The art of counterpoint: a Mazzola-type model of three-voice first-species counterpoint
Abstract
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.
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BibTeX
@misc{okumura2026counterpoint,
title = {{The art of counterpoint: a Mazzola-type model of three-voice first-species counterpoint}},
author = {Ren Okumura and Takuro Shibayama},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.01102},
eprint = {2606.01102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.01102},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - The art of counterpoint: a Mazzola-type model of three-voice first-species counterpoint
AU - Ren Okumura
AU - Takuro Shibayama
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2606.01102
UR - https://arxiv.org/abs/2606.01102
AB - 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.
ER -