majorThirdInterval
plain-language theorem explainer
The majorThirdInterval definition assembles the just major third as a MusicalInterval using the ratio 5/4 and its positivity proof. Researchers in harmonic analysis within Recognition Science cite it when constructing scales or evaluating J-costs for consonant intervals. It is assembled by direct application of the MusicalInterval constructor to the pre-established majorThird value and majorThird_pos theorem.
Claim. The major third interval is the structure with ratio $r = 5/4$ and proof that $0 < r$.
background
The MusicalInterval structure pairs a real ratio with a proof that the ratio is positive; its jcost method applies the J-cost function to that ratio. In the HarmonicModes module the majorThird constant is fixed at the just-intonation value 5/4, while majorThird_pos is the elementary positivity theorem proved by norm_num. Upstream definitions in Aesthetics.MusicalScale and Valence supply alternative major-third ratios (equal-tempered 2^(4/12) and the same 5/4), but the present declaration selects the just version for use inside harmonic-mode constructions.
proof idea
One-line wrapper that applies the MusicalInterval constructor to the majorThird ratio and the majorThird_pos theorem.
why it matters
This definition supplies the just major third for harmonic-mode constructions and subsequent J-cost calculations inside the Recognition framework. It feeds the MusicalScale and Valence modules but carries no direct dependence on the T0-T8 forcing chain or the phi-ladder. No open questions are attached; the declaration simply closes the interval-construction interface for music-theoretic applications.
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