Eight harmonics, sixteen knobs, one waveform. Every shape here comes from wave(t) = Σ ak · sin(2π(k·t + φk)) — a sine per harmonic, each with its own amplitude and phase, summed into a single periodic wave. This is the same Fourier-series trick that makes square, sawtooth, and triangle waves out of nothing but sines — turn a knob and the spectrum bars and the scope trace update live.
This is additive synthesis — building a complex periodic wave out of nothing but sine waves at integer multiples of a fundamental frequency (harmonics), each scaled by its own amplitude and shifted by its own phase. It's the same idea a pipe organ uses stacking ranks of pipes, and it's exactly how a Fourier series describes any repeating shape: a square wave is just the odd harmonics falling off as 1/k, a sawtooth is every harmonic falling off as 1/k with alternating phase, and a triangle is the odd harmonics falling off as 1/k² with alternating phase. Pick a preset and watch the spectrum bars show you that recipe directly.
It's the second instrument in the family Palette Synth started — both sculpt a continuous shape by summing periodic terms with tunable coefficients, just in a different domain: Palette Synth sums cosines across three color channels to make a gradient, this one sums sines across eight harmonic channels to make a waveform. Same generative principle — offset/amplitude/frequency/phase-style coefficients feeding a trig sum — reused rather than reinvented, per the family's own rule. The reuse runs both directions: the scope trace, card accents, and spectrum bars are all colored by Palette Synth's own cosine-gradient formula, driven by the harmonic mix's spectral centroid — bass-heavy settings and treble-heavy settings land in different parts of the same gradient.
Click Play and the shape you're looking at is also the sound you're hearing: the amp/phase coefficients feed a Web Audio PeriodicWave directly — amp·sin(2π(k·t+phase)) expands via the sine-of-a-sum identity into exactly the cosine/sine coefficient pairs createPeriodicWave expects — on a fixed-pitch oscillator, so every knob move retunes the tone live, not just the picture.
The rest of the roadmap is built too: the Lissajous / Harmonograph Plotter reuses this exact two-term harmonic sum for its X and Y axes, plotting them against each other instead of against time; the Audio-Reactive Reaction-Diffusion instrument and the Complex-Plane Fractal Mapper close out the family.