Quantal computation of tonality in music

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.