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

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.