THE PHYSICAL BASIS OF MUSICAL HARMONY. 357 



the successive wavelets are continually changing, is it possible for the 

 ear still to grasp the result as a unitary sensation ? 



If the ear could always separate impure harmonic or absolutely in- 

 harmonic partials from their fundamental tone, or if it always heard 

 I)ure harmonics as an indistinguishable part of the unity of the timbre 

 of a fundamental, then we might draw a hard and fast line between 

 mere mixtures of sound and timbres, even as the chemist distinguishes 

 between mere mixtures and true chemical compounds. But this is not 

 so; sometimes the ear can not unravel from the integral sensation the 

 inharmonious partial ; on the other hand, it can often distinguish the 

 presence of truly harmonious ones. Naturally, something will depend 

 on the training of the ear ; as is the case with the conductor of an or- 

 chestra, who will pick out single tones from a mixture of sounds which 

 to less perfectly trained ears may blend into a unitary sensation. 



Dr. Koinig accordingly determined to make at least an attempt to 

 determine synthetically hovr far the ear can so act, by building up spe- 

 cific combinations of i)erturbed harmonics or inharmonic partials, giv- 

 ing rise to waves that are multiform, as distinguished from the uniform 

 waves of a true periodic motion. The wave siren presented a means of 

 carrying this attempt to a result. On the table before me lie a number 

 of wave disks constructed with this aim. This will be successively 

 placed upon the whirling table, and sounded; but I must warn you 

 that the proper effect.s will only be perceived by those who are near the 

 apparatus, and in front of it. 



Upon the edge of the first of the series there has been cut a curve 

 graphically compounded of 24 waves as a fundamental, together with 

 a set of four perturbed harmonics of equal intensity. The first har- 

 monic consists of 49 waves (2 x 24 + 1), the second of 75 waves 

 (3x24+3), the third of 101 (4x24 + 5), the fourth of 127 (5x24 + 7). 

 The resulting curve possesses 24 waves, no two of them alike in form, 

 and somehighly irregular in contour. The effect of blowing air through 

 a slit against this disk is to produce a disagreeable sound, quite lacking 

 in unitary character, and indeed suggesting intermittence. 



The second wave disk is constructed with the same perturbed har- 

 monics, but with their amplitudes diminishing in order. This disk pro- 

 duces similar effects, but with more approach to a unitary character. 



In the third disk there are also 24 fundamental waves, but there are no 

 harmonics of the lower terms, the superposed ripples being perturbed 

 harmonics of the fifth, sixth, and seventh orders. Their numbers 

 are 6x24+6, 7x24+7, and 8x24+8, being, in fact, three harmonics 

 of a fundamental 25. This disk gives a distinctly dual sort of sound, 

 for the ear hears the fundamental quite separate from the higher tones, 

 which seem in themselves to blend to a unitary effect. There is also 

 an intermittence corresponding to each revolution of the disk, like a 

 beat. 



The fourth disk resembles the preceding; but the gap between the 



