octave
plain-language theorem explainer
The declaration supplies the octave frequency ratio of 2 within the strict positive-ratio music model. Workers on musical scales, coherence devices, and recognition categories cite it when composing octave homomorphisms or loops. The definition is a direct subtype construction with an automated positivity check.
Claim. The octave frequency ratio is the positive real number $2$.
background
The Strict/Music module realizes music over positive frequency ratios, with FrequencyRatio the subtype of positive reals. Equality serves as the comparison cost in this strict version. Upstream definitions establish the octave as the ratio 2 in MusicalScale and as 8 ticks in Constants, tying into the eight-tick evolution period.
proof idea
One-line definition that packages the real number 2 into the FrequencyRatio subtype, with the membership proof handled by norm_num.
why it matters
This octave definition feeds into parent structures including layerSysPlus_comp and OctaveAlgHom in RecognitionCategory, as well as OctaveLoop in CoherenceTechnology. It realizes the T7 eight-tick octave landmark from the forcing chain and supports phi-based constants in the mass ladder. The definition closes the musical interface for the universal forcing.
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