Mathematics Across the Curriculum: Music
The original music theory articles:
A mathematical approach to some of these concepts:
- John Clough, "Aspects of diatonic sets", J. Music Theory
23 (1979) 45-61.
- John Clough and Gerald Myerson, "Variety and multiplicity in
diatonic systems", J. Music Theory 29 (1985) 249-269.
- John Clough and Jack Douthett, "Maximally even sets",
J. Music Theory 35 (1991) 93-173.
A physics approach (including the proof that maximally even sets are
- John Clough and Gerald Myerson, "Musical scales and the generalized
circle of fifths", Amer. Math. Monthly 93 (1986) 695-701.
- Jack Douthett and Richard Krantz, "Energy extremes and spin
configurations for the one-dimensional antiferromagnetic Ising model
with arbitrary-range interaction", J. Math. Physics 37 (7) (1996),