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



nitude of the smallest consonant interval with its position in 

 the musical scale. 



Dr. Kcenig has shown that a consonant interval does not 

 exist among simple sounds of pitch below SOI^ [96 v.d.], 

 yet I have found that the sound of UTj |_64 v.d.], when 

 interrupted by a rotating perforated disk, blends perfectly, 

 to my ear, when these interruptions occur 23*1 times in a 

 second. It may appear strange that although 23*1 interrup- 

 tions per second of the sound U1V blend, yet a consonant 

 interval does not exist throughout the octave of U1V till the 

 interval of UTi : UT 2 is reached ; but the beats produced by 

 the rotating perforated disks are produced by the interrup- 

 tions of one tone, whereas when two simple tones are con- 

 joined two sets of beats are produced, inferior and superior : 

 thus, when UTx forms an interval with UT^ 23 v.d., the 

 inferior beats are 23 per second and the superior beats are 

 41 per second, and the interaction of these inferior and 

 superior beats produces secondary beats, which give to the 

 interval a confused rumbling sound *. Of this interval UT^ : 

 UTi + 23'1, Dr. Koenig wrote to me as follows: — "Your 

 23' 1 interruptions of U^ correspond, in number, to the 

 inferior beats of the interval of the simple tones UTj : UTj 

 + 23*1, but it is just at this magnitude of interval that the 

 superior beats begin to assert themselves, to produce with 

 what remains perceptible of the inferior beats the confused 

 rumbling, which evidently would be but a slight roughness 

 (disappearing entirely at a further increase of the interval), 

 if the superior beats, whose intensity from this point increases 

 with the interval, did not exist," 



3, The Durations of the Residual Sonorous Sensations as 

 deduced from the Smallest Consonant Intervals among 

 Simple Tones. 



If we assume that two simple tones form the smallest 

 consonant interval because the beats produced by these 

 conjoined sounds have blended into a smooth continuous 

 sensation, then we may deduce the durations of the residual 

 sonorous sensations from the observed smallest consonant 

 intervals in the following manner : — The reciprocals of the 

 numbers in column of Table II. are taken as expressing 

 the durations of the sonorous sensations given by tones whose 

 numbers of vibrations are the mean of those of the lower and 

 higher tones of the corresponding consonant intervals, for, 



* See Quelques Experiences d? Acoustique, par Rudolph Koenig' (Paris, 

 1882), pp. 89, 107, 113. 



