Additive Synth Playground

Additive synthesis builds a sound by adding sine waves together. Each sine is a partial: it has a frequency, usually a whole-number multiple of the note (the harmonics), and a level. Fourier showed that any repeating waveform can be written this way, so a saw is every harmonic at 1/k, a square only the odd ones, and a triangle the odd ones at 1/k².

The circles-on-circles picture is the same idea drawn as motion. Every partial is a circle that turns at its own speed while riding on the previous one. The height of the last point is the sum of all the sines, which is why its trace is exactly the waveform. Make one circle larger and you hear that harmonic get louder.

Real instruments are rarely perfectly harmonic. Piano strings are stiff, so their upper partials run slightly sharp; bells and bars have partials at ratios like 2.76 and 5.4. Moving the ratios away from whole numbers is what makes a tone sound metallic. And in most acoustic sounds the high partials die away first, which is what the Pluck switch imitates.

PADsynth, by Nasca Octavian Paul, takes additive synthesis one step further: instead of one exact frequency per partial, it spreads each partial into a narrow band of frequencies with random phases and computes the whole sound with one inverse FFT. The result is a long loop with no audible seam that sounds like an ensemble, ideal for pads and choirs.