octave
plain-language theorem explainer
Octave is defined as eight times the fundamental tick to fix the basic evolution period in RS-native units. Researchers on the forcing chain or coherence calculations cite this to anchor the T7 step. The definition is a direct scaling of the tick constant with no further lemmas required.
Claim. Let $τ_0$ denote the fundamental RS time quantum. The octave period is $8 τ_0$.
background
The Constants module fixes RS-native units with the fundamental time quantum set to one tick. The supplied doc-comment states: 'The fundamental RS time quantum (RS-native). τ₀ = 1 tick.' This octave supplies the eight-tick cycle for the T7 landmark in the forcing chain. Upstream results include the MusicalScale octave as the ratio 2 and the CoherenceExponent octave as 2^D.
proof idea
This is a direct definition that multiplies the tick constant by eight. No lemmas or tactics are invoked beyond the constant tick.
why it matters
The definition anchors the eight-tick octave at T7 of the forcing chain, where the period equals 2^3 and aligns with D = 3. It feeds algebraic constructions such as OctaveAlgHom and layerSysPlus_comp in RecognitionCategory as well as OctaveLoop in applied coherence technology. The period supports downstream phi-ladder mass formulas and device specifications that derive all parameters from φ with zero free parameters.
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