1890.] 



on the Physical Foundation of Music. 



231 



members of tlie series, as shown in Fig. 10. This is done by a 

 special template. Fig. 11 shows the positions required for phase 

 of J. Fig. 12 shows the template for zero phase. To produce this 

 there will be no movement required for the fourth, eighth, and 

 twelfth members of the movable set, but the intermediate ones will 



Fig. 12. 



Position of the Shts for Phase-difference 0. 



need to be shifted by J, J, and f of their respective waves. When 

 this set of positions is attained the condensation is increasing at the 

 same moment for all the component waves, and reaches its mean 

 values simultaneously. In experimenting the practice is to listen 

 first to the combined sound with the undisplaced slits, and then, 

 suddenly raising the lever, observe the change in the resultant 

 sound. 



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 differ- 

 ence of phase 8 = ^ (i. e. 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 predominated more than in other phases. The 

 intensity is least when 8 = j. If, however, attention is concentrated 

 on the octave note while the phase is changed, its intensity seems about 

 the same for 8 = ;J as for 8= J, 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 |, than for and J ; but the quality for \ is always the same as 

 for |, and the quality for is always the same as for J. This 

 corresponds to the peculiarity of the corresponding wave-form, of 

 which the fourth line of curves in Fig. 6 is an example. For com- 

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

 is, in every case, minimum intensity, brilliancy, and stridence with 



