Applications of Group Theory in a Microtonal Musical Framework
Composed in 2016 for string quartet (2 violins, 1 viola, 1 cello). In total, there are 4 bagatelles, each approximately 1 minute long.
"Abstract": There has been a great deal of research in the last few years concerning the relationship between group theory and music. However, these investigations have have been primarily with regards to harmonic theory and analysis and the author has not yet found any exploration into the use of groups to compose new music. In this paper, an mapping between Z24 and a 24 tone system of music will be stated, and a method for composing new music using permutations on Z24 will be discussed. Two permutations on Z24 were treated as 24 tone rows and used to create two 24 tone matrices similar to 12 tone matrices used in serialism. These matrices were used to compose a set of bagatelles for string quartet. Additionally, a method for using modulus arithmetic to generate the rhythmic content of a composition was developed. Further, a "homomorphism" between a 24 tone system of music and the more common 12 tone system is utilized.
Bagatelle #1 - Recorded April 2017 at the Baylor University by Joseph Duque (violin), Helena Bandy (violin),Tracie Walker (viola), and Emily Monk (cello)