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arXiv · 2605.22948

A Formal Graph-Theoretic Framework for Pitch Class Set Analysis

Aleksa Joksimović
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Abstract

We present a graph-theoretic reformulation of pitch-class set theory in which each set in $\mathbb{Z}_n$ is represented as a complete weighted graph whose edge weights are interval classes. We show that this construction is invariant under the dihedral group $D_n$, and that the full interval structure is encoded by a cyclic step composition, from which all interval data are recovered via an additivity principle. This framework yields a direct correspondence between T/I equivalence and graph isomorphism, and reinterprets Z-relation as non-isomorphic graphs with identical edge-weight multisets. We extend the model to weighted clique complexes, linking higher-order homometry to simplex-weight structure, and introduce a cent-weighted formulation enabling comparisons across different equal temperaments. Finally, we define a polynomial invariant derived from antipodal step pairings for algebraic analysis of pitch class space.

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Aleksa Joksimović. 2026-05-21. A Formal Graph-Theoretic Framework for Pitch Class Set Analysis. https://arxiv.org/abs/2605.22948

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