Analysis of Combining Musical Scale Vectors

Abstract

This interdisciplinary project uses mathematics to represent musically significant collections of notes such as scales, chords and intervals as combinations of each other. These note collection were converted into one-dimensional vectors so that matrices could be used to solve the systems of linear equations, which create the combinations. In some cases, this method produces combinations, which are too complex to have musical significance, so a new iterative method has been devised to create simpler combinations. All the mathematics used has been coded into MATLAB, resulting in combinations being quickly computed. In particular, we focused on the diatonic scale, interval of a major third, and the octatonic scale. Applications have been made to existing musical literature. We have found 15 examples of one type of note collection being used to evoke the structure of a different collection.