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.
Harmonic Sets and Music
Drag O and
C to see relative positions.
Timothy Peil, 6 February 2013, Created with GeoGebra |
4.5.2 Harmonic Sets and Music
© Copyright 2013 -
Timothy Peil