Tree
Click a segment to select it. Double-click to zoom into its branch, and double-click the centre to zoom out. Keys: ↑ parent, ↓ first child, ←→ siblings, Space play, Z zoom here, Esc zoom out.
Every voicing with a fixed bass and up to five more notes within 24 semitones: 55,455 shapes, arranged as a tree where each voicing grows from its parent by adding one note above the top. The bass sounds at 110 Hz (A2) and each note has 4 partials at amplitude 1/h.
Click a segment to select it. Double-click to zoom into its branch, and double-click the centre to zoom out. Keys: ↑ parent, ↓ first child, ←→ siblings, Space play, Z zoom here, Esc zoom out.
One change away from the selected voicing. Dashed chips are its tree parent and tree children; the rest are lattice-only links. The number is the change in roughness.
Share of voicings that fit inside some transposition of each scale.
Nearest to a liked voicing across all the measures above, skipping any that sit closer to one you disliked.
Roughness sums the Plomp–Levelt dissonance curve (Sethares' parameters) over every pair of partials. Pairs closer than about a critical band beat against each other. The band is wider in the low register, so the same interval is rougher lower down.
Periodicity is how nearly the summed wave repeats. For each lag τ between 2 and 40 ms it averages the wave's autocorrelation at τ, 2τ, … 6τ, then takes the best τ. Octaves and fifths score close to 1. Clusters score low because their near-repeat drifts after a few periods. The best τ gives the implied fundamental (1/τ).
Harmonic complexity is the highest harmonic of that implied fundamental that a note needs, and mistuning is the mean distance from each note to its nearest harmonic, in cents. Equal temperament keeps every chord slightly off the harmonic series.
Spacing slope is the trend of the gaps between adjacent notes from bottom to top. Negative means the gaps narrow going up. Fits in scale tests whether the voicing's pitch classes sit inside any transposition of that scale.
All measures use 4 partials per note. The timbre switch changes only what you hear.