IndisputableMonolith.Aesthetics.MusicalScale
The MusicalScale module supplies definitions for semitone counts and interval ratios that link musical harmony to the Recognition Science phi-ladder and eight-tick octave. Researchers examining aesthetic consequences of the forcing chain or harmonic structures would cite these constants when mapping T7 to concrete scales. The module contains only definitions, drawing the time quantum directly from Constants.
claimsemitonesPerOctave $:= 12$, semitoneRatio $:= 2^{1/12}$, perfectFifth, justFifth, majorThird, phi_fifth_power, twelve_from_phi, circle_of_fifths_closure, and pythagoreanComma.
background
The upstream Constants module supplies the fundamental RS time quantum τ₀ = 1 tick. This aesthetics module builds musical scale definitions on top of the phi-ladder and J-uniqueness from the forcing chain. It introduces semitonesPerOctave as the discrete division of the octave, consistent with the period 2^3 structure.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
These definitions support the T7 eight-tick octave landmark by providing concrete musical interpretations of phi-derived intervals. They enable calculations of just intervals and closure properties such as the circle of fifths within the Recognition framework.
scope and limits
- Does not derive the semitone count from the forcing chain.
- Does not prove numerical closure of the circle of fifths.
- Does not address non-Western or microtonal scales.
depends on (1)
declarations in this module (19)
-
def
semitonesPerOctave -
def
semitoneRatio -
def
perfectFifth -
def
justFifth -
def
perfectFourth -
def
majorThird -
def
justMajorThird -
def
octave -
def
phi_fifth_power -
theorem
twelve_from_phi -
theorem
circle_of_fifths_closure -
def
pythagoreanComma -
theorem
comma_small -
theorem
fifth_quality -
theorem
third_quality -
def
pentatonicSize -
def
diatonicSize -
theorem
pentatonic_diatonic_fib -
theorem
scale_fibonacci