174 On Music. 
The established practice of musicians in reading the mu= 
sical notes upwards, makes it more convenient, in computing 
and using tables like the above, to follow the same order; 
which is the reason that the title of the table is at bottom 
instead of the top; and it is to be read, and its intervals reck- 
oned, upwards. It is necessary here to remark, respecting the 
4th and 5th columns entitled the Diatonic System, that this 
term has too frequently been restricted by authors to the 
ratios set against the notes C, D, E, F, G, A, B and c, re- 
spectively; while others, who were writing on a tempera- 
ment of the scale, have introduced ratios answering to » C, 
bE, x F, x G, andbB: these in the above table consti- 
tute the chromatic octave, example No. 4, in Mr. Hawkes’s 
treatise. But the student must not be surprised, on looking 
into different authors who treat on the a of music, to 
find the poe key «C bearing a ratio of 43, or even 4% 
bE s,) or4z3-% F 43} «G23 ‘and hig =o siseuOe 
those in the atte. talsles and yet to find the same denomi- 
nated diatonic intervals ; because, on consulting Maxwell’s 
Essay on Tune, a work of great merit, printed in Scotland, 
(which was advertised in 1794, anda few copies vended in 
London, with a spurious title-page and date,) he will find 
that 56 notes or intervals, at the least, are required in each 
octave of the diatonic system to render modulation into.each 
of the twelve finger-keys, major and minor, practicable with- 
out false intervals, or such as a good ear would pronounce to 
be out of tune. Indeed, the diatonic system, when limited 
to the seven notes, C, D, E, F, G, A, and B, has but little 
of the perfection in practice, which is usually ascribed to it ; 
for, except in sounding the notes E, F, G,and A, with their 
fundamental note C, if the base note moves into D,E,F,G, 
&c., it will be found that the harmonies marked in the piece 
of music to accompany it, are but few of them to be found 
among these seven notes, or even among the five intermediate | 
orhalf notes, which are set down by the authors above alluded 
to, except Maxwell; but a false note, or one differing in an 
offensive degree from the true one, must be substituted for its 
By adding the logarithm of the octave .6989700, suc- 
cessiyely to those of the notes x C, D, bE, &c, in 5th, 
6th, 
Bitte “5 
