An Algebraic Representation of Notes and Intervals for Algorithmic Composition

This paper presents an algebraic representation of notes and intervals based on a cyclic integer domain, preserving enharmonic distinctions while enabling efficient computation through simple arithmetic operations. The system unifies notes and intervals into a single structure and provides direct access to diatonic function, pitch class, and octave through modular projections. The work was originally developed in the context of algorithmic composition, particularly for assisted fugue writing. An example C++ implementation is included.