Mr DE morgan, ON THE BEATS OF IMPERFECT CONSONANCES. 145 



I feel sure that the results of this principle of variety in the keys would, if fairly tried, be 

 found more satisfactory than those of equal temperament. Nor do I at all apprehend that 

 the principle is carried too far : on the contrary, I should predict that the system R, in which 

 the difference between dominantly successive keys is greater than in the others, would be the 

 best of all. But by making p, q, r, s, in R, and p, q, r, in S, more nearly equal than in the 

 instance given, any less amount of adherence to the distinctive feature might be secured. 



It is useless to speculate on systems with any view of materially diminishing the number 

 of beats/ in the thirds and sixths. In equal temperament, the consonance G A^ beats more 

 than 1150 times in a minute, while GD' (D' the octave above D) beats only 73 times. Nor 

 can the beats be reduced, in the different consonances of a chord, either to equality, or to near 

 commensurability, throughout any considerable portion of the scale. It is the irregularity of 

 the beating which is its chief disadvantage : regularity would give merely the effect of a faint 

 drum-accompaniment ; but such change as that from C F C, in which C F and F C beat 

 equally, to C G C, in which G C beats twice as fast as C G, is the real annoyance. A 

 further disadvantage is that the multitudinous beats are thrown on the consonances which 

 are least suited to take them. The fourths and fifths should be called martial consonances, 

 the thirds and sixths pastoral : but the bray of the beats is thrown on the thirds and sixths, 

 and is never so distressing in the fourths and fifths. 



The subject will never be fairly entered upon, as to true comparison of systems of tem- 

 perament, until the bearings are tuned from a system of forks, one to each semitone. I think 

 it probable that nothing but the general ignorance of the theory of beats, arising out of the 

 obscurity under which the subject has been presented, has hitherto prevented the construction 

 of such standard bearings. 



A. DeM. 



January 18, 1858. 



Vol. X. Paet I. 19 



