What you are learning
Explore a triadic relief where pitch ratios become a surface of consonance, roughness, and harmonic tension.
Animations
Triad Dissonance 3D
Explore a triadic relief where pitch ratios become a surface of consonance, roughness, and harmonic tension.
Triad Dissonance 3D projects a triad space onto a surface where two axes carry frequency ratios and the surface height expresses perceived roughness.
The page lets you switch music systems, constrain the note pool to a scale, adjust base frequency, grid density, and partial count, then recompute an entire harmonic landscape.
The goal is not only to show an attractive form, but to connect intonation, quantization, sensory roughness, local consonance, and listening to selected triads inside one exploratory instrument.
This experience works as a lab for comparing stable, unstable, or ambiguous zones across chords, scales, and tuning worlds.
Guided start
Start with a clear learning action
Try first
Read the summary to locate the musical goal.
Next step
Related pages continue the same musical thread.
Chords and scalesTriad Dissonance 3D
Explore a triadic relief where pitch ratios become a surface of consonance, roughness, and harmonic tension.
How to use this page
- Read the summary to locate the musical goal.
- Try the suggested setting or example before changing the context.
- Use related links to continue toward theory, listening, or analysis.
Example
Example: start from a simple musical idea, hear it, compare its function, then open a related page for deeper work.
The page first names the useful musical action.
Controls help verify a precise sound idea.
Related pages continue the same musical thread.
Tuning
Dyads map one free ratio, triads fill the full terrain, and tetrads keep a fourth note fixed as a slice.
In tetrad mode, this fixed ratio becomes the added color note for the whole surface 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
DSP transparency
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.
Why this terrain behaves this way
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.