1880.] Notes of Observations on Musical Beats. 



527 



loss in quality. This power of reducing the pitch slightly and 

 instantly restoring it, is of great service in experiments upon consi- 

 dence and dissidence, which the relations of the pitch of the reeds 

 allow of being tried in a very large number of cases. It also enables 

 considences to be rendered perfect when the instrument, as is neces- 

 sary generally the case, is slightly out of tune, as the intervals can be 

 made closer by flattening the upper, and wider by flattening the lower 

 reed. 



The nominal values of the reeds are as follows : 



Bass tonometer, 57 reeds, numbered by their nominal value in 

 double vibrations :— 8, 9, 10, 11, 12, 13, 14, 15—16, 17, 18, 19, 20, 21, 

 22, 23, 24, 25, 26, 27, 28, 29, 30, 31—32, 34, 36, 38, 40, 42, 44, 46, 48, 

 50, 52, 54, 56, 58, 60, 62—64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 

 108, 112, 116, 120, 124, 128. 



Tenor tonometer, 33 reeds, numbered to 32, nominal value = 4 X 

 number +128=128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 

 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 

 228, 232, 236, 240, 244, 248, 252, 256. 



Treble tonometer, 65 reeds, numbered to 64, nominal value =4 X 

 number +256=256, 260, 264, 268, 272, 276, 280, 284, 288, 292, 296, 

 300, 304, 308, 312, 316, 320, 324, 328, 332, 336, 340, 344, 348, 352, 

 356, 360, 364, 368, 372, 376, 380, 384, 388, 392, 396, 400, 404, 

 408, 412, 416, 420, 424, 428, 432, 436, 440, 444, 448, 452, 456, 460, 

 464, 468, 472, 476, 480, 484, 488, 492, 496, 500, 504, 508, 512. 



The correctness of these numbers had to be proved in the first place 

 by counting the beats. The sum of the various sets of beats in the 

 treble tonometer should be 256, in the tenor tonometer 128, in the 

 bass tonometer, from 8 to 16, 8 beats -, from 16 to 32, 16 beats ; from 

 32 to 64, 32 beats ; from 64 to 128, 64 beats. I counted the beats in 

 the treble tonometer at South Kensington several times. On 27th 

 October, 1876, each set of beats being counted for 20 seconds, I obtained 

 256 exactly. From 5th to 24th September, 1877, I counted each set 

 of beats for a minute, and many times over, and, owing to alterations 

 in the pitch of the reeds, the beats varied from 3*85 to 4*27 in a second, 

 their sums being 256*27. On 25th and 28th September, 1877, 1 again 

 counted each set for one minute, and obtained 256*28 as the sum. On 

 the 10th and 12th September, 1877, I counted the beats on Lord 

 Rayleigh's copy, and found the sum 256*38. My count of the King's 

 College copy, 13th November to 20th December, 1877, at two minutes 

 for each set, gave 254*75, and was certainly erroneous. The beats 

 + 6, of a disturbed considence, as y : x, which is supposed to be near 

 n : m, joined with the sum of the beats d, between y and x, when 

 b, d, m, n are known, give y and x by the equations — 



my — nx — + b , y — x=d s 

 and hence the value of I, the lowest note, is known, when y — I is 



