THE PHYSICAL BASIS OF MUSICAL HARMONY. 355 



cut at their edges into siausoidal wave forms. These represent a har- 

 monic series of IG members of decreasing amplitude, there being just 

 IG times as many small sinuosities ou the edge of the largest disk as 

 there are of large sinuosities ou that of the smallest disk. A photo- 

 graph of the a])paratus is now thrown upon the screen. It is described 

 fully by Dr. Kieuig in his volume ou "Quelques Experiences," and was 

 figured and described in Nature, July 20, 1882, vol. xxvi, p. 277. 

 Against the edge of each of the 16 wave disks wind can be separately 

 blown through a slit. This instrument therefore furnislies a funda- 

 mental sound with its first fifteen pure harmonics. It is clear that any 

 desired combination can be obtained by opening the appropriate stops 

 on the wind-chest; and there are ingenious arrangements to vary the 

 phases of any of the separate tones by shifting the positions of the slits. 

 The following are the chief results obtained with this instrument. If we 

 first take simply the fundamental tone and its octave together, the total 

 resultant sound has the greatest intensity when the difference of phase 

 d=^ [i. €., when the maximum displacement of air occurs at the same 

 instant for both waves); and at the same time the whole character of the 

 sound becomes somewhat graver, as if the fundamental tone predomi- 

 nated more than in other phases. The intensity is least wheu (5 = !|. If, 

 however, attention is concentrated on the octave note while the phase is 

 changed, its intensity seems about the same for S=^ as for S=^, but 

 weaker in all other positions. The compound tones formed only of odd 

 members of the series have always more power and brilliancy of tone 

 for phase differences of ^ and gi than for and ^; but the quality for ^ 

 IS always the same as for f, and the quality for is always the same as 

 for i. This corresponds to the peculiarity of the corresponding wave 

 form, of which the fourth line of curves in Fig. G is au example. For 

 compound tones corresponding to the whole series, odd and even, there 

 is in every case minimum intensity, brilliancy, and stridence with (5=f|, 

 and maximum with S=^. Inspection of the first and third lines of 

 curves in Fig. G shows that in these wave forms that phase which is 

 the most forcible is that in which the maximum displacement and re- 

 sulting condensation is sudden and brief 



Observing that wave -forms in which the waves are asymmetrical — 

 steeper on one side than on the other — are produced as the resultant of 

 a whole series of compounded partial tones, it occurred to I)i-. Kcenig 

 to produce from a perfect and symmetrical sinusoidal wave curve a com- 

 plex sound l)y the very simple device of turning into an oblique position 

 the slit through which the wind was blown against it. In Fig. 8 is 

 drawn a simple symmetrical wave form, cglnprtv. If a series of such 

 wav'e forms is passed in front of a vertical slit, such as ab, a perfectly 

 simple tone, devoid of upper partials, is heard. But by inclining the 

 slit, as at ab\ the same effect is ])roduced as if the wave form had been 

 changed to the oblique outline c'(/'l'n'p'r't'v\ the slit all the while re- 

 maining upright. But this oblique form is i)recisely like that obtained 



