282 Dr. A. M. Mayer's Researches in Acoustics. 



violinists of more than exceptional ability. Three were 

 graduates of the Conservatory of Music of Leipzig. 



These experiments were all made in the same manner, viz. 

 by taking the fork giving the lower tone and sounding it suc- 

 cessively with others which gave more and more beats per 

 second, till these beats blended into a continuous smooth 

 sensation, forming the smallest consonant interval. As musi- 

 cians rather avoid than dwell on dissonant intervals, I educated 

 each one in the special subject of the roughness of the sen- 

 sation given by beats by making the beats more and more 

 frequent till near consonance, then giving an interval which 

 is admitted by every one to be consonant. In this way their 

 hearing was trained in what I wished them to discern, viz. 

 that separation in the pitch of two forks which just gives a 

 consonant interval. 



The variation among the decisions of these different observers 

 never equalled two vibrations ; generally they agreed exactly. 

 The agreement among observers in the judgment of a 

 consonant interval is remarkable. I give the mean of these 

 experiments. The number of the paragraphs refer to the 

 number of the experiment given in Table II. : — 



[6] UT 3 : MI 3 = 256 : 320 gave a consonant interval. I 

 narrowed the interval by lowering the pitch of MI 3 from 320 

 to 315, 314, 313-5, and 313. 

 315 consonant. 

 314 just consonant. 

 313*5 slightly rough. 

 313 decidedly rough. 

 These experiments show that 256 : 256 + 58 = smallest con- 

 sonant interval. 



[7] ML, : 3OL 3 = 320 : 384 is decidedly rough. Separated 



the interval by lowering the MI 3 fork from 320 to 316; then 



ML, :SOL 3 = 316 : 384 = 316 : 316 + 68 = smallest consonant 



interval. 

 [8] LA 3 : UT 4 = 439 : 517*4 decidedly harsh. Separated 

 interval by lowering LA 3 of 439 v.d. to 432 v.d. ; then 

 LA 3 : UT 4 =432 : 517-4=432 : 432 + 85*4 = smallest conso- 

 nant interval. 

 [9] RE 4 :FA 4 = 576 : 682*65 slightly rough. Increased 

 the interval by lowering RE 4 of 576 v.d. to 575 v.d.; then 

 RE 4 : FA 4 = 575 : 682*65 = 575 : 575 + 107*65 = smallest 



consonant interval. 

 [10] SOL 4 : fork of 896 v.d. = 768 : 896 slightly rough. 

 Increased the interval by lowering SOL 4 of 768 v.d, to 766*2; 

 then 



UT 3 



