MUSIC OF THE PRIMES

The eigenvalue formula has five terms — one per prime {2, 3, 5, 7, 11}.
Map each prime to a harmonic of A2 (110 Hz). The CRT residues become volume.

Walk the ring. Hear the axiom.

5
HARMONICS
2310
RING SIZE (THIN)
288
EIGENVALUE CLASSES
9.000
MAX EIGENVALUE (K²)

The Five-Harmonic Player

n = 0  →  (0, 0, 0, 0, 0)   λ = 9.000

Arrow keys: step. Space: play. W: walk/stop. 1-5: toggle channels.

Live Waveform

The waveform shows your current chord — five harmonics mixing in real time.

Eigenvalue Spectrum

288 eigenvalue classes of Z/2310Z. Height = eigenvalue. Click any bar to hear it.

The Harmonic Series

Base frequency: A2 = 110 Hz. The five axiom primes ARE the harmonic numbers:

2nd harmonic220 Hz (A3) 3rd harmonic330 Hz (E4) 5th harmonic550 Hz (C♯5) 7th harmonic770 Hz (septimal) 11th harmonic1210 Hz (undecimal)

Residue = 0 means the channel is silent. n = 0 (the void) = total silence.
n = 1 (sigma) = all channels whisper at minimum. Existence.
Walking the ring is conducting a five-voice overtone choir. Each step shifts the chord. The carousel turns.

Contrast Panel

THIS DEMOSTANDARD APPROACH
SourceEigenvalue formula, 5 CRT channels Arbitrary frequency mapping
HarmonicsExact: {2,3,5,7,11}th of A2 12-TET or arbitrary
VolumeCRT residue (mod p) Fixed or random
Structure2310 positions, 288 classes No ring, no classes
WalkCarousel: each step = new chord Sequential notes (melody)

verify in .ax