1868. | On Musical Scales. 347 
Of the Fifths one only errs by a Comma, all the rest may be 
regarded as perfect, and the defective one (as we have seen) is 
inevitable if we insist on starting from an untempered scale. The 
chief blemish of this scale is the paucity of its perfect Thirds of 
both kinds, but on the other hand none of them err in excess or 
defect beyond a Comma. 
The peculiarities of these several scales will, however, be placed 
in a clearer light by exhibiting the several scales of natural notes 
resulting from their transposition into all the keys. Taking then 
C for an original or’ fundamental key, the values of the natural 
notes in all the keys, starting from the scale (A), will stand thus:— 
| | | | 
1 aes Dp. | Deeps |e re he he. a al) Beep Bt 
Do.. 0 0 0 0 0 0 0 0 | 0 0 0 0 
Re .. | 170 | 170 | 152 | 152 | 170 | 170 | 186 | 152 | 170 | 170 | 152 | 186 
Mi .. | 322 | 822 | 322 | 322 | 356 | 322 | 356 | 322 | 322 | 356 | 322 | 356 
Fa .. | 415 | 399 | 415 | 415 | 415 | 483 | 415 | 415 | 415 | 483 | 415 | 415 
Sol .. | 585 | 585 | 567 | 585 | 585 | 585 | 601 | 585 | 585 | 585 | 567 | 585 
VO tou) 100 | Tor | ae | Wil |) Foo | 77h | 737 | 738t ) tao | 13%) Wa 
Si .. | 907 | 907 | 923 | 907 | 941 | 907 | 923 | 907 | 907 | 941 | 889 | 941 
do .. 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 
From which it appears that—Istly, the transposition into Ab gives 
us back again the pure original scale of C unaltered; and, 2ndly, 
the transposition into either G or into Eb, gives again the diatonic 
scale, with the substitution of 152 instead of 170 for Re, constituting 
what we have above designated as the Co-diatonic scale. 
Operating a similar series of transpositions with (B) as a funda- 
mental scale, we find the following system— 
| 
| 
© TS HO RR RO SC 
Re .. | 170 | 170 | 152 | 186 | 170 | 170 | 152 | 152 | 170 | 170 | 186 | 152 
# | 356 | 322 | 322 | 322 | 322 | 356 | 322 | 356 | 322 
Fa .. | 415 | 433 | 415 | 415 | 415 | 399 | 415 | 415 | 415 | 433 | 415 | 415 
Sol .. | 585 | 585 | 567 | 585 | 585 | 585 | 567 | 585 | 585 | 585 | 601 | 585 
La .. | 737 | 755 | 737 | 771 | 737 | 755 | 737 | 737 | 771 | 755 | 771 | 737 
Si .. | 907 | 941 | 889 | 941 | 907 | 907 | 923 | 907 | 941 | 907 | 923 | 907 
do .. |1000 pon 1000 a 1000 1000 1000 1000 1000 1000 1000 1000 
| 
Here we are again presented with a similar phenomenon. The 
exact original scale of C is reproduced in HJ, and the co-diatonic 
scale in the keys of G and B. Lastly, making the same series of 
transpositions in the case of our scale (C), we obtain— 
