16 A. M. Mayer — Researches in Acoustics. 



The results in column E are given graphically in the curve 

 I of fig. 11. The unit on the axis of abscissas is 100 v. d. The 

 unit on the axis of ordinates is *01 second. 



The determination of the duration of the residual sensation 

 of TJT, (64 v. d.) was very carefully made and made many 

 times. The experiments gave "0361 second for the duration 

 of this sound. The formula gives *0369, which is -£-% greater 

 than the observed duration. The greatest difference existing 

 between the observed and computed duration of the remaining 

 sounds of the table is in the case of SOL 3 (381 v. d.) where the 

 computed is -3-I.-3 greater than the observed duration. In col- 

 umn L of Table I are given the number of wave-lengths of 

 the sounds which pass into the ear through a hole in the rota- 

 ting disks when these interrupted sounds blend into uniform 

 sensations. The average number of wave-lengths which pass 

 a hole is about 2J. As the sound rises in pitch more wave- 

 lengths pass the hole ; thus while only 1*38 wave-length passes 

 in the case of UTj, 3 wave-lengths pass in the case of TJT 6 . 



An examination of fig. 6 shows that sound passes to the ear 

 while a hole in the disk passes over three diameters of the hole 

 in the nipple of the resonator, while the distance between the 

 centers of neighboring holes in the disk equals six diameters 

 of the hole in the resonator; hence, to ascertain the number 

 of wave-lengths which enter the ear during the passage of a 

 hole, in the disk across the hole in the resonator we must 

 divide the number of vibrations per second of the sound, 

 given in column B, by twice the corresponding number in 

 column C. 



2. On the Smallest Consonant Intervals among Simple Tones. 



When two simple tones, which differ slightly in pitch, are 

 sounded simultaneously, beats are produced, which become 

 more frequent as the difference in pitch increases, and with 

 this increase in the interval between the tones the dissonance 

 becomes harsher, reaching a maximum of dissonance (when 

 the number of beats are about T \ of the number required to 

 blend), then becoming less dissonant as the interval increases 

 till, at last, the two tones blend into a consonance. These are 

 the phenomena observed from SOLj (96 v. d.) to the highest 

 tones used in music. 



Having the law which gives the number of beats (produced 

 by the interrupted sounds of tones of various pitch), which 

 blend, one might naturally infer that the consonant interval 

 could be computed by that law. Given the pitch of a tone 

 we compute by the law the number of interruptional beats of 

 this tone which blend, and adding this number to the frequency 



