Formal Structures of a Harmony in the Parabola

Delgado Vega E.A. · Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2022) · DOI: 10.1007/978-3-031-07015-0_30

Resumen

We develop a geometric analog of musical harmony from the group law of the affine parabola. First, we associate musical notes and intervals with points of a parabola. Immediately, we can define the usual affine and linear transformations for musical chords in module theory. Subsequently, we show that the actions of the groups T/I in PK-nets, PLR, UTTs, and JQZ behave identically to the circle space. Then, we propose to recreate the Planet-4D model, the study of musical distance and the DFT for subsets of points on the parabola. We believe that we have an innovative and motivational perspective to approach the parabola in a musical meaning.