The art of counterpoint: a Mazzola-type three-voice first-species counterpoint model
Abstract
We propose a three-voice extension of Mazzola's algebraic model of first-species counterpoint. A three-voice sonority is represented as \(a+1 .b+2 .c\), where \(a\) is the lower voice and \(b,c\) are the lower--middle and lower--upper interval classes. Starting from a strong dichotomy \((X/Y)\) of \( Z2k\), we introduce a harmonic mask \(H⊂eq X× X\) and define the admissible three-voice consonances \(XH\). We then construct a Hichert-type successor relation by applying the ordinary two-voice admitted-successor mechanism to the active pairwise projections. In the twelve-tone Fuxian case, the proposed mask has 26 admissible bass-rooted interval pairs, including complete and incomplete sonorities, and yields a finite directed successor structure.
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