•8 
i6i 
18 
10 
8 
9 
1 
(8*) 
placing the Frets on the Neck of a Viol, or other Mufical In- 
ftrument ; wherein a greater Exadnefs is thought not ne- 
ceffary.Afid this is very convenient>becaulc(thus) the Change 
of the Key (upon altering the Seat of mi) gives no new Trou- 
ble, for this doth indifferently ferve any Key ; and the Dif- 
ference is fo fmall, as not to offend the Ear. 
But thofe who choofe to treat of it with more exaftneG^ 
go thi^ way to work. 
Preiuppofmg the Proportion for an Odave (or Dia-fafm) 
to be that of 2 to i ; they divide this into Two Proportions ; 
not juft equal ffor that would fall upon /«r/f Numbers, as of v'2 
to 1 j) but mafet^ual (fo as to be expreffed in fmall Numbers.) 
In order to which, infteadof taking 2 to i, they take (the 
double of thefe Numbers) 4 to 2 ; (which is the lame Propor- 
tion as before*)) and iiiterpoie the middle Number 3. And, 
of thele Three Numbers, 4, 5, 2, that of 4 to 3, is the Pro- 
portion for a Fourth (or Dia-ujfsron.) Atid that of j to 2, the 
Proportion for a Fifth (or Dia-fente.) And thefe Two put to- 
gether, make up that of an 0(5i:ave ( or Diafafm^) that of 4 to 
2, (oT 2 to I.) And the Difference of thofe Two, that of a 
Tone or 9 to 8. As will plainly appear in the ordinary Me- 
thod of Multiplying and Dividing Fradions. That is, 
|x|=:?=:i Andf)l(f _ . ^ 
Thus, in the common Scale ( or 
Gam-ut) taking an Odave, in thefe 
Notes, la^fa folia, mi^fa fol la ; fup- 
pofe, from E to {placing mi, in 
bfa \Smi i which is called the Natu^ 
ral Scale {) the Lengths for the Ex- 
tremes la lay an Odave, are as 2 to 
or 12 to 6. Thofe for la la (m la fa 
fol la ) or 793i la (in mi fa fol ia) a 
Fourth, as 4 to 3, or 12 to 5, or 8 
to 6. Thofe for la mi (in la fa fol Is 
mi) or la la (in la mi fa folia) a Fifth, 
as 3 to 2, or 12 to 8, or 9 to 6. Thofe 
for la f»/Vthe DiazeuSicA-Tone (ordif- 
ferencc of a Fourth and Fifth,) as 9 
to 8. So have we for thofe Four 
Notes la la mi la, their Proportionate 
Length in the Numbers 12986. 
8 
12 
In 
Sol 
mi 
la 
Sol 
fa 
Then 
£ 
