Optimizing musical chord inversions using the cartesian coordinate system

TL;DR

This paper proposes a method to optimize musical chord inversions by representing chords as points in a 3D Cartesian coordinate system, aiming to identify the most suitable voicing for musical expression.

Contribution

It introduces a novel mathematical framework for chord voicing optimization using Cartesian coordinates, bridging music theory and spatial mathematics.

Findings

Chord inversions can be modeled as points in 3D space.

The method identifies optimal voicings based on spatial relationships.

Potential for improved musical expression and composition.

Abstract

In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and advanced. The theory sounds quite trivial, yet the application has vast options, each leading to inarguably different outcomes, characterized by scientific and musical principles. Chords and their importance are self-explanatory. A chord is a bunch of notes played together. As far as scientists are concerned, it is a set of tonal frequencies ringing together resulting in a consonant/dissonant sound. It is well-known that the notes of a chord can be rearranged to come up with various voicings (1) of the same chord which enables a composer/player to choose the most optimal one to convey the emotion they wish to convey. Though there are numerous possibilities, it is scientific to think that there is just one appropriate voicing for a particular situation of tonal movements. In this study, we attempt to find the optimal voicings by considering chords to be points in a 3-dimensional cartesian coordinate system and further the fundamental understanding of mathematics in music theory.