The art of counterpoint: a Mazzola-type model of three-voice first-species counterpoint
In this paper, we extend Mazzola's model of two-voice counterpoint to three-voice first-species counterpoint. The construction combines a fiber product over a shared lower voice with a harmonic mask and a two-stage maximization defining admitted successors. For the Fuxian dichotomy, we compute the successor relation and investigate connections with the Riemann dichotomy and neo-Riemannian transformations. Among pairs of same-mode triads, the model admits the most transporter realizations exactly at the pairs that generate Mazzola's Riemann monoid, but it does not single out the dominant-tonic pair, and it admits only 12 of the 192 parsimonious neo-Riemannian realizations, largely because it excludes transitions that keep a pair of voices stationary.