Of Winds and Sounds.

.Fourth as the Difference between the Firs ^Second is to the Difference between the 'Pbtrt*and Fourth, as in the Numbers 5, 6, 8, I 0 'For Strings of such Lengths will found al1OSlave, 5 to 1 o ; a Sixth Greater, 6 to *° *a Third Greater, 8 to 10 ; a Third Lef er ’

5 to 6 ; a Sixth Lesser, 5 to 8 ; a Fourth

6 to 8. r

It may be here observed, that a Series V

Numbers in Harmonic al Proportion areprocally as another Series in Arithmetical P 1 ®'grejjion,

C Harmonical 10 : 12: 15 : 20 : 30 : f>° \C Arithmetical 6: 5: 4: 3: 2 : 1 'for here 10 : 12 :: 5 : 6; and 12 : 15 '' ?: c ; and so of all the rest. Whence th 0 \

Series have an obvious Relation to,

aP

d

Dependence on, each other ; which in s 0l fProblems of speculative Philosophy widvery useful to know (CIX). ^

(CIX) 1. Let A, B, C, be three Numbers i stsical Proportion ; then because we have A : C • : R q jB : B —C, therefore A B — A p = A C — * iswhence if any twp of the three be given, theimmediately found by the following Canons, s-’ 255 '

Canon I. If A and B be given, then C ;

A it

2 A",2 A

Canon II. If A and C be given, then B =

CjL-.

Canon III. If B and C be given, then A = q C"-ss

2. T1-U--