[ 7\5 ] 
have written very obfcurely upon the fubjedl. His 
chief view was to reduce the fifteen modes, admitted 
upon the principle of the harmonic do&rirte, to thofe 
feven, which had the fupport alfo of the mufical: 
but this reformation was to be attempted with great 
precaution, on account of the obflinate prejudices it 
was likely to meet with, from the harmonicians of 
his own time : And we fhall therefore find him firfl 
artfully treating the modes upon the foot of the har- 
monic dodtrine only, and arguing ad homines for the 
reduction of the modes, even upon their own prin- 
ciples ; but, before he drops the fubjedl, his true 
reafons will appear; and, indeed, it will eafily be 
feen, that he had them conflantly in view from the 
firfl, though he does not argue openly upon them. 
This will account for that mixture of the two doc- 
trines, which is found in his writings, and will, with 
the afiiflance of a few explanations, render intel- 
ligible what he has delivered upon the fubjedt. 
The tones he confiders, after the harmonic doc- 
trine, as mutations by whole conflitutions, which, he 
tells us, are therefore properly called tones, as they 
are differences in refpedl to tenfion. Thefe differences 
he admits to be infinite in poflibility, but argues, 
that in efficacy, and in refpedl to fenfe, they are finite, 
and liable to certain limitations. Thefe limitations he 
derives from the theory of the confonances, by which 
means, he lays a foundation for his future argument, 
for reducing the modes to the number of fpecies of 
the confonance diapafon. The limitations of the tones, 
which he propofes to regulate by thofe of the con- 
fonances, are, as he tells us, threefold j viz, 
Vol, LI, 4 Z 
i„ As 
