1868. | On Musical Scales. oo 
from Eb or Bb, which will simply transfer the letters in the head- 
ing (d) into the order (e) in the upper of the two lines below the 
table in the former case, and into the order (f) in the latter case; 
and will give us for the values of the notes in the two scales as 
under— 
Do Re . Mi Fa Sol La Si do 
(ec) 0, 75, 170, 245, 320, 415, 490, 585, 660, 735, 830, 905, 1000; 
if) 0, 75, 150, 245, 320, 415, 490, 585, 660, 735, 830, 905, 1000; 
whose approximation to our scales (C) and (c) is very close. 
Exactly in the same manner, if we set out with either of the 
scales (A), (B), and, instead of commencing with C as a funda- 
mental note, commence with Ab, as Do, and tune upwards thence 
by the successive intervals of the other scale in their order, from the 
beginning to the end of the octave. we shall complete the scale— 
thus, commencing with 678, which corresponds to Ap in the scale 
(A), and adding to it in succession each of the numbers 59, 170, 
229, 322, &., belonging to the scale (B), we produce the numbers 
737; 848; 907; 1,000; 1,093; 1,170, 1,263; 1,322; 1,415; 
1,492 ; 1,585; 1,678; and vice versa. This places in evidence the 
musical relation of those two scales, and shows that in fact each of 
them is only a transposition of the other. 
The scale of equal temperament results from tuning upwards 
from Do twelve successive Fifths, each defective by 22, or each = 
5881; or, which comes to the same, dividing the octave into equal 
intervals of 832 each, thus giving the scale (to the nearest unit in 
each note)— 
Do Re Mi Fa Sol La Si do 
(z) 0, 88, 167, 250, 333, 417, 500, 583, 667, 750, 833, 917, 1000. 
This scale, of course, reproduces itself in all its transpositions, 
and is therefore exceedingly well adapted to the purposes of the 
mere Pianiste as affording him an unbounded range of modulation, 
and (by the free use of the equivocal chord, or diminished Seventh, 
and other similar artifices of modulation) allowing him, within the 
compass of the same piece of music, to pass into any, or if he 
please, all the keys, without fear of encountering “the wolf,” or any 
other musical monster but those of his own making. Its chief 
defect is that it does not afford a single good Third, either Major or 
Minor; ail the former being two-thirds of a Comma in excess, and 
all the latter as much in defect of their legitimate values. This is 
little felt in modern pianoforte music, in which brilliancy and 
rapidity of passages and startling turns of modulation, by the intro- 
duction of all sorts of extraneous notes into the discords, stand in 
the place of delicate and sustained harmony ; to which, besides, the 
instrument itself is little adapted, owing to the rapid degradation 
in the intensity of sound in its notes when once struck. As an 
