Mr. S. Taylor on Variations of Pitch in Beats. 63 



treated, we recognized the oscillations of pitch without difficulty. 

 By arrangements of this kind the inteimediateness^ of the beating 

 sound between the primaries at its maximum of intensity, and 

 its passage beyond their limits^, either of graveness or acuteness, 

 at its minimum, were brought out very distinctlJ^ 



Dissonance arises, as Helmholtz has proved, from the presence 

 of beats too rapid to be separately recognized. Except when 

 they are due to sounds of exactly equal intensities, they contain, 

 as we have seen, oscillations of pitch. It remains to inquire 

 whether alternations of this latter kind produce any appre- 

 ciable effect on the character of the combination in which they 

 occur. There seems some antecedent probability that they will 

 do so. The essential character of a musical sound is steadi- 

 ness of pitch. Here we have a sound which is never steady 

 for a moment, and thus comes under the definition of a mere 

 noise. The unmusical nature of such a sound can hardly fail 

 to make itself felt. We can, however, put the question to the 

 test of experiment by producing rapid alternations of intensity, 

 while the pitch is kept constant, and ascertaining whether the 

 whole sensation we call dissonance can be thus excited. In 

 order to do this, I employed the principle of interference, as ex- 

 hibited by a single tuning-fork. It is known that a fork in 

 making one revolution about its own axis passes through four 

 positions of maximum intensity separated by four positions of 

 absolute silence. By twirling the handle of the fork between the 

 fingers of both hands, I was able to command quick alternations 

 of intensity unaccompanied by changes of pitch. As a further 

 experiment, a resonance-box, with its fork screwed into it, was 

 fastened into a lathe, and, the fork having been struck, set ro- 

 tating, so that the open and closed ends of the box were alter- 

 nately presented to the ear. The lathe was then urged to its 

 fullest speed and a series of very rapid intensity-variations pro- 

 duced. I owe the means of performing this experiment to an 

 excellent amateur turner, Mr. J. Aspinall, of Crewe, who w^as 

 kind enough to place his lathe and his own dexterity at my dis- 

 posal for the purpose. The result of both the trials just de- 

 scribed was, that the effect, though distinctly rough ^ lacked the 

 peculiar sourness usually characteristic of a discordant interval. 

 These observations seem to show that it is the pitch-variations 

 which excite in our ears the special element of discord just men- 

 tioned. In fact the conditions under which dissonance arises 

 frequently themselves indicate that variations of intensity can 

 have but an insignificant influence upon the total result. Thus 

 the dissonance of two tuning-forks forming the interval of an 



* These facts were also experimentally ascertained by Heltnholtz,, p. 622. 



