28o M E M O I R S 5/^ ^>5^ 
fedtion in tliis noble inftrument, the chief of all. It nnay be 
ailed, why may not the pipes be 16 ordered, as to have their 
founds in jult proportion, as well as this Searing?' In anfwer, it 
might very well be fo, if all nnufick were compoled to the lame 
key, or, as the Greeks call it the lame mode, as for inftance, ii\ 
in all compolitions, r/U were always placed in S-fa-b-mi^ then 
the pipes might be ordered in fuch ratio's as had been now 
defined : But mufical compoGtions are made in a great variety 
of modes, or with great diverfity in the pitch 5 ;;;/ is not always 
placed in S-fa-b-miy but lometimes in E-la-mi^ Ibmetimes in 
^-h-mi-re^Scc. and in ium there is none of thofe 12 or 13 pipes, 
but may be made the feat of mi ^ and if they were exadly fitted 
to any one of thefe cafes, they would be quite out of order for all 
the rell^ as for inftance, if ^7/ be removed from 'B-fa-b-tniy by a 
flat in B, to E-la-raiy inftead of the ratio's, bijt jult now 
defined, they muft be thus ordered, 
B. i. C. t. D. $. E. F. i G. ^ a. b 
fa, $. fol. $. la. ^ mi. fa. ^. fol. t- la. fa. 
18 ^ 17 20 19 18 17 \6 18 17 20 19 16 
ij T6 Tg i^ 17 16 ij 17 16 r? 18 15 
where it is manifeft, that the removal of mi doth quite diforder 
the whole leries of ratio's : And the fame would again 
happen, if mi be removed from E to A, by another flat in E 5 
and again removed from A to D ^ and lb perpetually : But the 
Hcmi-iofies being made all equal, they do indifferently anfwer all 
the pofitions of mi^ tho' not exa6lly to any, yet nearer to Ibme 
than to others^ whence, it is, that the fame tune founds better at 
one key than at another. 
It is afked, vi^hether this may .not be remedied by interpofing 
more pipes, and thereby dividing a note, not only as now into 
half-notes, but into quarter-notes, or half quarter notes, ^c. In 
anfwer, it may be thus remedied in part • that is, the imper- 
fcdion might thus be fomewhat lefs, and the Ibunds fomewhat 
nearer to the juft ratio's 3 but it can never be exactly true, 
fo long as their founds, be they never lb many, are in continual 
proportion; that is, each to the next fubfequent in the fame 
ratio: For it hath been long fmcc demonftrated, that there is 
no fuch thing as a juft Hsmi-torie pra6licabie in mufick, and the 
like may be' laid, tor the divifion of a tone into any number of 
equal parts, three, four or more 3 for, fuppofing the ratio of a 
tone or full note to be f or as p to 8, the ratio of the half-note 
muft 
I 
