530 



Mr. A. J. Ellis. 



[June 17, 



a sea-shore, and forming a running accompaniment, totally dissimilar 

 from the bell-like beat of the partials. 



The pitch of the reeds on the treble tonometer furnishes not only 

 numerous cases of considences, but numerous cases of disturbed consi- 

 dences, beating four times in a second, when the reeds are in order. Thus 

 3 x 256=2 x 384, and hence 256 and 384 are a perfect considence. But 

 3 x 260-2 x 388= + 4, so that 260 and 388 form a disturbed Fifth, beat- 

 ing 4 times in a second, the upper note being too flat ; while 3 X 260—2 x 

 392 = —4, another disturbed Fifth, also beating 4 times in a second, the 

 upper note being too sharp. The fact of the upper note being too flat or 

 too sharp is shown immediately by flattening it, as previously described ; 

 the first beats are then made more rapid and the second more slow, but 

 it is impossible to destroy them entirely, as the upper note cannot be 

 sufficiently flattened. It is delightful, however, to take what should 

 be a perfect considence, as all were when I first examined the instru- 

 ment, and throw it out of tune by flattening either the upper or lower 

 note, or both unequally, producing the dissident beats, and then to 

 sharpen these notes gradually, and listen to the beats growing slower 

 and slower till they finally entirely disappear, and then reappear as 

 the sharpening is carried too far. The nature of considence and dissi- 

 dence is thus distinctly felt, and the delimitation of a considence is 

 determined by the possibility of hearing these dissident beats when 

 one of the extreme notes is flattened. The beats are clear, distinct, 

 and simple, and can be made very slow ; their pitch is also exactly 

 what has to be expected by the number of the partials. The other 

 partials of the two notes in the meantime beat roughly, strongly, and 

 very much faster than the dissident beats. Thus for the Fourth 4 : 3, 

 we may take reeds 264 and 352, then the partials will be — 



(1) (2) (3) (4) (5) 



264 528 792 1,056 1,320, &c. 



352 704 1,056 1,408, &o. 



(1) (2) (3) (4) 



Even when the 1,056 is consident, the 88 beats of 704 and 792, and 

 of 1,320 and 1,408 are easily heard, producing the well-known 

 " roughness " of the Fourth, while the 264, 352, and 528 boom along 

 loudly and independently. But if the upper note is flattened, the rate 

 of the two first beats is altered, one becoming faster and the other 

 slower, while slow beats of an entirely different character are intro- 

 duced at the high pitch of about 1,056, by the tearing apart of these 

 formerly coincident partials. I have watched the phenomenon over 

 and over again for different considences, and cannot imagine a better 

 demonstration of Helmholtz's theories. 



The following, among numerous other considences, have all been 

 clearly delimitated by me in the way mentioned, and most of the 



