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Mr. Farey’s Letter on musical Intervals, &e. 69 
measures of ratios admit of being thus modelled at will, 
how are we any longer to place confidence in those Writings, 
which speak always of the Concords, and the other Inter- 
vals of the scale derived from them, as being rigidly measur- 
ed by ratios, in small whole numbers, involving no prime 
larger than 5?” To this, it may not be unseasonable for 
me now to add, that in making the above mentioned re- 
noes of the sixth and following places of recip. logs., 
although so great an error as ;3,ths of the fifth unit figure 
the major Comma, the error is unavoidably ;’;ths, in the ex- 
pression for the Interval, which so often happens to be the 
unit of the Temperaments: and aon it may be said, 
that even this is but the ;;},th part of a comma, yet this is 
sufficient to shew the want of a natural foundation for this 
mode of representing Intervals ; however useful - oe Math- 
ematician, as approximations, ‘the same may with truth be 
contended for, as has been done by Ar etrg Fisher in 
your 17th page. 
Notwithstanding it is found thus difficult to define, or to 
assign intelligible measures to musical Intervals, owing to the 
remoteness | a the analogy by which such are connected 
with the ratios of Numbers, the most evident analogies con- 
nect many of. these Intervals with each other, and shew them 
to be quantities capable of addition and subtraction: thus, 
no one with the least ear for music, will dissent from the 
truth and conclusiveness of the experiment, performed on 
an Organ or Piano-forte in his presence, of tuning, perfect 
(and without any beatings) Ist, a major Fifth upwards from 
2 given note, (as C) to G, and then a minor Fourth upon 
his, or Ge, that then the compound interval Ce, is a true 
Claatisis 5 2dly, if the Ifld CE, and on it the 6th Ec, be 
tuned, he will agree, that the very same Note ¢ has been 
arrived at, as before ; and 3dly, when the 3d CED, and then 
the Vith th ED ¢ are tuned, he will still agree, that "the same 
note cis again* arrived at; proving clearly, that either. of 
these three pairs of Intorwals, make up, together, the same 
sum of Intervals, viz. an Octave. 
© in like manner, if the perfect Octave Cc be first tuned 
apovards, and then either of the above six concords tuned 
