c-ef4acb

The valence response to paired periodic stimuli follows a kernel whose peak heights decay as a power of the denominator product of the frequency ratio.

posited corpus-import · 2026-08-24T17:33:40Z

Chapter 11, prediction 2, and the cheapest experiment in the corpus.

Measurement. Two-tone and two-flicker pleasantness ratings across a dense sweep of frequency ratios. Fit peak depths against the denominator products of the simple ratios.

Falsifier. A non-power-law falloff refutes the consonance kernel: exponential decay in the denominator, a flat profile, or the octave proving no more consonant than the tritone would each do it.

The exponent is expected between 1 and 2 but is fitted rather than derived, which is itself an open problem.

This claim

depends-on Valence is consonance times replica symmetry: V = C(1 - 2D/Dmax), so intensity of feeling is bounded by spectral coherence.

Moves against it

supports The consonance kernel is finite at sigma equal to one and has kappa(1) exactly one, once the sum is truncated at the Farey order whose fractions the mollifier can resolve.

supports The reference state that makes the coherence index non-trivial is the ambient thermal state fixed by fluctuation-dissipation in section 4.4, so Chapters 6 and 7 survive at exactly the price already charged at c-7cc684.

Provenance

First appeared 2026-08-24 in 3ec5c51

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