C 74 ) 
abounding or deficient : And this is ncceflary, and can- 
not be avoided in any tuned Inftrument, as Organ or 
Virginal, becaufe the Intervals that are nectfTary to make 
one CiifF perfeft, are thereby neither true nor truly 
placed in the other. Nor can there be found any tole- 
rable kind of Divifion or proportioning of the Notes 
that will anfwer to all Cliffs, by reafon that the grounds 
of Harmony depend on Proportions, and thofe Propor- 
tions require differing Intervals to be placed in a Deter- 
iDinate order between the Unifon and the Oftave, whence 
neither the Degrees, nor the Order, that is fitted for 
one Cliff can be accommodated for the other. He adds 
alfo forr^e other Scales, in which he explains the Diffe- 
rences by enumerating the Tones, Hemitones, Diefes, 
or Comma's that are found in each and he adds three 
other Tables to explain the differences of the Differen- 
ces, which are found by the fame Method as the diffe- 
rences themfeives, and he could have added many more, 
but that he thought thofe fufficient. I {hall mention 
only one Example of his laft Table of Differences, in 
which he Colleds all the diflerences to be Nine, /. 
7 one major ^ Tone minor ^ Hemitone max. Hemitone maj. 
HemitenemiJ, Hemkone Fythag, Himitone minor ^ Diejisy 
Comma; and the eompofition of each of thefe bigger of 
the fmaller, as Tone major ^ contains, i. Tone minor and 
Comma. 2. Hemitonf max. and Hemitone minor. 3. He- 
mitone majory and Hemitone med. 4. Two Hemitones 
minor., omDiefiSy ont Comma, 
In the Ninth Chapter is his Conclufion, where he 
has fum'd up his whole Doftrine that is. Bodies by Mo- 
tion make Sound, found of Bodies fitly conftituted make 
Tone or Tune ; Tune is acuter by fwiftneft, graver by 
flownefs of vibrating Motions. The Proportions of 
theie are beft found by firings : If two Vibrations be 
commenfijrate within the Number 6, they produce Con- 
cords; if incijmmenfiirate, they make Difcords. Con- 
cords 
