Dr. A. M. Mayer's Researches in Acoustics. 283 



SOL 4 : 896=766-2 : 896 = 766-2 : 766-2 + 129*8 = smallest 



consonant interval. 

 [1]] LA 5 : Sl 5 = 1706-6 : 1920 consonant. Narrowed the 

 interval by lowering SI 5 of 1920 to 1917 ; then 



LA 5 : SI 5 = 1706-6: 1917 = 1706-6: 1706-6 + 2 10' 4= smallest 



consonant interval. 

 [12] EE 6 : MI 6 =2304 : 2560 consonant. Narrowed the 

 interval by lowering MI 6 of 2560 v.d. to 2549 ; then 



RE 6 : MI 6 =2304 : 2549 = 2304 ; 2304 + 245= smallest 



consonant interval. 

 [13] MI 6 : Fork No. 11 6 =2560 : 2816 = 2560 : 2560 + 256 

 is "just perceptibly rough. 



[14] Fork 11 : SOL 6 =2816 : 3072 slightly dissonant. 

 Increased interval by lowering Fork 11 of 2816 v.d. to 2806; 

 then • 



Fork 11 : SOL 6 =2806 : 3072= 2806 : 2806 + 266=smallest 

 consonant interval. 



In the experiments just described the intervals of the tones 

 that gave consonance were made by simple tones of small in- 

 tensity and without the slightest trace of the upper partial 

 tones of the forks, and the two forks were vibrated so that 

 they gave, as near as I could judge, the same intensity of 

 sound. The results given only refer to intervals so formed. 

 To obtain them the forks were gently vibrated by strokes of 

 rubber hammers that varied in hardness with the pitch of the 

 forks. The lower the pitch of the fork, the softer should be 

 the hammer. A hammer of hard rubber striking low-pitched 

 forks will develop the upper partial tones of the forks, and so 

 vitiate the experiments that a really consonant interval might 

 be judged as dissonant. 



The results of all the experiments may be summed up as 

 follows :— From SOL 2 of 192 v.d. to MI 6 of 2560 v.d. the 

 smallest consonant intervals are closely given by the formula 



N: N + 



For sounds be^ow SOL 2 the interval as computed by the 

 formula is too small to agree with the true interval. For 

 sounds above MI 6 (2560 v.d.) the intervals computed by the 

 formula, like those below SOL 3 , are too small. That the ex- 

 perimental determination of the smallest consonant intervals 

 throughout four octaves, upward from SOL 2 , or throughout 

 the tones given by the violin, should agree so closely with the 

 formula indicates the existence of a law connecting the mag- 



