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.
