Triad Dissonance 3D
Explore a triadic relief where pitch ratios become a surface of consonance, roughness, and harmonic tension.
Use the 3D terrain to compare dyads, triads, and tetrads: select a musical system, inspect roughness, harmonicity, beating, and tension, then play the selected structure.
Choose the structure to examine
- Load a music system and choose dyad, triad, or tetrad mode.
- Select a point or preset and read its roughness, harmonicity, beating, and tension values.
- Play the selected structure and compare the audible result with the terrain classification.
Tuning
Quantization
DSP
Visualization
Audio
Progressive harmonic surface
DSP transparency
Waveform scope
Spectrum scope
Roughness
Semantic color scale
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.
From pitch ratios to harmonic tension
Select the musical system
Choose the structure size before interpreting the terrain: a dyad, triad, and tetrad expose different interactions between partials.
Read roughness and beating
Hover to probe a pair and lock a point when you want to compare its measured profile with another voicing or preset.
Change one pitch and compare the surface
- Load a music system and choose dyad, triad, or tetrad mode.
- Select a point or preset and read its roughness, harmonicity, beating, and tension values.
- Play the selected structure and compare the audible result with the terrain classification.