Structuring Concept Space with the Musical Circle of Fifths by Utilizing Music Grammar Based Activations

TL;DR

The paper addresses how the brain can perform abstract cognitive operations without external symbols by proposing a neural code based on the circle of fifths, modeled as a ring attractor on a $\mathbb{Z}/12\mathbb{Z}$ manifold and extended to a $12\times12$ harmonic torus for multi-attribute reasoning. The authors implement a 1D ring attractor with Mexican-hat connectivity to achieve discrete path integration, then generalize to a 2D torus that supports compositional and multi-step reasoning across two cyclic axes. Key contributions include a concrete dynamical system for abstract rotation on the circle of fifths, demonstration of error-free path integration in simulation, and a proposed toroidal neural architecture enabling richer cognition with testable neuroimaging predictions. The work provides a principled link between music cognition and higher-order thought, suggesting a scalable, robust neural code grounded in musical structure that could inform future studies of cognition and its disorders.

Abstract

We propose a neural coding framework harmonic toroidal codes in which abstract cognitive operations are implemented through dynamical activity on manifolds derived from music theoretic structures.