1868. | On Musical Scales, 349 
Lastly, (¢) affords eleven Fifths (two defective by a single unit, 
and therefore to be received as perfect), and one defective by a 
Comma ; the Major and Minor Thirds also as in the case of ( C). 
Rejecting, then, (b), the transpositions of (a) and (c) will give 
the following systems :— 
eee ea ce ee hl 
DOW. 0 0 0 0 0 0 0 0 0 0 0 0 
es. || oa-| 170) V70"| P52) 186 170 170 | 1527) 1527) 170 | 170-186 
Mi .. | 322 | 322 | 356 | 322 | 356 | 322 | 322 | 822 | 322 | 356 | 322 | 356 
Fa .. | 415 | 415 | 433 | 415 | 415 | 415 | 399 | 415 | 415 | 415 | 433 | 415 
Sol .. | 585 | 585 | 585 | 567 | 585 | 585 | 585 | 567 | 585 | 585 | 585 | 601 
Mm tat | fat \eido,| Toes) TTL | 73%.) Tao | 737 | T3T | TTL | 755. | 77a 
Si .. | 907 | 907 | 941 | 889 | 941 | 907 | 907 | 923 | 907 | 941 | 907 | 923 
do .. \1000 |1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 |1000 
(c.) Cc. Dp. | De ||) Mies) VE. WP | Gp WAG.) (Ais |e cate lB | ore 
Do.. 0 0 0 0 0 0 0 0 0 0 0 0 
Liew |) 152) 170) | 170) 170) 69! | V70) |) 169) |) 152) 170) |) 170) || 170) | 168 
Mi .. | 322 | 340 | 339 | 340 | 338 | 322 | 339 | 322 | 340 | 338 | 322 | 338 
Fa .. | 415 | 416 | 4383 | 415 | 415 | 415 | 416 | 415 | 415 | 415 | 415 | 415 
Sol... | 585 | 585 | 585 | 585 | 585 | 585 | 584 | 567 | 585 | 585 | 585 | 584 
i aot || aot} too lusoo||| Foai|/ 7a || COL vor |loo| TO* | Too. | tee 
Si .. | 907 | 925 | 923 | 905 | 923 | 907 | 924 | 906 | 925 | 923 | 907 | 923 
do .. |1000 |1000 1000 aad 1000 1000 1000 |1000 1000 |1000 |1000 |1000 
Here we see reproduced in the scale (a) the peculiarity already 
noticed in (A), viz. that it gives to Ab the same identical scale with 
C and in Dh, (and with the exception of the single note La, also in 
Bg), the diatonic scale complementary to that we started from. 
Among the transpositions of (c), again, we find the key of F repro- 
ducing the complementary diatonic. 
Except these five scales, it does not appear possible to construct 
any others having the smallest pretension to be received, consist- 
ently with the condition of starting from one or the other of the 
two untempered diatonics,* unless, perhaps, we regard as entitled to 
enter into this competition that bugbear to the musical mind, the 
scale which arises from tuning up directly from Do eleven consecu- 
tive perfect Fifths ; the twelfth (which, with tempered Fifths, would 
lead to the seventh octave of the fundamental note), surpassing it 
* The minute temperament of a single unit in the two intermediate Fifths of 
the seales (C) and (c), it will be observed, does not affect any of the Natural notes 
of the fundamental scale. In those proposed by Dr. Young, on the other hand, the 
temperament is made to fall entirely on those notes, the accidentals being all free 
from it. 
