C H R 



According to Aristoxenus, in this genus the tetrachord 

 was divided into 30 equal parts, of which the tetrachord 

 was thus composed, viz. 4+4+22=30, whence 



|Jths or 4f x4th=186.367502 + 3f+l6m 



.^yths or vyx4th= 33.816252+ f+ 3m 



T%.ths or ^ x 4th= 33.816252+ f + 3m _ 



4th=25t.000002 +5f +22ra 



According to Ptolemy, the numerical ratios in this 

 genus were IT X 44 X =i r the tetrachord, whence, 



3d or =16 1.0000002 + 3f+ 14m 



44= 60.9*70962+ f+ 5m 



fj= 32.0529042+ f+ 3m 



25470000662 + 5f + 22m 



Dr Pepusch is of opinion, in which he is followed by 

 Mr Overend, that this genus was as follows, viz. 



3d+E=1822 + 3f+16m 



(S= 362+ f+ 3m 



d = 362+ f+ 3m 



2542 +5f+ 22m 



By having all these reduced to one rotation, as above, 

 the curious reader of the authors above mentioned, can 

 the readier compare these very different and discordant 

 scales, (j) 



CHROMATICUM SESQUIALTERUM, Homiolium, 

 or Sescuplum, was a genus of the Greek music, which, 

 according to Euclid, ascended by one and a half of his 

 euharmcnic diesis, or quarter of the major tone, another 

 such an interval, and an incomposit, as follows, viz. 



176.0689342 + 3f+16m 

 T= 38.9655332+ f+ 3m 

 |T= 38.9655332+ f+ 3m 

 4th=254.0000002 + 5f + 22m 



The first of these intervals was, it is said by Holden, 

 accounted to be 1^ of a major tone, or seven quarter 

 tones, = 1 82.0728652 + 3f+ 16m, differing 6.0039312, 

 or just half of the diaschisma, or ct, as before, in the 

 molle. 



According to Aristoxenus, the tetrachord, in this ge- 

 nus, was divided into 30 parts, and these distributed ai 

 follows, viz. 4|+4^+21=30, whence 



35ths or 44 X4th=177.8701142+3f+16m 



gjthsor^y x4th= 38.0649432+ f+ 3m 



g^ths or^jX4th= 38.0649432+ f+ 3m 



4th= 254.0000002 + 5f + 22m 



Dr Pepusch and Mr Overend state this genus ai fol- 

 lows, viz. 



401 C H R 



Sd=16l2 + 3f+14m 

 rf= 362+ f+ 3m 

 = 572+ f+ 5m 

 4th=2542 + 5t + 22m 

 This is also the chromatic in Didymus's genera. ($) 



CHROMATICUM TONIJEUM, or Tonicum, was a 

 genus, according to Euclid, where the tetrachord rose 

 by hemitone, hemitone, and trihemitone as follows, viz. 



149.9921 382 + 3f + 14m 

 fT= 52.0039312+ f+ 4m 

 |T= 52.0039312+ f+ 4m 

 4th=254.0000002 +5f+22m 



The first of the above intervals, is the comma- deficient 

 minor third, =1502+3f+13m, (though differently ex- 

 pressed, in order to throw the decimal parts, all on the 

 schisma,) and is the trihemitone of Euclid. 



According to Aristoxenus, this tetrachord is thus di- 

 vided, viz. 6+6+18=30, whence 



4ths or f x 4th= 152.393702 + 3f + 14m 

 -^thsorf x4th= 50.803152+ f+ 4m 

 T Vhs or f x 4th= 50.803152+ f+ 4m 

 4th=254.000002 + 5f + 22m 



Dr Pepusch and Mr Overend state this genus as fol- 

 lows, viz. 



T+<f =1402 + 3f+12m 

 S = 572+ f+ 5m 

 S = 572+ f+ 5m 

 4th=: 2542 + 5fx 22m 



The genera that are ascribed to Archytas, have a 

 chromatic different from any of the above, viz. 



K= 1 50.0000002 + 3f+ 1 3m 

 H|= 71.9470962+ f+ 6m 



$j= 32.0529042+ f+ 3m 

 4th =254.0000002 + 5t + 22m 



Aristides ascribes another chromatic to the ancient 

 Pythagoreans, having the same comma-deficient minor 

 third as above, viz. 



ff = 1 50.000002 + 3f+ 1 3m 

 44= 50.468192+ f+ 4m 

 44=^53.531812+ f+ 5m 

 4th=254.000002 + 5f + 22m 



A genus ascribed to Eutosthenes, also differs fro 

 any 01 the above, as follows, viz. 



i=l6l.0000002 + 3f+ 14m 

 4|= 47.7290182+ f+ 4m 

 f= 45.2709822+ f+ 4m 

 254.0000002 + 5i + 22m 



TOL. TI. PART ir. 



3 E 



