74 Mr. Farey’s Letter on musical Intervals, &. 
In the work last quoted, vol. XIII, p. 41, the 59 notes 
of Mr. Liston’s Scale will be found expressed i in the nota- 
tion that has now been described; from whic ave ex~ 
tracted, and placed in ‘Table sh the 12 notes of his original 
Scale already mentioned her 
The seven last lines of the shies Table have been added, 
in order to mclude the concords of minor Sixth, 
Tone, the major Semitone and the Comma; and the Séhin- 
ma, the lesser L’raction, and the most Mistabee This Table 
can hardly need further explanation: 1 wi therefore pro- 
ceed to some furtherremarks. 
he expressions in col. 3 of the above Table, aceurately 
express the values of the Intervals in cols. 4 and 2: and 
such is the peculiar and natural commection, between the 
rates of increase upwards in the ‘Table, for each of the terms 
=, fand m, that whatever result or truth appears conjointly 
from the three terms, after any process of adding or sub- 
iracting Intervals i in yeh erat has oe performed, the 
separately i there bein: baere;| no carr rying oF ag (in 
Ww 1umbers, at least) from one column to ie as ip 
common Arithmetic. $ endently of the other 
rations performed with these Spee as giving a rough 
value in artificial Semitones, or 12th part the octave : 
every” tke result in the m column will oe a considerably 
more accurate value, in the artificial Commas of Nicholas 
Merion or 53d parts of the octave, very nearly : and 
every result of like operations in the z column, will give 
rigidly accurate results, in all such Euharmonie or untem- 
pered caleulations as are alluded to above, and will approx- 
imate to the truth, abundantly sufficient for nearly every 
practical purpose of Harmonics, being extremely near to the 
Gia parts of the octave, and to “the 11th’ parts of the 
r comma. 
When Tempered Systems are to be calculated, fractional 
arts of the major comma, expressed in Schismas, ma} 
joined with these artificial commas without at alt disturbing 
the consistency of their results: thus, if the Jsetonie scale 
of equal Semitones were required to be calculated, the flat 
ning Seige a: of the Vth is known to be extremely near 
to 7th of a major comma, which is 2, and the true Vth 
———— ee ee aa Oe 
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