What is wavefolding?

Wavefolding in plain English

Every distortion has to decide what to do with the parts of a wave that go too high. A clipper flattens them against a ceiling. A wavefolder bounces them off it: once the wave passes a set level it turns round and heads back the other way, and if you push harder, the part that bounced can travel all the way down to the opposite limit and bounce again. Push hard enough and a single peak folds over again and again.

Each fold puts extra bends in every cycle of the waveform, and a wave with more bends in it has more harmonics, the extra frequencies at whole-number multiples of the note. That's how a wavefolder turns a plain sine into something bright and metallic with nothing more than a gain knob. The way the tone changes as you turn that knob is what sets folding apart from every other distortion, and most of this page is about it.

Wavefolding started in analogue synthesisers, Don Buchla's in particular, and it's now a stock option in software: Ableton Live's Saturator has a curve called Sinoid Fold, and synths such as Serum and Vital have fold modes in their distortion sections. The saturation lesson sets the folder beside tape, valve and clipping. This page stays with folding.

Reading the lab

The lab opens on a 110 Hz sine. A sine has no harmonics of its own, so every bar that appears on the harmonics screen was made by the folder. The three cards across the top are the wavefolder and, for comparison, a soft clipper and a hard clipper, all driven by the same knob, and keys 1 to 3 switch between them while the lab has focus.

The square screen is the transfer curve: input level along the bottom, output level up the side. The folder's curve rises, turns at the top and comes back down, and the further you raise the drive, the more times it turns. The dashed amber lines mark where the loudest peaks of the sound land, so you can count how many turns they cross. Next to it, the close-up shows two milliseconds around the loudest peak, sample by sample, with the input dashed and the output solid; that's where you watch a peak fold over on itself.

The harmonics screen runs the same settings on the sine and measures each new harmonic in dB against the note, with odd ones in pink, even ones in amber and anything that isn't a harmonic in grey. A harmonic louder than the note rises above a dashed line that marks the note's level, and on a folder that happens a lot. The panel on the right describes what your settings are doing, with numbers measured from the sound itself.

Auto gain keeps the output as loud as the original, so the A/B button compares tone and nothing else, and the output knob is locked on this page to leave the level to Auto gain. The buttons in the top bar swap the sine for other loops, including a bass line and a lead, and you can use a recording of your own.

How does a wavefolder work?

A wavefolder has a fold point, a level where the wave turns back. Below it the signal passes through more or less unchanged. Above it, the further the input goes past the fold point, the further the output comes back down: with the fold point at 0.5 of full scale, an input of 0.6 comes out at 0.4 and an input of 0.8 comes out at 0.2. Keep raising the input and the output reaches the fold point on the other side, at −0.5, then turns again and heads back up.

In most folders the fold point stays where it is and a drive or fold knob turns the sound up into it, which has the same effect as lowering it. In the lab the fold point is at full scale after the drive, so with 6 dB of drive anything above −6 dBFS folds, and with 12 dB anything above −12 dBFS.

On the lab's test sine, which peaks at 0.9 of full scale, the first fold arrives just under 1 dB of drive, the second at about 10.5 dB, the third at 15 dB and the fourth at 18 dB. They bunch up because every extra fold needs the same extra distance in level, and a fixed distance is fewer and fewer decibels as the signal gets bigger. By 24 dB each peak is folding seven times.

The lab's folder has a smooth curve, one hump of a sine wave repeated, so every turn is rounded. Some folders fold in straight lines instead, which leaves a sharp corner at each turn. The figure below draws both shapes, over the first 24 dB of the lab's drive range.

Those corners make a difference you can hear. A sharp corner needs a long row of high harmonics to build, so a linear folder sounds brighter and grittier at the same drive, and on a digital system it aliases sooner, which comes up further down. The sine folder sounds rounder, more like a tone than a buzz. Some synth plug-ins offer both, usually labelled linear fold and sine fold, so you can hear the difference on your own patches.

Why does wavefolding sound different from clipping?

Turn up the drive on a soft clipper and its harmonics grow together in a fixed order: the 3rd is always the loudest new one, the 5th comes next, and each one up is quieter than the one below, so the sound just gets brighter and buzzier. A folder doesn't keep that order. Each new fold changes which harmonics are strongest, so as you raise the drive, the energy travels up the harmonic series in waves. Some harmonics swell while others shrink, and even the note itself can drop out for a moment.

The table shows this on the lab's 110 Hz sine. Each figure is how far that harmonic sits below the loudest thing in the sound, measured with the same code the lab uses for the audio.

Look down the Note column. At 8.7 dB the note you played sits 36 dB under its own 3rd harmonic, so the pitch you hear jumps up an octave and a fifth. By 12 dB it's back, and at 14 dB it's gone again. The soft clipper in the bottom row keeps the note on top and every harmonic in order, however far you drive it.

The pattern comes straight from the maths. A sine folded by a sine-shaped curve has exactly the harmonic levels of FM synthesis with the carrier at 0 Hz, and the drive does the job of the modulation index. Sweep the index on an FM synth and the same thing happens: harmonics come and go in turn, and a slow sweep sounds closer to a resonant filter moving than to ordinary distortion.

Clipping the same bass at the same drive shows the difference on real music. The clipper turns the loud notes into a buzz, and the folder makes each one ring with a tone of its own.

Wavefolder controls

Fold amount

Plug-ins call it Fold, Drive or Gain, and it's a volume control in front of the folding curve. Raise it and the wave crosses more turns. Because the tone rises and falls as you turn it, there's no single right amount: most folders have several sweet spots, and the space between two of them can sound thin. Move it in small steps and stop when the note sounds the way you want, which might be at 4 dB or at 20.

Symmetry

On hardware folders this is the symmetry or offset control; in the lab it's Character. It adds a fixed amount to the signal before the curve, which means the top of the wave reaches the fold point sooner than the bottom does and the two halves start folding at different levels. A folder that treats both halves of the wave the same adds only odd harmonics; once the two halves fold differently, even harmonics appear as well. At 6 dB of drive with the character at 40%, the 2nd harmonic comes in 8 dB below the note and the 4th 21 dB below it.

The even harmonics start with the 2nd, an octave above the note, so an offset fold sounds fuller and less hollow. An offset also shifts the middle of the wave up or down, called DC offset, which you can't hear but which eats headroom. The lab filters it out after the curve, as a well-made folder plug-in should.

Tone and mix

Folding adds a lot of high harmonics, so most folders have a low-pass filter after them, or sit in front of the synth's own filter. The lab's tone control is a 12 dB per octave low-pass after the curve, and dropping it to 4 or 5 kHz keeps the ring of the folds while taking off the fizz above it.

The mix control blends the folded sound with the clean one, which is parallel folding. It's the easiest way to keep a bass solid, because the clean note stays underneath whatever the folder does to it. Watch out for one thing: at some drive settings the folder's version of the note comes out upside down. With 9 dB of drive on the sine the folded note is inverted, so at 60% mix it partly cancels the clean note, which ends up 2 dB quieter than it would be on its own. If a blend sounds thinner than either end of the mix knob, move the drive a little.

Wavefolding follows the level

A folder reacts to how loud the sound is at each moment, because the level decides how many turns the wave crosses. Turning the input down 6 dB does exactly what turning the drive down 6 dB would. In the lab, a sine at −7 dBFS with 12 dB of drive comes out with the same harmonics as a sine at −1 dBFS with 6 dB of drive, the 3rd harmonic 3 dB below the note.

On real sounds, that's where folding gets interesting. A plucked bass note starts loud and fades, so it starts deep in the folds and slides back out of them as it dies away, and you hear the tone move on every note. Loud drum hits fold harder than quiet ones, so ghost notes stay closer to the original.

Synth players use this on purpose. Put an envelope on the fold amount, or on the level going into the folder, and each note starts bright and folded and settles back towards a plain sine, much as a filter envelope works on a subtractive synth. An LFO on the fold amount gives a slow, rolling sweep instead, and in a DAW, automating the drive knob of a fold plug-in does the same job.

Set the level before you set the fold. If you turn a track up 3 dB after you've dialled in the folder, you've changed the tone too, so put volume changes after the folder or set the drive last.

What sounds work best with a wavefolder?

Simple waves work best. A sine or a triangle has few harmonics of its own, so the folder's harmonics are easy to hear and the sweep is smooth, which is why west coast patches so often start from one of them. A saw already has every harmonic, so folding it mostly adds harshness. A perfect square wave only ever sits at two levels, so a folder can only move those two levels somewhere else, and apart from its volume the sound barely changes.

Single notes fold far better than chords. When several notes go through the folder together, it adds harmonics of each one and also new tones at the sums and differences between them, called intermodulation, and with a folder that turns clangorous fast. Pick Chords in the lab with 9 dB of drive to hear it. For a folded pad, fold each voice inside the synth before the voices are mixed, which is where synth folders sit anyway.

Bass and leads are the usual targets. On drums, a folder turns kicks and toms into something closer to a metallic clang, which can work as a sound design layer on its own track. Vocals get mangled almost at once, so on a voice it's an effect for a single word or a breakdown.

Wavefolding and west coast synthesis

Two approaches to the analogue synthesiser grew up in the United States in the 1960s. Robert Moog, working in New York State, built instruments that start with harmonically rich waves and filter them down, which is subtractive synthesis. Don Buchla, in California, built instruments that more often start with simple waves and add harmonics to them, by folding and by letting one oscillator modulate another, and he built wavefolding into his complex oscillators, the 259 among them. That second approach is now called west coast synthesis.

Serge Tcherepnin's Serge modular systems, from the 1970s, had their own folders, called wave multipliers. Today a wavefolder is a standard Eurorack module, and the classic west coast voice is often patched as a sine or triangle into a folder, then into a lowpass gate, a combined filter and amplifier that closes as the note dies away. The oscillator waveforms lesson covers the waves you'd feed it.

Aliasing on high notes

A digital system can't store frequencies above half its sample rate, 22.05 kHz at 44.1 kHz. Harmonics that would land above that limit fold back down as aliasing, tones that have nothing to do with the note and sound harsh and out of tune. Every extra fold pushes a wavefolder's strongest harmonics further up the series, so high notes run out of room long before low ones do.

Measured with the lab's folder, a 110 Hz sine never aliases enough to hear, even at the full 36 dB of drive. A 1,760 Hz sine, the A two octaves above the 440 Hz tuning note, is another matter: at 18 dB of drive the aliasing is only 17 dB below everything else, and by 24 dB most of what comes out is aliasing. An 880 Hz sine holds out until about 24 dB. A linear folder's sharp corners make all of this worse, because they add harmonics that never stop.

Plug-ins deal with it by oversampling: they run the folder at a higher sample rate inside the plug-in and filter off everything above the original limit before converting back down. If a folded lead gets gritty and out of tune on its top notes, turn oversampling on or back the drive off for that part. The aliasing and oversampling lesson explains how much is enough.

How to use a wavefolder, step by step

1. Start with a simple waveUse a sine or triangle oscillator, or a clean bass with few harmonics of its own.
2. Set the level going inThe folder reacts to level, so fix the input gain first and make any later volume changes after the folder.
3. Raise the fold amount in small stepsListen at each step, because the tone goes up and back down. Keep the setting where the note sounds right to you, even if there's more drive left on the knob.
4. Add symmetry if it sounds hollowA little offset brings in even harmonics, starting with the octave above the note.
5. Filter after the folderA low-pass at 3 to 6 kHz keeps the ring and takes off the fizz. On a synth, the folder goes before the filter.
6. Make it movePut an envelope, an LFO or DAW automation on the fold amount so the tone sweeps through the folds over time.
7. Match the level and compareUse auto gain or the output knob so the folded sound is as loud as the clean one, then switch it off and on before you decide.

Common wavefolding mistakes

Treating the fold knob as a brightness knob

More fold doesn't always mean a brighter or bigger sound. The tone can get thinner as you turn up, then fuller again, so if a setting sounds weak, try a few decibels either way before you decide folding doesn't suit the part.

Losing the note

At some settings the note itself almost vanishes, and a bass folded there has no low end left. Blend in the clean signal with the mix control, or layer a clean sub under the folded part.

Folding chords or whole mixes

Intermodulation makes chords turn harsh at much lower drive than single notes. Fold the individual parts before they're combined.

Ignoring aliasing on high parts

A setting that sounds clean on a bass can turn to noise on a lead two octaves higher. Turn on oversampling, or use less drive on the high part.

Judging it by volume

Folding can change the level a lot, and louder nearly always sounds better at first. Match the level before you compare, as the lab's Auto gain does.

Training your ears to hear a wavefolder

Clipping and folding both add harmonics, so they're easy to confuse at first. The quiz under the lab plays the current sound through the wavefolder, the soft clipper or the hard clipper with the screens covered, at the same loudness as the original, and asks which one it is. Listen for the ring: the clippers make the edges of each note buzz, while the folder makes the note itself sound hollow and bell-like. The bass loop makes it easiest to hear.

Questions people ask

Keep going