Animations

Triad Dissonance 3D

Explore a triadic relief where pitch ratios become a surface of consonance, roughness, and harmonic tension.

Quick guide

Explore music differently

Change the settings, watch the visualisation, and hear how each adjustment transforms the result.

  • Visualisation
  • Interaction
  • Sound
  • Patterns
  • Discovery
Psychoacoustic harmonic laboratory

Triad Dissonance Terrain

Stream a 3D roughness landscape, inspect the strongest partial clashes, and hear how quantization reshapes harmonic topology.

Preparing deterministic startup…
Preparing deterministic startup…
Tuning
Dyads map one free ratio, triads fill the full terrain, and tetrads keep a fourth note fixed as a slice.
Hz
Active reservoir: 0 · Music system details will appear here once the loader resolves a valid state.
Quantization
Smaller steps reveal finer saddles and valleys but require heavier computation.
DSP
Visualization
Audio

Progressive harmonic surface

The mesh streams in chunks so the camera remains responsive while the worker computes partial interactions.
Drag to orbit, wheel to zoom, hover to inspect local structure, and click to lock and audition a quantized triad.

DSP transparency

Every hover and lock exposes the snapped sonority, dominant beating pair, and composite consonance reading.
Locked point
Hover probe

Waveform scope

Spectrum scope

Roughness

Semantic color scale

Consonant Unstable Rough

Axis guide

This instrument keeps height mapped to dissonance while color can switch between derived metrics.

X = ratio r1
Y = dissonance / roughness height
Z = ratio r2

Why this terrain behaves this way

The page is designed as a teaching instrument, not only a decorative graph.
What is roughness?

Roughness estimates how strongly nearby partials interfere inside the auditory critical band. Valleys usually indicate smoother spectra, while ridges mark stronger sensory dissonance.

What is beating?

When two close frequencies interfere, the ear hears an amplitude pulse. Slow beating can feel animated or tense; faster beating can merge into grainy roughness.

Why do consonance valleys appear?

Simple ratios align many partials or keep them far enough apart to reduce interference. The surface therefore develops troughs near stable harmonic relations.

Why does quantization change topology?

Snapping the continuous grid to a finite tuning reservoir bends the terrain toward the available intervals. The same pointer position can land on very different harmonic neighborhoods in different systems.

Helmholtz and Sethares

This lab follows the broad intuition of Helmholtz-style beating and later roughness-driven tuning work often associated with Sethares: consonance is not a fixed label, but depends on spectral structure and tuning context.

What do contours show?

Contour lines slice the surface at equal roughness heights. They help reveal hidden passes, ridges, and local basins that are harder to read from shading alone.

Exploration ideas

How to use this experience

Watch and listen

The visible shapes express musical behaviour. Connect what you see with what you hear instead of looking for a single correct answer.

Explore effectively

  • Begin with the suggested settings.
  • Change one setting at a time and observe its effect.
  • Compare several configurations and remember the useful contrasts.

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