Counterpoint in 2k-tone equal temperament

Abstract

This paper presents a brief overview of Mazzola's counterpoint theory for the 12-tone equal temperament [G. Mazzola, The Topos of Music, Birkhauser-Verlag, Basel, 2002]. A similar theory for a 2k-tone equal temperament is shown to be feasible for k2, a positive integer. More precisely, strong dichotomies in such temperaments are proven to exist for k2 and a counterpoint theorem is obtained. Hichert's algorithm [J. Hichert, Verallgemeinerung des Kontrapunkttheorems fur die Hierarchie aller starken Dichotomien in temperierter Stimmung, Diplomarbeit, TU Ilmenau, 1993] for the calculation of admitted successors is described for this new setup.