{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.01102",
  "author_total": 2,
  "authors": [
    {
      "name": "Ren Okumura"
    },
    {
      "name": "Takuro Shibayama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/08ha5hej1est5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.01102",
  "fulltext_url": null,
  "id": "08ha5hej1est5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.01102",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "1210|Musicology and Musical Analysis"
    ]
  ],
  "openalex": "W7163162663",
  "pdf_url": "https://arxiv.org/pdf/2606.01102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/08ha5hej1est5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2606.01102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.01102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The art of counterpoint: a Mazzola-type model of three-voice first-species counterpoint",
  "title_text": "The art of counterpoint: a Mazzola-type model of three-voice first-species counterpoint",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/08ha5hej1est5",
  "venue": "arXiv",
  "versions": []
}