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Encyclopedia of Microtonal Music Theory

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Hamiltonian scale

[Gene Ward Smith, Yahoo tuning-math message 11300 (Tue Aug 10, 2004 2:59 pm)]

A Hamiltonian graph is a graph with a circuit -- a path starting and ending at the same point -- which visits each node exactly once.

Given an octave-equivalent scale, we can form the q-odd-limit graph of the scale by making the degrees of the scale the nodes, and the concordances of the scale the edges. If the resulting graph is Hamiltonian, we can say the scale is Hamiltonian in the q-limit.

A Hamiltonian scale has a tone row where each succesive element of the row is related via a concordance to the last, including the last to the first again.

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