Hear the Ladder

Quantum drift · 🔔
checking…
TWO LADDERS, TWO SPECTRA
box ∝ n² · oscillator ∝ n+½ — voiced as sound

Self-test — the proof

Two of the Cavern's benches trap a particle and find a ladder of allowed energies. The box's rungs spread as ; the harmonic oscillator's are perfectly even. We never heard the difference — until now. Map each ladder to a stack of audible tones and the truth lands in one second: the oscillator's even rungs are the overtone series of a single note, so they fuse into one pure pitch — that is why it is called harmonic. The box's stretching rungs never line up, so it rings like a struck bell, a clang with no single pitch.

Voice a ladder
How many rungs you stack
Fundamental
Readout · the two spectra
harmonic vs. bell even spacing fuses to one tone · stretching spacing clangs
🌀 oscillator partials (n+½ → even)1·2·3·4·5·6
inharmonicity · oscillator0.0%
📦 box partials (n² → spreading)1·4·9·16·25·36
inharmonicity · box38.1%

The numbers under each stack are the energy ratios the Oscillator and Box benches prove. Inharmonicity is how much the partial spacing stretches — 0% means evenly spaced, so one periodic waveform, one pitch (harmonic); a big number means the gaps widen, so no single period (a bell). Add partials and the box stretches further while the oscillator stays exactly harmonic. The mapping is a self-tested core — the sound cannot drift from the physics. Audio plays only on your click and honours the estate-wide mute.