[ 7 ™ ] 
in the pitch of the fydem : but, by taking in the 
abidance of the harmonic dodrine, we fhall not only 
gain the true pitch for each fpecies in the mufical, 
but be led to fee the agreement between the two 
dodrines, which, I have already faid, was my prin- 
cipal view in thefe fheets, and which, having gone 
through the explanation of each dodrine feparately, 
as far as concerns the feven modes, we are now ripe 
for confidering ; for the eight modes, whofe expla- 
nation I have deferred, have no concern in this agree- 
ment, being rejeded by Ptolemey, as will appear, 
for this very reafon, in fubdance, that they would 
fiand the trial of the harmonic dodrine only, whereas 
the red had the fupport of both. Let us then con- 
dder how the two dodrines, as I have explained 
them, may be made to agree. 
By the harmonic dodrine, we are told the pitch 
of the fyftem for each mode ; and by the mufical, 
in what part of the fydem to take the fpecies of dia- 
pafon : now, by combining thefe two directions, we' 
gain the following plain canon, for finding any mode, 
required. - 
Canon. 
Fird pitch the fydem for the mode, as diredeck 
by the harmonic dodrine ; then feled from it. 
the diapafon, direded by the mufical; and we 
have the charaderidic fpecies of the. mode in its 
true pitch. 
To make this more plainly appear, and alfo to 
avoid the length of particular explanations, I have 
annexed a. diagram of the feven lpecies, which will 
fhew at what pitch of the Guidonian fcale each found 
of. 
