168 Mr. R. H. M. Bosanquet on Temperament, 



is that any mechanism, whether stops or pedals, for the selec- 

 tion of the notes required is unpractical in relation to the rapid 

 modulations of modern music. 



There is an interesting- passage in which Smith anticipated to 

 some extent the doctrine of Helmholtz that dissonance consists 

 of beats (p. 227): — "For nothing gives greater offence to the 

 hearer, though ignorant of the cause of it, than those rapid rat- 

 tling beats of high and loud sounds which make imperfect con- 

 sonances with one another; and yet a few slow beats, like the 

 slow undulations of a close shake now and then introduced, are 

 far from being disagreeable." 



I may here remark that there is a discrepancy between the 

 practice of musicians and that introduced by Helmholtz as to 

 the employment of the term dissonance. The principal autho- 

 rities in technical music are unanimous in regarding a fourth as 

 a dissonance. I propose to call such combinations as the fourth 

 or harmonic seventh, neither of which gives sensible beats, 

 " unsatisfied combinations" Dissonances may then be divided 

 into beating dissonances and unsatisfied combinations. 



Woolhouse's ' Essay on Musical Intervals' (1835). This 

 writer uses equal-temperament semitones for the first time. 

 The principal systems he discusses are those of 50, 31, and 19, 

 all negative. 



In a paper by De Morgan " On the Beats of Imperfect Con- 

 sonances" (Camb. Phil. Trans, vol. x. p. 129), equal-tempera- 

 ment semitones are employed as the measure of interval. The 

 rules there given for the transformation of logarithms of vibra- 

 tion-ratios into equal-temperament semitones, and vice versa, 

 are substantially the same with those I employ. The treatment 

 of the problems of beats and of resultant tones is superseded by 

 HelmhohVs work. 



In a paper by Herschel (Quarterly Journal of Science, vol. v. 

 p. 338) various scales are proposed. In one of these, which is 

 preferred, all the fifths except one are perfect, the remaining one 

 erring of course by a Pythagorean comma. His observation is, 

 " The chief blemish is the paucity of perfect thirds of both 

 kinds; but, on the other hand, none of them err in excess or 

 defect beyond a comma." The defective fifth is taken to be 

 d~\a (Table at top of p. 348, column D, row sol). Now an 

 error of a comma in a fifth makes it unfit for use in music ; 

 no ear can tolerate a fifth which is a comma out of tune; so 

 that this arrangement would exclude from use the keys of G, 

 D, and A major, to say nothing of minor keys. 



I here pass over the instruments of Mr. Poole * and General 



Silliman's American Journal, vol. xliv. p. 1. 



