( ) 
to fet down the Divifions of the whole Tones, which 
arc the true Chromatick half Notes, bccaufc there is 
great ufe of them in Praftical Mufick. 
To make all our whole Notes, and all our half Notes 
of an equal fize, by falfifying the proportions, and bear- 
ing with their imperfeftions, as the common praftice is, 
may be allow 'd by fuch Ears as are vitiated by long cu- 
ftome : But it certainly deprives us of that (aiisfadtory 
pleafurc which arifes from the exadtnefs of fonorous num- 
bers 5 which we (hould enjoy, if all the Notes were truly 
given according to the Proportions here aflign'd. 
It is very eal^ to fatisfie our felves in the Arithmetical 
Scheme, by thofe operations which GaJfcMdus has fet down 
in his Manuduftion to the Theory of Mufick, Tom. V. 
pag, 655 As for example, his rule for Addition is, That 
two Proportions being given, if the Greater number of 
one be rrsuUiplied by the Greater number of the other, 
and the Lefler by the Lcller, the two numbers produced 
exhibit the compounded Proportions. Thus take a 
PraOlcai Fifth ^ and a Pradical Fourth \ for the two 
Pfoportions given, multiply 5 by 4 and you have 12, 
th«d multiply 2 by j and you have 6 : which com- 
pounded proportion of 12 to 6 makes the Practical 
Oaavei. 
Thus, accofdingtohis Arithmetical operations of Ad- 
dition, Subftraaion, Multiplication or Continuation, and 
Divifion, is our whole Syftcm proved, which for the 
more eafie application to Pra£?"ical Mufick, (hall be alfo 
fet forth Geometf ically^upon the 6 firings of a Viol. See 
Figure the 2d. 
The 
