348 On Musical Seales. [July, 
Coy | DR D. | ep. | |e. Gp. |G. | Ab. | Bp. | B. 
Do.. 0 0 0 0 0 oe" "0 0 0 0 0|-°0 
Re .. | 170 | 170 | 152 | 168 | 170 | 170 | 170 | 152 | 169 | 170 | 169 | 170 
M .. | 322 | 338 | 322 | 338 | 340 | 322 | 339 | 322 | 338 | 340 | 339 | 340 
Fa .. | 415 | 415 | 415 | 415 | 415 | 416 | 415 | 415 | 415 | 433 | 416 | 415 
Sol... | 585 | 585 | 567 | 584 | 585 | 585 | 585 | 585 | 585 | 585 | 584 | 585 
La .. | 737 | 754 | 737 | 753 | 755 | 755 | 755 | 737 | 753 | 755 | 754 | 755 
Si .. | 907 | 923 | 907 | 923 | 925 | 907 | 923 | 907 | 923 | 925 | 906 | 924 
do .. |1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 
where the co-diatonic scale appears in G, as in the case of (B). And 
it is sufficient to run the eye along the several horizontal lines of 
the table to perceive the much greater uniformity and regularity 
prevailing in this system than in the other two, between which it 
offers a sort of mean. 
§ 2. 
Let us now go through exactly the same set of operations, set- 
ting out from the co-diatonic scale in which Re = 152; and instead 
of the system of values of «, 8, &c. in (VII.), we shall find our- 
selves conducted to the following :— 
(VIIL.) 
a=59, B=229, y=474, 5=644, «=796; 
a=93, B=263, y=508, 5=678, e=830; 
while the systems of values in (VI.) remain unaltered. Here, then, 
the link of connection between the two sets which give a Fifth in 
the one and a Third in the other, is e = 830, instead of y = 492; 
and thus, proceeding as before, we are led to three scales, (a), (b), 
(c), each having its own especial claims to consideration. 
Do Re Mi Fa Sol La Si do 
(a) 0, 93, 152, 263, 322, 415, 508, 585, 678, 737, 880, 907, 1000. 
(b) 0, 59, 152, 229, 322, 415, 474, 585, 644, 737, 796, 907, 1000. 
(c) 0, 75, 152, 245, 322, 415, 491, 585, 660, 737, 830, 907, 1000. 
Examining these by the criterion afforded by their Fifths and Major 
and Minor Thirds, as in the cases of the former scales, (A), (B), (C), 
we shall find that (a) affords, just as in the case of (A), nine per- 
fect Fifths, and three excessive or defective by a Comma; eight 
perfect Major Thirds, and four excessive by 34; and six perfect 
Minor Thirds, three deficient by a Comma, and three by 34, or nearly 
two Commas. 
The scale (b) similarly tried affords only eight perfect Fifths, 
three defective by a Comma, and one excessive by 34; eight per- 
fect Major Thirds, the other four all excessive by 34; and seven 
perfect Minor Thirds, the others defective—two by 18, two by 34, 
and one by 52. ‘This scale, then, is decidedly inferior, and may at 
once be rejected. 
