A Method of Incorporating Matrix Theory to Create Mathematical Function-Based Music

TL;DR

This paper introduces a mathematical approach using matrix theory and polynomial functions to compose music by transforming note sets, inspired by Schoenberg's tone rows and linear algebra.

Contribution

It presents a novel method that applies matrix equations to map note sets to new sets, enabling systematic composition of musical harmonies.

Findings

The method successfully maps input note sets to new sets using matrix equations.

It allows permutation of note collections to generate diverse musical harmonies.

The approach integrates linear algebra with musical theory for composition.

Abstract

This paper attempts to look for a mathematical method of composing music by incorporating Schonbergs idea of tone rows and matrix theory from linear algebra. The elements of a note set S are considered as the integer values for the natural notes based on the C Major Scale and rational numbers for semitones. The elements of S are effectively mapped by a polynomial function to another note set T. To accomplish this, S is treated as a column vector, applied to the matrix equation Ax equals b, where x denotes the vector S, b denotes the resulting set T, and A represents a square matrix. This method yields functions capable of mapping input note sets to others, thereby creating collections of sets that can be permuted in any order to form musical harmonies.