of Musical Intervals. ^'IS 



Thus it happens, that the whole Table is composed, of 21 ho- 

 rizontal ranges, of dift'erent lengths, of consecutive perfect Vths *, 

 diflferentlv placed over each other, so as to form, at the same 

 time, 49 vertical ra.i\ges of consecutive perfect Illdsf, of different 

 lengths, and positions. 



The artificial Commas, at the left- hand ends of the 21 ranges of 

 Vths, beginning at the top, are 180, 179, 17S, 131, 292, 95, 510, 

 417, 324, 485, 34; 553, 460, 263, 66, 227, 388, 295, 306, 63, 

 and 5S2, respectively; and those at the right-hand ends, 30, 549, 

 306 :, 317, 224, 385, 546, 349, 152, 59, 578, 127, 288, 195, 

 102, 517, 320, 481, 434, 433, and 432, respectively. 



And the number of Vths in each of the 21 ranges above men- 

 tioned, Ijeginning at the top of the Table, are 4, 14, 27, 34, 35, 

 36, 37, 35, 33, 34, 33, 34, 33, 35, 37, 36, 35, 34, 27, 14 and 4, 

 respectively, which together, amount to 613, the number of arti- 

 ficial Commas, and of Notes here, in the Octave, including both 

 Bb'" and D«', in the middle of the Octave, which reckon as one 

 Note, bv the artificial Commas, although differing by 2f-}-m. 



The number of Notes in this Table, without either acute or 

 grave marks (' or '), is 75. Of those bearing one acute mark (') 

 it is 74, of those with two acutes (") 70, with three acutes ('" or 

 '•) 51, with 4 acutes ('^) 40, with 5 acutes C^) 26, and with 

 6 acutes (' ') the number of Notes is 8 ; in all 269 acuted Notes. 

 Of those Notes bearing one grare mark ('), the number is 74, 

 with two graves (") it is 70, with three graves ('*) 51, with 4 graves 

 ( '•») 40, v/ith 5 graves ('5) 26, and with 6 graves b(') the num- 

 ber of Notes is 8 : in all 269 graved Notes. 



The number of Notes without either Flat or Sharp is 83 ; the 

 number bearing one Sharp (*) is 77, of 2 Sharps (*«<) it is 63, 

 of (*') 47, of (*') 37, and of («') it is 17 : in all 241 sharpened 

 Notes. Also, the number of Notes bearing one Flat (b) is 83, 

 of (bb) it is 71 ; of (b?) 54, of (bi) 45, of (bs) 32, and of (b') 

 it is 4: in all 289 flattened Notes. 



The natural Notes, i. e. without either Sharps or Flats, but 



* Whose differences, in artificial Commas, are either 358, or (358 — 612 

 =)— 254; and to the terms of wliicii series of Vths, tlio seven Liternh 

 F, C, G, D, A, E and B are affixed, in successive series; and these are 

 marked witli one or more b's or *'s, in similar progressions; and also with 

 {<r:ive or acute marks, forniin;; series of 4, 5, 5, 4, 5, 5, &c, successive 

 inai'ks of the same number and kind, except in one instance in each rauj^e 

 of Vths; occasioned by the anomaly in the scale, with regard to Cj and 

 C'b, which has been mentioned in page 443, where the successive numbers 

 of graves or acutes is 4, 5, 5, 5, 4, &c.: which appears owing, to the tuuing 

 botli wuxfifrom C, a thing which docs not occur in any other p;ut of the 

 Scale. t Whose differences are cither 197, or (197 — 612=) — 4 15. 



X This Note only, being twice inserted, because being in the middle of 

 the Octave, it was so required, for preserving complements, to octaves, 

 throughout. 



bearing 



