Analysis of Combining Musical Scale Vectors

Abstract

The motivation for this project stems from a paper by Dr. William A. Sethares. One of the topics this paper explores is how scale vectors that represent musically significant collections of notes (MSCN's), such as musical scales, chords, and intervals - essentially any collection of notes with a periodic structure- can be expressed as linear combinations of other types of MSCN’s. These scale vectors are 12 by 1 (for the 12 notes of the chromatic scale) and consist of 1’s and 0’s, where 1’s symbolize the inclusion of a note, while the 0’s indicate the exclusion of a note. Dr. Sethares devised a method for creating combinations using these scale vectors, and provides a couple examples of this method in action. Our goal was to use his method to generate more combinations and improve upon his method based on our results.