( ^x; ) 
many) be in continual proportion; that is, earh to the next 
fubfequent in the fame Proportion. 
For it hath been long fince Demonftrated, that there is 
no fuch thing as a juji Hemitom practicable in Miifickj (and 
the like for the divilion of a Tone into any number of Equal 
parts ; three, four, or more. ) For, fuppoiing the Proportion 
of a Tone ot Full not to be \ (or, as 9 to 8 ;) that of the 
Half -note muft be as V'p to ( as the Square-root of p to" the 
Square-root of 8 ; that is, as 3 to V8, or 3 to 2^1,) which 
are Incommenfurahk quantities. And that of a ^l^arter-notey 
as Vqq 9 to Vqq 8, (as the Btquadrate root of p, to the Bt- 
quadrate root of 8 , ) wh^ch is yet more Incommenfurate, 
And the like for any other number of Equal parts. Which 
will therefore never fall-in with the Proportions of Number 
to Number. 
So that this can never be perfectly adjufted for all Keys 
(without fomewhat of Bearing ) by multiplying of Pipes; un- 
lefs we would for every Key ( or every di&rent Seat of Mi ) 
have a different Set of Pipes, of which this or that is to be 
nfed, according as ( in the Compofition ) Mi is flippofed to 
ftand in this or that Seat. Which vafi: number of Pipes (for 
every 06tave ) would vailly increafe the Charge. And (when 
all is done ) make the whole impraCHcable. 
Thefe are my prefent thoughts, of the Queftion propofed to 
me, and upon thefe grounds. 
You will pleafe to excufe me for the trouble I give you of lb 
long a Letter. 
I thought it neceflary, to give a little intimation of the Anci- 
ent Greek Mufick compared with what is now in praCtife; 
which is more the fame than moft men are aw^are of : though 
the Language be very different. But I was not to be large in it. 
Thofe who defire to know more of it ; may fee my thoughts 
more at large, in that Appendix which I have added at the end 
of my Edition of Ptolemy's Harmonicks in Greek and Latin. 
The two Eminent Se6ts araongfl: them,the Arijloxenian and the 
Tythagorian^ differ much at the fame rate as doth the Language 
of our ordinary pradical Muficians, and that of thofe who treat 
of it in a more Speculative way. 
Our Practical Muficians talk of Notes and Half -notes ^ juft as 
the Artjloxentans did ; as if the Whole Notes were all Equal ; 
and the Half -notes likewife each the juft Half of a Whole Note, 
^ And 
