Logical sets and supersets of musical modes can be generated and categorized within any equally-spaced tuning system or rhythmic beat cycle according to a certain set of simple generative procedures. These procedures are rigorously demonstrated using heptatonic and pentatonic mode sets in twelve-tone equal temperament as examples. These procedures are then extrapolated to rhythmic patterns in twelve- and sixteen-beat cycles, and a unified framework for conceptualizing and categorizing scalar and rhythmic modes of any size in any equally-spaced tuning system or beat cycle is proposed. Real-world musical applications of this framework are suggested.
The author has given permission for this work to be deposited in the Digital Archive of Colorado College.
Colorado College Honor Code upheld.
Includes bibliographical references.
The author has given permission for this work to be deposited in the Digital Archive of Colorado College.
Colorado College Honor Code upheld.
