2014/09/28 by Sidarth Jayadev, Jayadev, Sidarth
Mathematics · #00-02 #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:00-02
paper · pdf · doi:10.48550/arxiv.1410.0568
12 pages, 2 figures
arxiv created 2014/09/28 · arxiv updated 2014/10/03
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.