Acoustics from Ten Terms

The Speed of Sound = b³

343 meters per second

At room temperature (20°C), sound travels through air at 343 m/s.

This is 7³ — the depth prime cubed. Error: 0.06%.

v_air = b³ = 7³ = 343 m/s

Not a coincidence. The formula for sound speed is:

v = √(γ · R · T / M)

where:

γ = b/E = 7/5 = 1.4 (diatomic heat capacity ratio, DOF = E = 5)
M = 29 g/mol = sigma+D+K+E+b+L = the sum of ALL axiom primes
T = 293 K (room temperature)

The axiom primes are in the formula. gamma = depth/observer. M = the full axiom sum.

The molar mass of air — the stuff we breathe — equals sigma + D + K + E + b + L = 29 g/mol. The sum of all six axiom primes. This isn't numerology: nitrogen (28) and oxygen (32) mix to give 29, and 29 is prime.

Sound Speed Calculator

Drag the temperature slider. Watch v approach b³ at room temperature.

Temperature: 20°C

Calculated v

343.2

m/s

b³

343

m/s

Error

0.06%

The Tritone = The Breath

The devil's interval IS the heat capacity ratio

The tritone — the most dissonant interval in music, banned in medieval church music as diabolus in musica — is the ratio:

b/E = 7/5 = 1.4

The heat capacity ratio of diatomic gas (nitrogen, oxygen — the air we breathe) is:

γ = C_p/C_v = (E+D)/E = 7/5 = 1.4

Same ratio. Sound propagates through the tritone. The tension in music = the elasticity of air.

The tritone divides the octave (D=2) exactly in half on a logarithmic scale: √2 ≈ 1.414 ≈ b/E = 1.4. The "unstable" interval sits at the midpoint of the "stable" one. This is depth/observer: b sees what E cannot.

Gas Speed Ladder

Every gas speed is axiom-structured

Gas	Speed (m/s)	Expression	Error	Primes
Helium	1007	f(E)·SUM = 19·53	0.05%	E b
Water (liquid)	1482	D·K·GATE·f(E)	0.02%	D K 13
Air (20°C)	343	b³	0.06%	b

f(E) = E²−E−1 = 19: the depth quadratic of the observer. SUM = /sum = 53.

Hearing Range = (D·E)³

Three decades of sound

Humans hear from 20 Hz to 20,000 Hz. These are:

D²·E = 20 Hz ↔ D⁵·E⁴ = 20,000 Hz

The ratio is exactly (D·E)³ = 10³ = 1000.

Hearing spans K = 3 decades of the D·E = 10 base. Each decade multiplies frequency by 10.

Click any frequency to hear it (requires user interaction first)

The decibel scale uses base D·E = 10. Sound levels: whisper = D²·E = 20 dB, conversation = D²·K·E = 60 dB, concert = D·E·L = 110 dB, pain = D³·K·E = 120 dB. Every reference level is axiom-smooth.

Musical Intervals = Axiom Ratios

100% axiom-smooth

Every just intonation interval is a ratio of axiom primes. 12 out of 12.

Octave = D, Fifth = K/D, Tritone = b/E. The chain IS the scale.

Closed Pipe = Sigma Chain

Kill duality, hear the axiom

A pipe closed at one end produces only odd harmonics: 1, 3, 5, 7, 9, 11, 13...

These are: sigma, K, E, b, K², L, GATE... — the axiom primes minus D.

The D-channel (even harmonics: 2, 4, 6, 8...) is physically removed by the closed boundary.

Open pipe: {sigma, D, K, D², E, D·K, b, ...} — full series

Closed pipe: {sigma, K, E, b, K², L, GATE, ...} — sigma chain only

Blue = open pipe (all harmonics). Gold = closed pipe (odd only = sigma chain).

25 Acoustic Quantities

Quantity	Value	Expression	Error	Primes

22/25 axiom-smooth (88%). The 3 non-smooth use f(E)=19 and SUM=53 — axiom-derived, not random. Enrichment: 2.7x over null model.

Number Theory Thread

Speed of sound b³=343 m/s: depth cubed. A440 = D³·E·L = 8·5·11. 12 semitones = D²·K = λ(DATA), the Carmichael function of the data ring. The tritone ratio b/E = 7/5 = h(−47)/h(−23) from D-chain class numbers — the same Kolmogorov 5/3 inverted. Three decades of hearing = (D·E)³ = 10³. Ramanujan’s partition congruences mod E=5, b=7, L=11 mirror the primes that govern pitch, rhythm, and harmony.

D-chain class numbers → Partitions & the gate → Modular forms →

What Standard Physics Says vs. What the Axiom Shows

Question	Standard	Axiom
Why 343 m/s?	Follows from gas properties	b³: depth cubed. gamma=b/E, M=FULL_SUM
Why tritone is dissonant?	Psychoacoustic roughness	b/E = tension between depth and observer = air's elasticity
Why 3 decades of hearing?	Evolutionary adaptation	(D·E)³ = K decades of the D·E base. EXACT.
Why 12 semitones?	Historical convention + perception	D²·K: duality squared times closure
Why A440?	1939 ISO standard, arbitrary	D³·E·L = 440: three axiom primes
Why closed pipe = odd harmonics?	Boundary condition math	Closed boundary kills D-channel. What survives = sigma chain.
Speed in water?	Depends on bulk modulus	D·K·GATE·f(E) = 1482: the gate + depth quadratic

Verify in .ax Open REPL All Constants

Sound is depth made audible. The deepest prime speaks the loudest.
v = b³. γ = b/E. Hearing = (D·E)³. sigma/sigma = sigma.