History of World Music Duration: Mathematical Semiotic Modeling of Parabolic Function f(x) = -x^2 + 45x + 1/4 - Analysis of Duration Transformation Through RPM Rotation

This study proposes a mathematical semiotic model for the history of world music duration using the parabolic function f(x) = -x² + 45x + 1/4. The function reveals a precise homology between mathematical properties (roots, axis of symmetry, vertex, area) and physical-industrial properties of the music industry (45 RPM, 22.5 RPM, 506.5 rotations, 15,198 rotations). The axis of symmetry 22.5 serves as both the optimal duration limit for LP vinyl and a 22.5-year industrial transition cycle from 1954 to 1976 to 1998.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-09
DOI
https://doi.org/10.5281/zenodo.24084292
Primary Topic
Musicology and Musical Analysis
Type
preprint
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preprint

History of World Music Duration: Mathematical Semiotic Modeling of Parabolic Function f(x) = -x^2 + 45x + 1/4 - Analysis of Duration Transformation Through RPM Rotation

Heryanto Sembiring
Zenodo (CERN European Organization for Nuclear Research)
Musicology and Musical Analysis
preprint

History of World Music Duration: Mathematical Semiotic Modeling of Parabolic Function f(x) = -x^2 + 45x + 1/4 - Analysis of Duration Transformation Through RPM Rotation

Heryanto Sembiring
preprint en

Abstract

This study proposes a mathematical semiotic model for the history of world music duration using the parabolic function f(x) = -x² + 45x + 1/4. The function reveals a precise homology between mathematical properties (roots, axis of symmetry, vertex, area) and physical-industrial properties of the music industry (45 RPM, 22.5 RPM, 506.5 rotations, 15,198 rotations). The axis of symmetry 22.5 serves as both the optimal duration limit for LP vinyl and a 22.5-year industrial transition cycle from 1954 to 1976 to 1998.

Zenodo (CERN European Organization for Nuclear Research)
Musicology and Musical Analysis
DOIOpen Access PDFOpenAlex
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History of World Music Duration: Mathematical Semiotic Modeling of Parabolic Function f(x) = -x^2 + 45x + 1/4 - Analysis of Duration Transformation Through RPM Rotation — Heryanto Sembiring · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS