[ 7 68 ] 
with the fubjed? But not to inlift farther on the 
flips of a writer, to whom the learned world ftands 
fo highly indebted, I lhall take leave of him, with 
this remark only, that v/hatever he may have feen of 
the truth of thefe dodrines himfelf, his explanations 
have not fucceeded in making the fubjed clear to 
fucceeding writers ; thofe I have feen having either 
adopted the harmonic dodrine only, or been fo con- 
founded between the two, as to give a right account 
of neither. This has, in particular, been the cafe 
with Malcolm, who, in his X reatiie on Mulic, ex- 
plains that of the antients, and has taken lome pains 
to reconcile the two dodrines of the modes. 1 he 
greateft part of what this writer delivers is not only 
falfe, in refped to the order, politions, and, indeed, 
almoft every other circumftance attending the modes, 
but, at the fame time, fcarce intelligible ; or, if any 
meaning can be put upon it, it is too foreign to the 
truth of either of the dodrines, to be worth con- 
fidering. I lhall content myfelf with citing apaffage 
from him, where his reafoning is the cleat ell, and 
where we may fee, that, after all the pains he has 
taken to reconcile the tv/o dodrines, he owns himfelf 
unable to make any fure decilion upon the fubjed. 
“ He (Ptolemey) fays, in the beginning of that 
chapter (cap. y. lib. ii.), the mutations, which ate 
made by whole fyftems (which we propetly call 
tones, bccaufe thefe differences conlift in tenfion), 
are infinite, with refped to poflibility, as founds ate; 
but adually, and with refped to fenfe, they are finite. 
All this feems plainly to put the difference of the 
tones only in the acutenefs or gravity of the whole; 
clfe, how do their differences confift in tenfion, w hicn 
fignifies 
