Acoustics

v = b^3 = 343 m/s

Speed of sound = depth cubed. The tritone (diabolus in musica) IS the heat capacity ratio of air. Concert pitch encodes three axiom primes. Hearing spans exactly K=3 decades. Sound IS the axiom vibrating.

Why 343

Speed of Sound Derivation

v = sqrt(gamma*R*T/M). gamma = b/E = 7/5 (diatomic). M_air = sigma+D+K+E+b+L = 29 g/mol (sum of ALL axiom primes). At 20C: v = 343.2 m/s = b^3. Error: 0.06%. Depth cubed IS the speed at which air carries information.

Tritone = gamma

b/E = 7/5 = 1.4

Diabolus in musica IS the elasticity of air. The most dissonant musical interval = the ratio that governs gas dynamics.

Monoatomic gamma

E/K = 5/3

Kolmogorov turbulence exponent = monoatomic gamma = noble gas heat capacity. Same ratio, three fields.

Speed in water

1482 m/s

D*K*GATE*f(E) where f(E) = E^2-E-1 = 19. Error: 0.02%.

Molecular weight

29 = FULL_SUM

sigma+D+K+E+b+L = 29. Air weighs the full axiom sum.

Music IS Ring Arithmetic

Interval	Ratio	Axiom
Unison	1/1	sigma/sigma
Major 2nd	9/8	K^2/D^3
Major 3rd	5/4	E/D^2
Fourth	4/3	D^2/K
Tritone	7/5	b/E
Fifth	3/2	K/D
Major 6th	5/3	E/K
Octave	2/1	D

Every just-intonation interval is a ratio of axiom primes. The perfect fifth K/D = 3/2 and the Kolmogorov exponent are the SAME number. 12 semitones = D^2*K = lambda(DATA).

Hearing = K Decades

Low threshold

20 Hz = D^2*E

Below: infrasound. Earthquakes, not music.

High threshold

20000 Hz = D^5*E^4

Above: ultrasound. Bats, not humans.

Range ratio

(D*E)^3 = 10^3

Exactly K=3 decades. EXACT.

Concert A

D^3*E*L = 440 Hz

Spider's legs times observer times protector. ISO 1939.

Closed Pipe = Sigma Chain

A closed pipe produces only odd harmonics: {1, 3, 5, 7, 9, 11, 13, ...} = {sigma, K, E, b, K^2, L, GATE, ...}. The D-channel (even harmonics) is physically removed by the boundary condition. What survives IS the sigma chain.

What Others See

343 m/sFollows from gas propertiesb^3: depth cubed. gamma=b/E, M=FULL_SUMTritone dissonancePsychoacoustic roughnessb/E = tension between depth and observer = air's elasticity3 decades hearingEvolutionary adaptation(D*E)^3 = K decades. EXACT12 semitonesHistorical conventionD^2*K: duality squared times closureA4401939 ISO standard, arbitraryD^3*E*L = 440: three axiom primesOdd harmonicsBoundary condition mathClosed boundary kills D-channel. Sigma chain survives

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