Bouba-Kiki for Schwung

A six-voice stereo contour synthesizer for Ableton Move via Schwung. The published Bouba and Kiki silhouettes are the neutral bases; six geometric controls deform them. The outline on screen and the sound are the same object: the curve you see is the curve the oscillators read.

Version 0.4 adds an amplitude ADSR, six factory presets and six voices. A per-note modulation envelope with a routable destination was built and then removed: the two controls worth modulating carry their character in the operator ratio, and moving that under a held note is heard as a glissando rather than as timbre. Version 0.3 replaced the 0.2 waveform-family engine with direct contour scanning.

How the engine works

The shape is a closed 2D curve sampled at 256 points, so every point is an (x, y) pair rather than a single sample. Three things follow from that.

The curve is the operator waveform. Each voice runs two phase accumulators, and the second one's Y channel phase-modulates the first one's read position with a one-sample feedback term — two-operator feedback phase modulation whose operators are arbitrary geometry instead of sines.

The two operators do not read the same curve. The carrier scans the shape you see; the modulator scans its own contour, sharpened relative to it. A modulator's own harmonics multiply out into sidebands, so a spikier modulator is a brighter result, and this is what gives Morph and pressure real range — 171 to 972 Hz for Morph — while both stay at a 1:1 ratio and therefore stay in tune. The sharpening retreats, squared, as Pinch and Spikes open, because those two earn their character from an irrational ratio and flooding the spectrum with harmonic sidebands would dilute it; at their extremes the modulator is the carrier's own contour again, bit for bit.

One shape drives three FM parameters at once. The geometric controls set the operator waveforms, the operator frequency ratio and the modulation index together, so sharpening the shape changes what the operators play, moves them apart in frequency and drives them harder in a single gesture:

index = (.025 + .3*morph + .28*spikes + .22*pinch
         + .2*bulge + .2*pressure) * keytrack
ratio = 2 + 0.414*spikes + 1.732*pinch

The ratio is free-running and irrational, and only Spikes and Pinch reach it. Two operators at an irrational ratio produce partials that never line up into a harmonic series, which is the clangorous quality the instrument is for: at full Pinch the off-harmonic energy is 0.68.

It starts at 2 rather than 1, and that is the difference between metallic and out of tune. Sidebands land at f*(1 - n*ratio), so for a ratio between 1 and 2 the first of them falls below the fundamental and takes the perceived pitch with it — Pinch at 0.5 put the lowest strong partial 246 cents flat, and Spikes at 1.0 put it 1508 cents flat. From 2 upwards every sideband folds back above the fundamental. Measured across the full travel of both controls, the lowest strong partial now sits on the note to within a cent, and the note's own fundamental is the strongest partial throughout.

What matters is which controls are allowed to do that. Morph is the primary axis and pressure is a continuous gesture under a held note, so either one moving the tuning is heard as the note drifting rather than as timbre. Both are kept out of the ratio and drive brightness through the index instead: Morph sweeps the centroid 171 → 562 Hz with periodicity still at 0.990. Constraining the ratio was tried instead — snapping it to whole numbers, to halves, and crossfading neighbours — and every variant cost the character across all four controls to fix a problem that only ever affected two. tests/test_pitch.sh holds both halves of this: Morph, Bulge, Tilt, Wobble and pressure must stay periodic, and Pinch and Spikes must not.

The contour is a wavetable, so its narrow teeth are high harmonics of it and fold down at the top of the keyboard. It is smoothed by a width that follows the note, inert below 420 Hz, keeping only what lands under about 15 kHz — below the voice's own 13 kHz lowpass, so nothing audible is lost.

That leaves the top of the keyboard with far fewer harmonics to be bright with: about seven at C7 against a couple of hundred at C2. Nothing returns them, so the index is key-tracked upward instead, to fill the band that remains — relative brightness at C6 goes from 2.2x the fundamental to 5.3x and at C7 from 1.9x to 3.8x, with the bottom two octaves untouched and the energy below the fundamental lower than before. A downward key-track was tried first, on the assumption that the modulator's harmonics fold up there; they do not, and it only made the top smooth while the bottom stayed growly.

Each voice also carries its own ripple phase, so a held chord moves internally rather than breathing in lockstep.

X and Y are the stereo pair. The two channels are matrixed to left and right (.85x + .35y / .35x + .85y), so the outline is traced across the stereo field the way an oscilloscope in X/Y mode draws it. This is why Tilt, which shears Y into X, reads as a change in stereo width rather than brightness.

Everything else is conventional: 4x oversampling through a six-pole lowpass before decimation, a DC blocker per channel, linear ADSRs with quadratic time mapping, and a rational saturator before the output clamp. There is no detuned oscillator pair and no separate sub oscillator.

Prior art

Most of this engine is established technique, and it is worth being precise about which part is not.

The closed 2D curve as a waveform is the polygonal / geometric oscillator line of work: Chapman & Grierson's n-gon waves (ICMC 2014), Hohnerlein, Rest & Smith's continuous-order polygonal synthesis (ICMC 2016, DAFx-17), and Peschke & Berndt's Geometric Oscillator (Audio Mostly 2017), whose Cyclone prototype already made the edited shape be the timbre rather than a picture of it. Argentieri & Scagliola's Arbitrary Polygon Oscillator (arXiv:2608.24726, DAFx 2026) generalizes this to morphing between arbitrary shapes and delivers x and y as native stereo channels — the curve-as-waveform and the X/Y stereo pair used here, arrived at independently. Further off: scanned synthesis (Verplank, Mathews & Shaw, ICMC 2000) scans an evolving mass-spring system as a 1-D mono wavetable, and wave terrain synthesis (Mitsuhashi, JAES 1982) orbits a 2-D height field.

E-RM's Polygogo (2019) is the closest thing shipped, and the fair comparison. Its stereo output is taken directly from the polygon's X and Y, its Order control sets the ratio of the overtones, and it carries an FM operator with its own ratio and index. Every ingredient here is on that front panel.

Two-operator feedback phase modulation with non-sinusoidal or wavetable operators is likewise ordinary — Yamaha's RCM in the SY77 (1989) onward, and any modern wavetable synth that can point FM at its own table.

What appears not to have been done before is the coupling. Polygogo has a shape control, an FM ratio and an FM index, but they are three independent panel knobs. Here they are one function: the geometry simultaneously defines the operator waveforms, the modulator's frequency ratio and the modulation index, so a single shape gesture moves timbre, harmonicity and brightness together and cannot decouple them. That is a mapping, not a new DSP primitive, and it is the only claim worth making.

The bouba/kiki framing rests on real work — Köhler (1929), Ramachandran & Hubbard (2001), Adeli, Rouat & Molotchnikoff (2014) on timbre/shape correspondence, and Ćwiek et al. (2022), which identifies spectral balance and rise time as the governing acoustic parameters. Zacharakis, Velenis & Cambouropoulos (CMMR 2025) already used a single slider morphing a contour from smooth through rough to spiky as a timbre-matching stimulus. No synthesizer appears to have been built on that axis; this one is not the first to notice it.

Yonatan Rozin's "The Contour Synthesizer" (2021) independently uses captured object contours as waveforms, and shares this instrument's name.

Controls

Ten controls across three pages.

Shape — the live outline, and the six geometric controls as ordinary knobs alongside Attack and Release: Morph, Bulge, Pinch, Spikes, Tilt, Wobble.

Morph interpolates the base contours. Bulge inflates lobes; Pinch squeezes deep waists; Spikes grows narrow teeth; Tilt shears the contour; Wobble sends ripples around it. The reference silhouettes are exact with the other controls neutral (zero, except Tilt at 0.5), which is also the shipped default.

Pinch and Spikes are the two that reach the operator ratio, so they are the two that make the sound inharmonic — and the two that stay put while a note sounds. Morph, Bulge, Tilt and Wobble hold the pitch exactly.

Envelope — one ADSR for level, drawn as a graph. Attack and Release also sit on the shape page for quick reach; Decay and Sustain live here.

Factory Presets — six sounds: Pure Bouba, Kiki Knock, Slow Prickle, Rubber Mouth, Glass Creature, Held Breath. Selecting one replaces all ten values.

Velocity drives the modulation index as well as the level, so playing harder brightens rather than only getting louder, and it sets the outline pulse. Polyphonic pad pressure adds bite and swells the level without changing the saved Morph value. The outline follows the newest active note, drawing the deformation the DSP actually applied.

The outline is band-limited by the played note exactly as the DSP band-limits the wavetable, so the teeth you see at the top of the keyboard are the teeth you hear — Spikes at full draws sharp at C3 and visibly rounded at C6. The note's frequency rides the telemetry line for that.

The modulator's own contour is deliberately not drawn. Two curves exist in the DSP and it is tempting to show both, but every curve here is normalised to fill the frame, so the modulator's extra spikes come back the same size as the carrier's whole body and the two cross everywhere: a relationship in the numbers, a scribble on screen.

There is deliberately no scanning playhead. The carrier crosses the contour about 130 times a second at C3 against a display refreshing at a few tens of frames, so a marker at its true position would be an aliasing artifact rather than a playhead — the one thing on this instrument that cannot be drawn honestly.

Build and test

for t in tests/*.sh; do bash "$t"; done
./scripts/build.sh

The default build uses Docker to cross-compile dist/bouba-kiki/dsp.so for Move's ARM64 CPU and creates dist/bouba-kiki-module.tar.gz. Use NATIVE=1 ./scripts/build.sh for a host smoke build.

Regenerate the source-derived visual and DSP contour tables with node tools/compile_contours.mjs, and the manifest and its matching DSP contract with node tools/compile_contract.mjs; generated files are committed so a release build does not require Node. tests/test_generated.sh checks them. node tools/preview_shapes.mjs renders previews. For audio comparisons, install numpy and run python3 tools/render_sound.py build-host/bouba-kiki-host.so sounds-out --check. The optional spectral checks require numpy and cover the six geometric controls, both envelopes, every modulation destination, and the presets. The visual gallery in shapes-out/sweeps.svg shows five positions per knob at both Morph endpoints. These checks supplement, rather than replace, listening.

Install

After building, run ./scripts/install.sh. Set DEVICE to override the default ableton@move.local target. Reload the chain after DSP changes; restart shadow_ui after canvas changes because page drawers are cached.

Software: MIT. Reference and derived contour artwork/data: CC BY-SA 3.0, attributed in NOTICE. The 0.1 design in docs/plans/ is historical; 0.2 replaced the additive runtime with contour-derived wavetable playback; 0.3 replaced those fixed families with direct contour scanning.