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



in which N equals the number of vibrations of the lower tone 

 of the interval, and 



—the number of vibrations of the higher tone of the interval. 

 In column E are given the differences between the com- 

 puted values [D] and the observed values [C]. The formula 

 gives quite closely the true values from SOL 2 [192 v.d.] to 

 MI 6 [2560 v.d.]. In column F are given the smallest con- 

 sonant intervals as determined experimentally from SOI^ 

 [96 v.d.] to the tone of 2806 v.d., expressed in semitones of 

 the equal-tempered scale. 



In fig. 11 these intervals, computed from the numbers in 

 column 0, are expressed graphically by the curve N.C.I. 

 The units of ordinates (on the left of figure) are semitones, 

 and the units of abscissas are 100 vibrations. This curve 

 shows in a striking manner the contraction of the smallest 

 consonant interval as we ascend the musical scale ; while 

 SOLi [96 v.d.] requires a sound separated from it by 6^ 

 semitones to give the smallest consonant interval, SOL 6 of 

 3072 v.d. forms a consonant interval with a higher sound 

 separated from it by only 1-| semitones. 



The curve AY, of fig. 11, which has the same units of 

 abscissas as curve N.C.I., and the units of whose ordinates, in 

 number of vibrations, are on the right of the diagram, shows 

 graphically the number of vibrations to be added to the tones, 

 on the axis of abscissas, to obtain the smallest consonant 

 intervals. 



The experiments which form the basis of the statements 

 given in Table II., I shall now describe. 



Having but few forks below UT 3 in pitch, and those not 

 numerous enough to determine with accuracy the consonant 

 intervals, I requested my friend Dr. Rudolph Koenig, of 

 Paris, to determine for me the smallest consonant intervals 

 among sounds below UT 3 in pitch. The numbers in the table 

 referring to tores SOL_ 1? UT 1? SOL 1? UT 2 , and SOL,,, ex- 

 periments nos. 1, 2, 3, 4=, and 5 of Table II., were furnished 

 by Dr. Koenig - ' s experiments. The account of these experi- 

 ments, which Dr. Koenig so obligingly made for me, I give 

 in his own words :— 



