Prof. A. M. Mayer's Researches in Acoustics. 365 



C, of 



64 



C 2 ,, 



128 



C 3 » 



256 



C 4 ,, 



512 



C 5 » 



1024 



= fourth -f | semitone. 

 = fourth -f§ „ 

 = major third -\-'j- „ 

 = major third -\--^ „ 

 = minor third —jjy » 



= one tone H-yV 



» 



Ce „ 2048 „ „ 



We thus see that while in the neighbourhood of 0, the near- 

 est consonant interval is over a fourth, in the octave of C 6 the 

 nearest consonant interval has contracted to a tone. This result 

 seems to show why it is that the middle portion of the musical 

 scale is best adapted for expression, and is most used in musical 

 composition ; for while in the lowest octaves the available conso- 

 nant intervals are few on account of the extended spaces separa- 

 ting them, in the highest octaves the consonances are so con- 

 tracted that their highest consonant intervals lose the sharp- 

 ness of definition given when these are bounded by distinctly 

 marked dissonances. 



It is here to be remarked that in our experiments we have 

 obtained continuous and discontinuous sensation from beats pro- 

 duced by one sound of a constant pitch; but with musical inter- 

 vals we obtain beats from two sounds differing in pitch. In the 

 latter case De Morgan, Gueroult, Helmholtz, and Mr. Sedley 

 Taylor have shown that there exists a variation, or oscillation, in 

 pitch whenever the two sounds are not of the same intensity. 

 Mr. Taylor*, from this fact, advances the idea that these oscilla- 

 tions in pitch cause a noise in place of a sound, and to this result 

 is due, in great part, the dissonance produced by beats of two 

 different sounds. That oscillations of pitch occur when the two 

 sounds are of unequal intensity is a fact of which there can be 

 no doubt; but that this oscillation of pitch is the principal cause 

 of the dissonant sensations which are perceived when beats occur, 

 my own experiments do not verify; yet I admit that the pheno- 

 menon has its effect in increasing slightly the dissonant character 

 of the beats. But even assuming that Mr. Taylor's explanation 

 of the dissonance of beats is correct, yet our views hold good 

 when we regard the intervals as formed of sounds which are 

 equal in intensity. 



In concluding this paper, I should call attention to the evi- 

 dent difference existing between the dynamic constitution of the 

 sonorous waves belonging to beating pulses produced by the 

 action of a perforated rotating disk on a continuous stream of 

 sonorous vibrations, and those waves which cause beats and 

 which are formed by the joint action of sonorous vibration? dif- 

 fering in pitch. That these two kinds of beats are alike in their 

 effects when following in the same rapidity I have assumed to be 

 the fact in this paper. 



* " On the Variations of Pitch in Beats," by Sedley Taylor, Esq., Phil. 

 Mag. July 1872. 



Phil. Mag. S. 4. Vol. 49. No. 326. May 1875, 2 C 



