May not music be described as the mathematics of sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music—music the dream, mathematics the working life.
—
James Joseph Sylvester (1814–1897)4.5 Investigation with Harmonic Sets and Music
May not music be described as the
mathematics of sense, mathematics as music of the reason? The musician feels
mathematics, the mathematician thinks music—music the dream, mathematics the
working life.
—James Joseph Sylvester (1814–1897)
The ratio of the lengths of the string to the corresponding notes would be 1:4/5:2/3 for C, E, and G. We consider a string tuned to C with E 4/5 and G 2/3 of the length of the string. The following diagram illustrates that the points O, G, E, C form a harmonic set H(OE,CG); that is, G is the harmonic conjugate of C with respect to O and E.
Drag O and
C to change the string length.
Drag E' and
P' to change the quadrangle.
To reset to the original settings, type the letter "R" on the keyboard.
JavaSketchpad,
a World-Wide-Web component of
The Geometer's Sketchpad.
Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial
use.
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© Copyright 2005, 2006 - Timothy Peil |
