chromaticCount
ChromaticCount sets the constant 12 for the number of notes in the chromatic scale. Ethnomusicologists and Recognition Science researchers cite this value when checking the predicted five canonical scale types across cultures. The definition is a direct numerical assignment with no lemmas or computation.
claimThe chromatic scale contains twelve notes, so the chromatic count equals 12.
background
The module derives musical scale counts from configDim D = 5, matching the five-element classification pattern seen elsewhere in Recognition Science. Canonical scales are pentatonic (5 notes), diatonic (7 notes), hexatonic, octatonic, and chromatic. Note counts follow the phi-ladder: pentatonic as 3 + 2, diatonic as 5 + 2, and chromatic as approximately phi^5 / 2.
proof idea
Direct constant definition assigning the value 12.
why it matters in Recognition Science
This constant enters the ScaleCountCert structure and supports the chromatic_pos theorem that proves positivity. It realizes the Recognition Science prediction of five scale types forced by configDim D = 5 and aligns with the phi-ladder approximation for the chromatic octave. The module supplies an explicit falsifier based on cross-cultural surveys.
scope and limits
- Does not derive 12 from the phi-ladder equation inside this module.
- Does not prove the approximation 12 ≈ phi^5 / 2.
- Does not address cultural variations beyond the stated falsifier.
formal statement (Lean)
51def chromaticCount : ℕ := 12
proof body
Definition body.
52