{"paper":{"title":"Voicing Transformations and a Linear Representation of Uniform Triadic Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Thomas M. Fiore, Thomas Noll","submitted_at":"2016-03-31T15:27:02Z","abstract_excerpt":"Motivated by analytical methods in mathematical music theory, we determine the structure of the subgroup J of GL(3,Z12) generated by the three voicing reflections. As applications of our Structure Theorem, we determine the structure of the stabilizer H in Sigma3 semi-direct product J of root position triads, and show that H is a representation of Hook's uniform triadic transformations group U. We also determine the centralizer of J in both GL(3,Z12) and the monoid Aff(3,Z12) of affine transformations, and recover a Lewinian duality for trichords containing a generator of Z12}. We present a var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09636","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}