IndisputableMonolith.Ethnomusicology.ScaleCountFromConfigDim
The module defines five canonical scale types in ethnomusicology by deriving counts for pentatonic, diatonic, and chromatic scales from Recognition Science parameters. Researchers in music theory and RS applications would cite it to connect musical structures to the time quantum and configuration dimension. The module consists of definitions, equalities, and a validity certificate rather than extended proofs.
claimThe module defines the canonical scale count as five, with pentatonic scales numbering five, diatonic scales numbering seven, chromatic scales numbering twelve, and a certificate establishing their validity under the RS configuration dimension.
background
The module sits in the ethnomusicology domain and imports the fundamental RS time quantum τ₀ = 1 tick from Constants. It introduces definitions for scale counts derived from configuration dimension, including the canonical count, pentatonic count, diatonic count, chromatic count, and a ScaleCountCert for validation. The setting links musical scales to self-similar RS structures such as the phi-ladder and eight-tick octave.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies foundational scale-count definitions that support higher-level Recognition Science results connecting music to the T7 eight-tick octave and T8 spatial dimensions. It fills the ethnomusicology slot in the framework by grounding scale types in the time quantum and phi fixed point, with no downstream theorems listed yet.
scope and limits
- Does not derive scale counts without the RS configuration dimension.
- Does not treat non-canonical or microtonal scales.
- Does not include empirical checks against historical music traditions.