We verify that the harmonic domain — the system of pitched sounds under octave equivalence and finite auditory resolution — satisfies the three axioms of a constrained generative system (CGS): finite alphabet, irreversible consumption, and observable iteration with contextual classification. The verification proceeds by applying the six constraints of the pixel minimo to the harmonic domain and deriving, by elimination, the minimal operational unit (the musical pixel). A forced finiteness theorem establishes that the number of operationally distinct harmonic classes is bounded by ⌈1/L⌉ ≤ 240, independently of the algebraic structure of the generating group, where L is the just-noticeable difference for pitch. The consumption type is T3 (trajectory-consumptive): the transition graph is invariant; irreversibility operates through the accumulated trajectory, not through structural depletion. The dominant dynamic regime is R2 (branched attractor): persistent branching sustained by graph invariance and the cyclic boundary of octave equivalence. This is the first verified instance of both T3 and R2 in the CGS framework. The four structural properties — finite vocabulary, early saturation, interaction bottleneck, efficiency paradox — manifest in a form specific to T3/R2: stable vocabulary, oscillating diversity, invariant bottleneck at the voice-leading surface, and topological confinement (the Pythagorean comma) rather than premature termination. The twelve-tone technique is analysed as a natural experiment in which T1 (node-consumptive) constraints are imposed on a T3 system, producing the predicted consequences: bounded trajectory, monotonically decreasing maneuverability, and termination.
davide lugli (2026) studied this question.