20 H. W. Poole on Perfect Harmony, etc. 
division into 53 notes, and how each division serves for six dif- | 
ferent notes in. such close approximation that the eye would — 
take them as one; 2. the perfectly tuned notes in their order as 
regards acuteness of pitch; as they result from successive trans- 
positions by sharps and by flats to the 53d degree: and 3. any ~ 
other adjustment in order to economize in the number of organ- — 
pipes. 
88. If the ear is content with the thirds 0:065 of comma sharp, 
we can have 53-signatures in sharps, and as many in flats— 
noe Se in all except the perfect sevenths: these will all 4 
be supplied by 53 other pipes, making 106 pipes in the octave 
for what mathematically requires 640, 
39. But there is an arrangement by which we can have per- — ! 
fect thirds and all other intervals. By flatting the fifths 00113 — 
of comma, as described in § 30, and adding eight pipes, we have 
the triple diatonic scale perfect in 53 signatures, with 61 pipes. 
The perfect sevenths are supplied, and the double diatonic scales _ 
completed, by 53 additional pipes. For the minor mode we re- — 
quire 8 pipes each for the dominant thirds and sevenths; mak- — 
ing a total of 130 to the octave for 53 keys absolutely perfect. — 
They can be taken above or below the natural signature, as 
from 26 flats to 26 sharps: or in any other connected series of 
signatures. We should not have the circle joining exactly, §36, — 
> 
but we should have perfect intervals. within these wide limits. 
An enharmonic key-board for 58 signatures, on the scale] have _ 
drawn, would require about four feet of width, which could be 
livided 3 ; 
1 into two or three boa 
_ 40. Other adjustments can be made which are favored by the 
loseness of the intervals, and the large range within which the 4 
differences can be divided. In a temperament of 12 sounds, the — 
grand difficulty is to dispose of a comma among 5 intervals, viz., 
4 fifths and a major third—ignoring the chord of the seventh. 
The third of C, e, must serve for E. In any system the sum of 
mean-tone temperament gives it all to the fifths, one-fourth of a 
comma each, and the equal temperament, dividing but one- 
elfth to each fifth, leaves the third sharp by two-thirds of a 
comma. Here we have a difference of only one-eleventh of a 
comma, and have 8 fifths among which to divide it. 
41. The following table gives the names of the key-notes of 
106 regular transpositions by fifths, according to common musi- 
cal rules, and the number of sharps or flats in the signature of 
each. It gives, besides, the thirds and dominant thirds of the 
minor mode which are closely approximate to the key-notes, to- 
gether with the signature in ehok each note of the two latter 
es is found. A column of figures ascending from 1 to 54 in- 
; there are so many notes arranged in the order of 
in these 5 intervals is always exactly acomma. The — 
acl 
