Spelled heptachords

Abstract

This paper develops a theory of spelled pitch classes (spcs) and spelled pitch-class sets (spc sets), incorporating pitch spelling into the techniques of pitch-class set theory. The symmetries of spc space are transposition and inversion along the line of fifths. Because of the inextricable link between pitch spelling and diatonic scales, spelled heptachords - seven-note spc sets that include each letter name exactly once - occupy a privileged position in this theory. Spelled heptachords may be regarded as inflected diatonic scales, and possess a number of structural characteristics not shared by other spc sets. The 66 equivalence classes of spelled heptachords without enharmonic doublings or voice crossings are enumerated. A diatonic musical structure together with a spelled heptachord determine an spc structure in which the notes of the diatonic structure are inflected by the corresponding accidentals from the heptachord; spc structures arising in this way show promise as powerful tools in analysis of chromatic harmony. © 2011 Springer-Verlag.