jcost_minorThird
plain-language theorem explainer
The J-cost of the minor third interval with frequency ratio 6/5 equals exactly 1/60. Researchers ordering musical intervals by Recognition costs cite this value when constructing consonance hierarchies. The proof is a one-line wrapper that invokes the matching computation from the HarmonicModes module.
Claim. The Recognition cost of the interval with frequency ratio 6/5 satisfies J(6/5) = 1/60.
background
Recognition Science assigns costs to musical intervals via the J-cost function, which follows from the J-uniqueness property T5 in the forcing chain. The minor third is introduced as the real number 6/5 in both the HarmonicModes and Valence modules. The consonance module imports these definitions together with the base Cost module to build explicit cost values for standard intervals.
proof idea
The proof is a one-line wrapper that applies the J-cost computation for the minor third from the HarmonicModes module. That upstream result establishes the equality by simplifying the cost definition and applying ring normalization.
why it matters
This result feeds the two hierarchy theorems that place the minor third strictly between the unison and the major third in cost order. It supplies a concrete numerical anchor for the interval ranking used to model consonance, consistent with the eight-tick octave structure and the phi-ladder mass formula in the broader framework.
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