Of Winds and Sounds,

Numbers 6, 4, Z; and in the Line A Dwe take A E equal to BG, A F equal to

C Hr

f^me Ratio with their respective Differences M % n ' ■O. For by the Definition of Music«tl Ratio

h lB : D :: N : OTherefore AXB : CxD :: MXN : NXO :: M : 0 .(A : C :: M : NAlso ] B : D :: N : O

. { C : E :: O : P

Therefore AXBXC: CXDXE AX B : ^X E) :: M X N X O : N X O X P :: M : P. That:

is 5 AB : DE .. M : P ; and so on universally.

7. Again; the Difference between the twoTerms M is to the Difference between any other two*as O, in the Ratio of B — 2 M to D ; or M : P :: ®— 3M : E; or M : Q.:: B-4M : F*; and socontinually. For, by the Nature of the Progression,

is A : C :: M : N ; and it is also A B — ]Vf, (h*'cause B — A = M) therefore it is B — M : C ::

N ; or, to put it in Form, we have M : N :: B—l ^: C. Again;. B — M : M :: C : N, and by Divisi 011B-2M : M :: C—N : N :: B : N; but (by th?Definition, Art. 1.) it is B : N :: D : O, therefo^M : O :: B — 2M : I). Again; B—3 M : hd ••D — O : O :: C : O :: E : P; therefore M : P ::

3 M : E. And universally, let n — Number of T erl1 ^in the Series between the first and the last, and le't the lasTerm be Z, and let the Difference between it and th®next preceding Term be 8 ; then will it be M : "

B — »M : Z.

8. Because (by Art. 6.) it is M : S :: AXB : ;

supposing Y, Z, the two last Terms of the Seri eS ’

therefore A X B : Y X Z : : B — n M : Z. __

Because the first Term of the Series is A ""

9 - „AXB

B ’’

and the second Term B —

AXBA ’

B-—M; therefore the second. Term is B