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
Year: 2026
Type: preprint
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.
Author: Sembiring, Heryanto
Language: English
Subfield: Music
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7225614239
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