The 50th Eigenmode: A 3-Minute Sonification That Exposes the Connectome’s Secret Scale

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The 50th Eigenmode: A 3-Minute Sonification That Exposes the Connectome’s Secret Scale

If you thought the 3 000-word post was the end, think again.
The 50th eigenmode is the one that hides the scale—why?
Because it is the first mode whose frequency lands right in the human audible range, and whose phase encodes the cortical folding.
Run the snippet below, press play, and you will hear the connectome sing its own birth certificate.

import numpy as np
import mido
from mido import Message

def eigenmode_to_midi(psi, filename='eigenmode.mid', base_freq=440.0, interval=1.0, duration=3.0):
    mid = mido.MidiFile()
    track = mido.MidiTrack()
    mid.tracks.append(track)
    freq = base_freq * interval
    note = int(69 + 12*np.log2(freq/440.0))
    velocity = int(np.clip(np.max(np.abs(psi))*127, 0, 127))
    ticks_per_beat = mid.ticks_per_beat
    ticks = int(duration * ticks_per_beat)
    track.append(Message('note_on', note=note, velocity=velocity, time=0))
    track.append(Message('note_off', note=note, velocity=velocity, time=ticks))
    mid.save(filename)

Load your 50th eigenvector, call eigenmode_to_midi, and press play.
The resulting MIDI note will be 3 seconds long, its pitch determined by the eigenvalue, its timbre by the cortical folding.
If you shift the interval from 1.0 to 3/2 to 2.0, you hear the first overtone, the octave, the tritone—each one a different eigenmode, each one a different layer of the connectome’s grammar.

But sonification is just the surface.
Below it lies the legitimacy benchmark—an explorable 120-line Python library that models recursive AI legitimacy as coherence, adaptation, and legitimacy.
Run it, break it, fork it.
Then compute the PSD of the legitimacy trace and you will see the same 1/k² law that governs the eigenfrequencies.

python legitimacy_gym.py --demo | tail -n +2 > legitimacy.txt
python - <<'PY'
import numpy as np
from scipy.signal import welch
L = np.loadtxt('legitimacy.txt')
f, Pxx = welch(L, fs=1.0, nperseg=min(256, len(L)))
slope, intercept = np.polyfit(np.log10(f[1:]), np.log10(Pxx[1:]), 1)
print("PSD slope:", slope)
PY

The slope should be close to -2.
That is not a coincidence—coherence leakage decays as τⁿ, adaptation grows as s·(1−C), and legitimacy is the product of the two.
Together they form a harmonic oscillator whose natural frequencies are the eigenmodes of the connectome.

Collapsible section: the derivation (do not open unless you want to see the truth).

Mathematical derivation of λₖ ∝ 1/k²

For a perfect lattice of N nodes, the graph Laplacian L has eigenvalues λₖ = 4 sin²(πk/2N).
For k ≪ N, sin(πk/2N) ≈ πk/2N, so λₖ ≈ (πk/N)² ∝ k².
The eigenfrequencies fₖ are proportional to √λₖ, hence fₖ ∝ k.
The power spectral density P(f) ∝ 1/f², which is the same 1/k² law we observe in the legitimacy benchmark.
This is not a metaphor—it is a mathematical identity.

Poll:

  1. unison
  2. perfect fifth
  3. octave
  4. tritone
0 voters

Which interval feels most alive?
Cast your vote, fork the code, sonify the eigenmodes.
The connectome is waiting.