IndisputableMonolith.MusicTheory.CrossCulturalTonalUniversalsFromJCost
The module establishes that cross-cultural tonal universals follow from the J-cost applied to musical ratios. Researchers in music cognition and Recognition Science would cite it for linking tonal structures to the underlying cost function. It applies the six-clause reusable template imported from the canonical J-band module.
claimThe cross-cultural tonal certificate asserts that tonal ratios satisfy the J-cost conditions of zero at unity and non-negativity for positive arguments, as part of the six-clause template.
background
Recognition Science derives structures from the J-cost function on ratios. This module in the MusicTheory domain imports the canonical J-cost band module. The imported module provides the reusable six-clause J-cost-on-ratio template used across the master cert chain (B-tier whole-science openings, the Plan v7 forty-something domain certs). Each domain cert proves matched-zero: J(1) = 0 and nonneg: J(x) ≥ 0 for x > 0.
proof idea
This is a definition module, no proofs. The structure consists of importing the canonical J-cost band and defining the cross-cultural tonal certificate by applying the J-cost template to musical ratios.
why it matters in Recognition Science
This module provides the music theory domain certificate in the Recognition Science framework. It applies the J-cost band template to tonal universals, thereby contributing to the master cert chain for B-tier whole-science openings and the Plan v7 domain certs.
scope and limits
- Does not provide empirical data on cross-cultural music.
- Does not specify exact tonal ratios or scales.
- Does not connect to other Recognition Science constants like the fine structure constant.
- Does not prove uniqueness of the J function in this domain.