| Citation |
PP-P.771.028
23 Dec 1771:12 (9 Supplement)
[A solution to a question in Supplement 7 of this paper (not
available) relates to determining what length and tensions
to strings produce fifths and unisons]
Let x = the longer tended by 16, whose sq. root is 4.
y = the shorter tended by 9, whose sq. root is 3.
By the principles of music, the vibrations of strings are in
proportion directly as their lengths, and reciprocally as
the square roots of their tension, which vibrations, to
sound fifths, must be in the ratio of 3 to 2:
Whence 3x:4y::3:2. Therefore, 6x=12y.
. . . [8 more lines]
16 inches long and 16lb. tension,
8 inches long and 9lb. tension, sound fifths.
16 inches long and 16lb. tension,
12 inches long and 9lb. tension, sound unisons.
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