{
  "annotation_id": "d143f1a9-9a61-4d90-bd0f-30c04d4206c4",
  "date_created": "2026-02-17T05:53:12.431000Z",
  "date_modified": "2026-02-17T05:53:12.431000Z",
  "file_hash": "468200438a5a20ade84e9e21582ee6d36accba277ad0c7a1c42701a11c03994b",
  "private": false,
  "record": {
    "abstract": "We extend a property of Mazzola\u0027s theory of cadential sets in relation to the modulation between minor and major tonalities from triadic to tetradic harmony, using the PLRQ group of Cannas et al. (2017) as the analogue of the classical PLR group. While the PLR group connects triadic cadential sets via the relative morphism $R$, the tetradic case reveals a richer structure: two pairs of cadential sets connected by distinct morphisms forming a \"prism\" in the slice category over the tonic seventh chord, and a single pair for those that allow quantized modulations. We demonstrate this structure through analysis of Charlie Parker\u0027s \"Blues for Alice\" (1951) and Ray Noble\u0027s \"Cherokee\" (1938), showing how the prism morphism, PLRQ transformations and quantized modulations organize harmonic navigation in bebop. The categorical framework captures what syntactic approaches miss: the transformational v\\\u0027{e}cu that musicians actually experience when navigating between cadential regions.",
    "arxiv_id": "2601.07161",
    "authors": [
      "Octavio A. Agust\u00edn-Aquino"
    ],
    "categories": [
      "math.HO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Blues for Alice: The Interplay of Neo-Riemannian and Cadential Viewpoints",
    "url": "https://arxiv.org/abs/2601.07161",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "57bc7aba-0eaf-41a5-a1cc-69cbbbac666c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}