70 Air. Farey’s Letter on musical Intervals, &. 
downwards from c, another one of these concords, which is 
called its complement, will in every case result or remain 
(true, and without any Beats, as all experiments prove) as 
the difference, between the lower Octave note C and the 
lowest note of such subtracted concord. 
It has been, therefore, with some propriety, that the ma- 
jority of the writers of ‘Treatises, have adopted, and adhered 
to the principle, of defining Intervals, as the sums or differ- 
ences of other Intervals, or of some of their multiples : and 
the very frequent use of the major 'Tone T (having the ratio 
8), of the minor Tone t (,%;), and of the major Semitone S 
(22), as degrees or leaps in the Seale of melody, have led 
these Writers almost unanimously to adopt those three Inter- 
vals, as the terms of their Notation of Intervals, in general: in 
which manner, for example, the above seven Concords, 
beginning with the smallest, are expressed as follows, viz. 
T+S, T+t, T+t+S, 2T4+t+5, 2T4+t4+28,27T+2% 
+S, and 3T+ 2t+ 285 which answer to the Literals, 
Eo, E, F, G, A®, A and ¢, respectively. If now we omit 
A°, and supply the six remaining discords, and also the 
lower octave note, for completing, in this notation, the 
Douzeave which Mr. Liston calls the Original Scale, (p. 28 
of his ‘ Essay on perfect Intonation,”) they are as follows, 
viz. C=o, C#=T-—S, D=T, Fx#=2 T+4+t, Gh=2 T+ 
2+, Bo =2 T4+2t4+258, and B=3 T+21t+8. 
Those who may proceed no further than to the con- 
sideration of the scale of 12 notes, which is defined above, 
without proceeding to supply the other intermediate notes, 
which become necessary in extending the modulation, (as 
Mr. Liston has done,) may remain in a great degree igno- 
rant of the great defect of this particular mode of Notation: 
arising, not frem any defect in its principle, as has been ob- 
served above, but merely from the largeness of tis terms, 
T, t and $3 which occasion negative signs so frequently to 
occur, and connecting such varied multiples of these terms, 
as almost certainly to bewilder and disgust most of those 
who may attempt to follow Mr. Liston, through the large 
folding Tables inserted in his Essay. I have conversed 
with more than a score of Musicians, who had previously 
perused Mr. L.’s Essay, but not one of whom had got over 
the stumbling-block last mentioned.—One of these Gentle- 
men, having more perseverance than others, observed to me 
