Optimizing musical chord inversions using the cartesian coordinate system (2206.06117v1)

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.