Additive synthesis and resynthesis: building timbre from partials

This module builds toward one whole task: taking a real recorded tone — a plucked string, a struck key — apart with an FFT and putting it back together as a bank of enveloped sine oscillators you can actually perform with. In a live-coding rig this matters because additive patches are pure code: a SynthDef summing sines is trivially cheap to write mid-set, but naive versions clip the output bus and offer no single knob worth touching on stage. The craft here is making a hundred-parameter instrument feel like a one-parameter one.

The arc starts supported: build a small hand-tuned tone from a fundamental plus a few harmonics, leaning on the core idea that summing sine partials constructs timbre and on the harmonic-generator model of individually controllable harmonics. From the first exercise, the divide-by-N normalization move is drilled until automatic — every sum you write in the set needs it. The middle exercises confront why raw additive feels dead: the expressiveness problem, fragile transients, and noise-floor accumulation. Each pain gets a JIT counter-move: grouping harmonically related partials under shared envelopes, morphing between two complete parameter sets for a single performable control, and noise-modulating partials to reach breathy or drum-like timbres.

The required atoms gate the capstone directly — you cannot resynthesize a tone without the analysis-to-partial-tracks workflow, nor perform the result without grouping and morphing. Supporting atoms enrich rather than gate: Fourier duality and the harmonic series explain why the reconstruction works at all, cheap tricks like a sawtooth standing in for the highest partial or the odd/even harmonic warp offer resource-saving shortcuts beyond the capstone, and concatenative synthesis sketches where resynthesis goes next.

Runnable examples

Generated from the context/ instrument corpus by concept (redistributable idioms only). Do not edit — regenerate with gen-module-examples.mjs.

additive-synthesis

{ Klang.ar(`[[100, 200, 300, 400], [0.4, 0.3, 0.2, 0.1]]) * 0.1 }.play

_{supercollider-0022 · CC0}