of Consonances of the Form h : 1. 433 



The twelfth of the C was plainly distinguishable, but it 

 appeared to keep separate from the mass of tone; it was 

 perfectly steady and unaffected by combination with c. 



C : c, 2 beats sharp. Phenomena undistinguishable from 2 

 beats below. 



, 4 beats sharp. Perhaps a little less roll in the strong- 

 part of the beat. 



, 8 beats sharp. The mass of the beats is of pitch near 



C; but the exact pitch is very difficult to distinguish. It 

 is a deep heavy rattle, quite distinct in pitch from the 

 upper note. 



C : e. Ifthereisany slow beat in passing through this, it 

 is very difficult to distinguish. I am inclined to nega- 

 tive it. 



C :/*. Roll. 



Slow beats up to 



C : g. These beats consist of alternations of intensity of C. 

 They are more difficult to count than those of C : c. I 

 counted them at 5 below. 



. Slow beats above. 



C : b\). Rattle, turning into beats easily counted at 4 below 

 & '. These beats also consist of variations of intensity of 

 the lower note. 



C :c'. 



The beats above </ were also counted at 4 above, while 

 the engine was going, without difficulty. 



45. Above this, in the neighbourhood of the binary con- 

 sonances C : e' &c, I have never been able to obtain slow 

 beats in such a way that they could be readily perceived (even 

 without the engine) or certainly counted. 



46. The mode adopted to examine cases in which the beats 

 could not be perceived was, to introduce a third note, such as c f , 

 which gave beats with the C, and tune it true. Then any 

 note, such as e' or </, could be readily tuned so that the whole 

 three notes gave 1, 2, 3, or 4 beats. When this had been 

 done, the intermediate note d was removed. If the pair exa- 

 mined was capable of giving beats at all, they should then 

 have been audible. 



47. The details of the above course furnish no new results ; I 

 have not, therefore, thought it worth while to give similar 

 courses for other sets of notes. Those results which are worthy 

 of mention have been already stated. 



Theory of the Beats of Mistuned Consonances of the form 

 h :1. 



48. Let n be the frequency of the lowest note, m the number 



