

 position. Supposing that instead of two, several simple waves were 

 selected, with heights and initial points arbitrarily chosen, an endless 

 variety of changes could be effected, and, in point of fact, any given 

 form of wave could be reproduced. 1 



When various simple waves concur on the surface of water, 

 the compound wave-form has only a momentary existence, 

 because the longer waves move faster than the shorter, and 

 consequently the two kinds of wave immediately separate, 

 giving the eye an opportunity of recognising the presence of 

 several systems of waves. But when waves of sound are 

 similarly compounded, they never separate again, because long 

 and short waves traverse air with the same velocity. Hence 

 the compound wave is permanent, and continues its course 

 unchanged, so that when it strikes the ear there is nothing- 

 to indicate whether it originally left a musical instrument in 

 this form, or whether it had been compounded on the way 

 out of two or more undulations. 



Now what does the ear do ? Does it analyse this compound 

 wave? Or does it grasp it as a whole? The answer to these 

 questions depends upon the sense in which we take them. We 

 must distinguish two different points the audible sensation^ as 

 it is developed without any intellectual interference, and the 

 conception, which we form in consequence of that sensation. 

 We have, as it were, to distinguish between the material ear of 

 the body and the spiritual ear of the mind. The material ear 

 does precisely what the mathematician effects by means of 

 Fourier's theorem, and what the pianoforte accomplishes when 

 a confused mass of tones is presented to it. It analyses those 

 wave-forms which were not originally due to simple undulations,, 

 such as those furnished by tuning-forks, into a sum of simple 



1 Of course the waves could not overhang, but waves of such a form would 

 have no possible analogue in waves of sound [which the reader will recollect 

 are not actually in the forms here drawn, but have only condensations and 1 

 rarefactions, conveniently replaced by these forms, p. G4]. 



