IndisputableMonolith.Music.CrossCulturalTonalUniversals
CrossCulturalTonalUniversals supplies the core definitions for tonal assignments across three acoustic axes and certifies universal categories such as seven-tone scales in empirical ranges. Music theorists and cognitive scientists modeling cross-cultural patterns would cite these objects when grounding observed tonal structures in a formal framework. The module contains only definitions and a certification record with no proofs.
claimA tonal assignment $T$ maps tones across three acoustic axes, with distinguished tonic tone, predicate IsNonTonic, cardinality tonal_space_card, and certified universal categories universal_tonal_categories together with the predicate seven_in_empirical_range.
background
The module sits in the music domain of Recognition Science and imports only Mathlib. It introduces TonalAssignment as the central object, the reference tonic, the predicate IsNonTonic, the cardinality function tonal_space_card, the set universal_tonal_categories, the range predicate seven_in_empirical_range, and the certification record TonalUniversalsCert with its witness tonalUniversalsCert. These objects formalize cross-cultural tonal patterns using the same structural style as the framework's forcing chain.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The definitions supply the objects required by TonalUniversalsCert and thereby feed any downstream theorem that invokes cross-cultural tonal universals. The module aligns with the eight-tick octave structure already present in the framework and provides the musical counterpart to the phi-ladder constructions used elsewhere.
scope and limits
- Does not contain any theorem or proof.
- Does not derive the listed objects from the J-functional equation.
- Does not assert empirical coverage beyond the named certification record.
- Does not model concrete musical works or performances.