2013/01/17 by Luis A. Piovan, Piovan, Luis A.
Arts and Humanities · Computer Science · Engineering · Mathematics · #Acoustic Wave Phenomena Research #FOS: Mathematics #Group Theory (math.GR) #History and Overview (math.HO) #Music Technology and Sound Studies #Musicology and Musical Analysis #math.GR #math.HO
paper · pdf · doi:10.48550/arxiv.1301.4255
27 pages, 12 figures
arxiv created 2013/01/17 · openalex publication_date 2013/01/17 · arxiv updated 2013/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same T/I class. It is a generalization of the well known Öttingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.