Mersenne's laws

A string half the length (1/2), four times the tension (4), or one-quarter the mass per length (1/4) is an octave higher (2/1).
If the tension on a string is ten lbs., it must be increased to 40 lbs. for a pitch an octave higher.[1]
A string, tied at A, is kept in tension by W, a suspended weight, and two bridges, B and the movable bridge C, while D is a freely moving wheel; all allowing one to demonstrate Mersenne's laws regarding tension and length[1]

Mersenne's laws are laws describing the frequency of oscillation of a stretched string or monochord,[1] useful in musical tuning and musical instrument construction.

  1. ^ a b c Jeans, James Hopwood (1937/1968). Science & Music, pp.62-4. Dover. ISBN 0-486-61964-8. Cited in "Mersenne's Laws", Wolfram.com