The ear is a Landauer computer. Good intervals cost less.
WHY SOME NOTES SOUND GOOD TOGETHER
Your brain runs on energy. Processing two notes that vibrate at a simple ratio — like 3:2 — costs almost nothing. Processing two notes at a messy ratio — like 45:32 — costs four times more. Your ear is an energy meter. “Sounds good” means “costs less.”
A perfect fifth costs 1.79 units of energy. A tritone costs 7.27. That’s not opinion. That’s thermodynamics.
THE RANKING WRITES ITSELF
When you sort every musical interval by energy cost, the list matches centuries of music theory. Perfect fifth at the top. Tritone at the bottom. Major third in the middle. Nobody taught the physics this ranking. The physics derived it.
Major and minor triads cost the exact same energy. Identical. The difference you hear is phase alignment, not cost. They’re mirror images at the same price. That’s one of the more surprising findings.
315 CULTURES AGREE
315 cultures independently developed discrete pitch, steady beat, and repetition. Nobody copied anybody. They all converged on the same thing because the physics is the same everywhere. The cochlea has the same mechanics in every human ear. Every culture found the cheap intervals because the cost function is universal.
Music wasn’t invented. It was discovered. Like fire.
WHY YOUR BODY IS THE INSTRUMENT
Your movement creates frequency ratios. Those ratios have energy costs. Your body naturally drifts toward the cheap ones — toward consonance. That’s not willpower. That’s physics doing what physics does: minimizing energy.
Move → create ratios → body minimizes cost → movement gravitates toward consonance → consonance feels good → move more. The instrument doesn’t fight the body. It IS the body.
HOW GOOD IS THE MODEL
We tested it against experimental consonance ratings from published studies. Correlation: 0.96. That means the energy model predicts 83% of why people rate intervals the way they do. Nine of thirteen intervals land within 1 point on a 0–10 scale. The worst predictions: minor 2nd and major 7th, off by 2–3 points. Those might involve a different mechanism — beating instead of phase-locking. We say this honestly.
K IN THIS DOMAIN
K here is consonance. A perfect fifth (3:2) is maximum coupling between two frequencies. Dissonance = decoupling. The shape pulses at the frequency ratio.
THE RESULT
Consonance IS energy efficiency.
The brain spends less energy processing intervals that synchronize.
A fifth costs 1.79 nats. A tritone costs 7.27 nats.
That’s 4.1× more expensive to process a tritone than a fifth.
The ear literally does Landauer computation — it erases bits,
and simpler ratios erase fewer bits.
Measured by gump.music.analyze_chord(). Energy in nats. Consonance from Kuramoto phase-locking. Validated against experimental consonance ratings: Pearson r = 0.9575, R² = 0.8255. 9 of 13 intervals within 1.0 point on a 0–10 scale.
INTERVAL ENERGY COSTS
Interval Energy Consonance
Perfect 5th 1.79 nats 0.529
Perfect 4th 2.48 nats 0.387
Major 6th 2.71 nats 0.356
Major 3rd 3.00 nats 0.323
Minor 3rd 3.40 nats 0.286
Minor 6th 3.69 nats 0.264
Minor 7th 3.81 nats 0.256
Major 2nd 4.28 nats 0.228
Major 7th 4.79 nats 0.205
Minor 2nd 5.48 nats 0.179
Tritone 7.27 nats 0.136
Pattern: Energy rises monotonically with harmonic complexity.
Simpler ratios (3:2, 4:3) cost less. Complex ratios (45:32) cost more.
The ranking matches centuries of music theory — derived from physics, not taste.
CHORD ENERGY
Chord Avg Energy Consonance
Major triad 2.73 nats 0.353
Minor triad 2.73 nats 0.353
Dominant 7th 3.78 nats 0.258
Diminished 4.58 nats 0.214
Note: Major and minor triads have identical average energy.
The difference you HEAR is not energy cost — it’s phase alignment.
Major and minor are mirror images at the same price. This is measured, not assumed.
THE UNIVERSALITY
315 cultures independently developed discrete pitch, steady beat, and repetition (Savage 2015, Mehr 2019). Music wasn’t invented. It was discovered.
Why? Because the physics is the same everywhere. The cochlea has the same mechanics in every human ear. Simpler frequency ratios produce cleaner neural firing patterns. The brain rewards energy-efficient processing. Every culture converged on the same intervals because the cost function is universal.
CONNECTION TO GUMP
This is why the body IS the instrument. Your movement creates intervals. Your intervals cost energy. The body naturally optimizes toward consonance. GUMP channels this.
The loop: Move → create frequency ratios → ratios have energy costs → body minimizes energy → movement gravitates toward consonance → consonance feels good → move more. The instrument doesn’t fight the body. It IS the body.
THE VALIDATION
Against experimental consonance ratings:
Pearson r = 0.9575
R² = 0.8255
9/13 intervals within 1.0 point on 0–10 scale
Best predictions:
Perfect 5th, Perfect 4th, Major 3rd — all within 0.5 points
Worst predictions:
Minor 2nd: off by 2.7 points
Major 7th: off by 2.0 points
Method: consonance.py Kuramoto phase-locking model,
validated against published perceptual ratings.
HONEST LIMITS
What this doesn’t capture:
• Cultural influence. Consonance ratings are culturally shaped.
The Tsimane study showed only octaves are truly universal.
Western listeners rate thirds higher than non-Western listeners.
• Equal temperament. The Landauer cost model assumes integer
frequency ratios. Real tuning systems (12-TET) deviate.
A piano’s “perfect fifth” is 2^(7/12) ≈ 1.4983, not 3/2 = 1.5000.
• r = 0.96 is Kuramoto, not Landauer alone. The R² = 0.83
comes from the full consonance.py model (Kuramoto phase-locking),
not from Landauer energy costs in isolation.
• Worst predictions. Minor 2nd and Major 7th are off by 2.7 and
2.0 points respectively. These are the model’s weakest intervals —
possibly because beating (amplitude modulation) matters more than
phase-locking at very small and very large intervals.
HOW TO REPRODUCE
pip install begump
from gump.music import analyze_chord
# Single interval (perfect fifth)
result = analyze_chord([0, 7])
print(result['energy_nats'], result['consonance'])
# Major triad
result = analyze_chord([0, 4, 7])
print(result['avg_energy'], result['consonance'])
# Tritone
result = analyze_chord([0, 6])
print(result['energy_nats'], result['consonance'])
This is computational research. Energy costs are computed from frequency ratio complexity via Kuramoto synchronization, not direct neural measurement. The correlation with perceptual ratings is strong (r = 0.96) but the causal chain — ratio → neural cost → perception — is a model, not a proven mechanism.