Abstract
Each independent scale interval structure with N semitones and M notes contains a multiplet of N scales (for example, the major scale has the interval structure 2212221; and its twelve multiplet members are: C‐major, D flat‐major,..., B‐major scales). Operators that step through these multiplet members (by sharping or flatting the notes of the multiplet members) are identical with those of N‐level finite state quantum mechanics. It is possible to construct orthonormal basis states which represent the multiplet members of a given interval structure. A musical score can then be expressed as a mixture of various tonalities, using the density matrix formalism of quantum mechanics. Several examples help illustrate this quantitative approach.
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