Royal b o c i e ty. ^^(^ 
now received as the mofl proper; where tJ is what we call the 
Heml-mie or half-tone in rnhfa-y f that of the greater tone iny}<r, 
fol, and J- the leiTer tone in foh l^ h only with this addition, 
that each of thefe tones is upon occafion divided by flats and 
fliarps, into two Hemi-tones or half-notes, which anfwers to 
what was called by the Greeks Mutatio quoad Modos, i. e. the 
chanf'e of mood, and what is now done by removing mi to ano- 
ther key, namely | = f f := If X f^ and ^^ =z n - ^ x H: 
Thus by the help of flats and fliarps, dividing each whole note, 
be it the greater or lefTer, in two half-notes, or what we call fo, 
the whole 06iave is divided into twelve parts or intervals, con- 
tained between thirteen pipes, which are commonly called Hemi- 
foz/g-i or half-notes ; not that each is precifely half a note, bat 
fomewhat near it, and is fo called , for inftance a flat m D or a 
fliarp in C, do either of them denote a middling found, tho' not 
precifely in the middle between C and D, yet iharper than G and 
flatter than D ; accordingly, fuppofing ;;;/ to iland m 'B-fa-b-mi^ 
which is accounted its natural fear, the founds of each pipe are to 
bear thefe ratio's to each other, viz. 
B. C. i. D. $. E. F. t' G- t. ^' t- ^. 
mi. fa. *. fol k la- fi- f • M t- ^^' i- f^i- 
»6 18 17 20 19 ±6 iS i-2 2^ J.9 JL3 J. J. 
XT T7 T7^ 79 li ': *' ^f '^ '^ '' ''? 
l^^y'Nj L^vxJ : O^vNj u^vNj" L/^ysj 
: 9 1 Q '2. i-o. 2. 
3" , ^ 
•■\y 
"V- 
J. 
And fo in each 05fave fucceffively following; and if the pipes 
in each OElave be fiited to founds in theie proportions of gravity 
and acutenefs, it Vv^ill be fuppofed, according to this hypotheiis 
to be perfectly proportioned: But inftead of thefe fucceffive 
ratio's of each Hemi-tone, it is found neceffary, fo to order the 
1 5 pipes, containing 1 2 intervals, called Hemi-tones, as that their 
Ibunds, as to gravity and acutenefs, may be in continual propor- 
tion, each to its next following, in one and the fame ratio, which 
all together lliall complete tliat of an 05fave or 2)ia-pafon^ as 
2 to I ; whereby it comes to pafs that each pipe doth not exprefs 
its proper found, but very near it, yet fome fmall matter varying 
from it, which they call jBearing-^ and is fomewhat of imper- 
few^iofi 
