We propose a three-voice extension of Mazzola's algebraic model of first-species counterpoint. A three-voice sonority is represented as \(a+\varepsilon_1 .b+\varepsilon_2 .c\), 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 \(\mathbb Z_{2k}\), we introduce a harmonic mask \(H\subseteq X\times X\) and define the admissible three-voice consonances \(X_H\). 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.