Additive synthesis explained: building sound one harmonic at a time

Additive synthesis is the most honest form of sound design. Instead of carving a rich waveform down to shape, you build the sound from individual sine waves, one harmonic at a time, each with its own level and its own envelope. It is the direct application of Fourier's insight that any periodic waveform can be described as a sum of sines.

It is also the reason drawbar organs feel intuitive: each drawbar is a harmonic, and pulling one out adds it to the total.

The harmonic series is the map

Play a fundamental at 100 Hz. The harmonics sit at 200, 300, 400, 500 Hz and upward. Their relative levels determine the character of the sound:

• Only odd harmonics, falling steeply: hollow, clarinet-like.
• All harmonics, falling gently: bright and buzzing, close to a sawtooth.
• Strong fundamental with a few widely spaced upper partials: flute-like, pure.
• Partials that are not whole-number multiples: bells, metal, gongs.

That last category is where additive earns its keep. No filter can turn a saw wave into a convincingly inharmonic bell, because the harmonics you need simply are not in the source. Additive can, because you place each partial by hand.

Envelopes per partial: the part that actually matters

Static harmonic recipes sound like organs. Real instruments change their harmonic balance over the length of a note, almost always losing upper partials faster than lower ones. Give each partial its own decay time — fastest at the top, slowest at the bottom — and a lifeless additive patch turns into something that sounds struck.

If your instrument only lets you group partials, split them into three bands and give each band a different decay. Upper band fast, middle medium, fundamental long. That crude approximation gets you most of the realism.

Additive thinking on a subtractive synth

You probably do not own a dedicated additive instrument. You can still use the method:

Stack sines. Three oscillators tuned to the fundamental, the octave, and the twelfth, with independent volume envelopes, is a three-partial additive patch. It is enough for convincing electric-piano and bell tones.

Use resonance as a partial. A self-oscillating filter is a sine wave. Tune it to a non-harmonic interval above a sine oscillator and you have inharmonicity with two modules.

Layer, do not filter. When a patch is too dull, the reflex is to open the filter. Try adding a quiet, high, separate voice instead. It is more controllable and it does not drag the low end with it.

Where additive struggles

Two honest limitations. First, it is expensive: a convincing piano tone can require dozens of partials per note, times polyphony. This is why additive stayed rare until computers got cheap. Second, it is bad at noise. Breath, bow scrape, hammer thud and pick attack are broadband and aperiodic, and you cannot build them efficiently from sines. Nearly every serious additive instrument therefore pairs the harmonic engine with a noise or sample-based transient layer.

Knowing that limitation tells you when to reach for it: sustained, pitched, harmonically specific material. Bells, mallets, choirs, organs, glassy pads, evolving drones.

A ten-minute exercise

Take any synth with at least three oscillators. Set all three to sine. Tune them to the fundamental, the second harmonic (one octave up), and the fifth harmonic (two octaves and a major third up). Give the top one a 300 ms decay, the middle one 1 second, the fundamental 4 seconds. Play a single low note.

You have just built the skeleton of a tubular bell without touching a filter. Detune the fifth harmonic by 15 cents and it becomes a slightly cracked, more believable bell — because real bells are inharmonic, and now yours is too.

That is the whole discipline: decide which frequencies should exist, decide how long each one lives, and let the sum do the work.