  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.
