Formal structures of a harmony in the parabola. (English) Zbl 1495.00017

Montiel, Mariana (ed.) et al., Mathematics and computation in music. 8th international conference, MCM 2022, Atlanta, GA, USA, June 21–24, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13267, 356-362 (2022).
Summary: 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.
For the entire collection see [Zbl 1492.00048].


00A65 Mathematics and music
Full Text: DOI


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