Subtractive vs FM vs wavetable synthesis

At a glance

Reading the lab

The lab has one synth with three engines. Press Play riff and it loops a two-bar riff in A minor at 120 BPM; the cards under the header switch engine, or press 1, 2 and 3. Each engine keeps its own settings, so when you switch you're comparing two patches, and the lab trims each one to the same average level so the louder engine can't win by being louder.

The big screen is a spectrogram of one A at 220 Hz played through the current engine. Time runs left to right and frequency runs up from 0 to 8 kHz in even steps, so the harmonics of the note sit as evenly spaced lines 220 Hz apart. The white line is brightness, measured as the spectral centroid, which is the balance point of all the energy in the note. When it falls, the note is getting darker.

Underneath, the scope shows two cycles of the waveform and the partials screen shows every frequency in the note. Pink bars sit on a harmonic of 220 Hz; amber ones fall between harmonics, and only FM makes those here. Hover over the big screen and both small screens jump to that moment in the note. The panel on the right explains what your settings are doing, with numbers measured from the note itself.

What is subtractive synthesis?

Subtractive synthesis starts with too much and takes some away. An oscillator makes a wave that's already full of harmonics, usually a saw or a square, and a low-pass filter removes the top of it. Everything you hear is whatever the filter let through.

A saw wave has every harmonic of the note, and the nth harmonic is n times quieter than the fundamental. In decibels that's 6 dB down for the 2nd harmonic, 9.5 dB for the 3rd, 12 dB for the 4th and 20 dB for the 10th. On an A at 220 Hz those harmonics sit at 440, 660 and 880 Hz and on up past 20 kHz, which is why a raw saw sounds so buzzy and bright.

The filter's cutoff sets where it starts removing harmonics, and its slope sets how fast they fall away beyond that. The lab's filter is 24 dB per octave, the same slope as the classic Moog ladder filter, so with the cutoff at 800 Hz a harmonic at 1.6 kHz comes out about 24 dB quieter than it went in, and one at 3.2 kHz about 48 dB quieter. Resonance feeds some of the filter's output back into itself so it rings at the cutoff, lifting the harmonics right there. Push it far enough and the harmonic nearest the cutoff becomes louder than the fundamental, which is the squelch of a Roland TB-303 acid line.

A filter that stays put sounds static, so most subtractive patches put an envelope on the cutoff: it opens the filter at the start of each note and closes it again, so every note starts bright and settles darker. Set the envelope to open the filter 3 octaves above an 800 Hz cutoff and each note starts with the filter at 6.4 kHz. A fast close turns that into a pluck, a slow one into a swell. The filter envelopes lesson covers this in detail.

Subtractive is the oldest of the three methods. Robert Moog's modular synths of the 1960s worked this way, and so do the Minimoog, the Roland Juno and Jupiter synths and most of the analogue gear that came after. Its strength is that it's predictable: turning the cutoff down always makes the sound darker. Its limit is that a filter can only take away what the oscillator gave it, and every partial it leaves is still a harmonic of the note.

What is FM synthesis?

FM synthesis goes the other way: it starts with plain sine waves, which have no harmonics at all, and creates new frequencies. One sine, the modulator, pushes the pitch of another, the carrier, up and down hundreds of times a second. That wobble is far too fast to hear as vibrato, so you hear it as a change in tone instead, because the carrier has picked up new frequencies called sidebands, spaced exactly one modulator frequency apart on both sides of the note.

Two numbers run the sound. The ratio sets the modulator's frequency as a multiple of the note, and that decides where the sidebands land. The modulation index sets how hard the modulator pushes, and that decides how many sidebands you hear. With an A at 220 Hz, a 1 : 1 ratio and an index of 2, the modulator runs at 220 Hz and pushes the carrier 440 Hz either way. The sidebands land at 220 Hz plus and minus 220, 440, 660 Hz and so on, which are all harmonics of 220, so the note stays an A and just gets brighter.

Change the ratio to 1.41 : 1 and the modulator runs at about 310 Hz. Now the sidebands fall at 530 Hz, 840 Hz, 90 Hz and other frequencies with no whole-number relationship to the note, which makes the sound inharmonic. Struck metal behaves like this, which is why bells and gongs sound the way they do. A filter on a saw can't produce it, because it can only take away harmonics the saw already had.

A rough guide to how far the sidebands spread is Carson's rule: the highest one worth counting sits at about the carrier frequency plus (index + 1) times the modulator frequency. Put an envelope on the index, the way you'd put one on a filter, and the sound starts wide and narrows as the index falls, which is the bright strike and darker ring of an electric piano or a bell.

John Chowning worked out FM synthesis at Stanford University and published it in 1973. Yamaha licensed it and released the DX7 in 1983, with six sine wave operators, 32 ways of connecting them, called algorithms, and no filter at all. The FM synthesis lesson goes much further into ratios and operators. FM's trade-off is that small moves make big changes: nudge the ratio from 2 to 2.1 and a hollow tone turns into a clang, and that makes it hard to design a sound from scratch.

What is wavetable synthesis?

A wavetable synth stores the shapes themselves. Each frame in the table is one cycle of a wave, and the oscillator plays that cycle over and over at the pitch of the note, so a frame recorded as a saw sounds like a saw and a frame drawn with a hump in its harmonics sounds a little like a vowel. The table holds a run of frames, and the position control picks which one plays. Between two frames, the synth blends them.

The lab's table has eight frames: a sine, a triangle, a saw, a square, three shapes with a peak at the 4th, 8th and 16th harmonic, and a thin pulse. Serum's tables hold up to 256 frames, each one cycle of 2,048 samples, so a sweep through a full Serum table can pass through hundreds of shapes.

The point of a wavetable is movement. Put an envelope or an LFO on the position and the shape changes as the note plays, which can sound like a vowel changing, a bass growling or a pad slowly turning over. A filter sweep moves one edge up and down the spectrum; a wavetable sweep can rearrange the whole set of harmonics.

A frame stores its tone as harmonic numbers, so a peak at the 8th harmonic sits at 1,760 Hz on an A at 220 Hz and at about 2.6 kHz on the E above it. The peak follows the note, whereas a filter at 1.76 kHz stays at 1.76 kHz whatever you play, which is closer to how the body of a real instrument behaves.

Wolfgang Palm's PPG Wave synths brought wavetables to musicians in the early 1980s, and Waldorf carried the idea on with the Microwave. On computers, Native Instruments Massive arrived in 2007 and Xfer Serum in 2014. They're easy to start with. Designing a good table is the hard part, and the wavetable synthesis lesson covers tables and how to move through them.

How do they sound different?

Played still, the three can sound much alike: a saw is a saw, whether it comes from a subtractive oscillator, a wavetable frame or an FM pair at a 1 : 1 ratio. They part ways when the sound moves, so listen to what happens inside each note.

A subtractive note with a filter envelope sounds like something closing. The top of the sound gets cut away and the whole note gets duller and rounder, and if the resonance is up you hear a whistling peak slide down through the harmonics. An FM note with an index envelope sounds struck: the start is bright and complex, the tail is closer to a pure tone, and with an in-between ratio there's a clang no other engine here can make. A wavetable note moving through its table sounds like its shape is changing, which can be smooth or jumpy depending on how different the frames are.

Which is best for each sound?

In practice the lines blur. Most wavetable synths have a full subtractive filter section after the oscillators. Serum and Surge XT can run FM between oscillators, and Ableton's Wavetable has an FM mode on each oscillator. Logic's Retro Synth puts four engines in one plug-in (analogue, sync, wavetable and FM), which is a good way to hear the differences if you already use Logic.

Which should a beginner learn first?

Subtractive. Its controls each do one thing you can hear: the oscillator picks the raw sound, the filter takes some away and the envelopes shape it over time. Once that's familiar, a wavetable synth feels like a subtractive synth with a much bigger choice of oscillator, because that's mostly what it is. FM makes more sense after both, when you already know what harmonics are and can hear a filter sweep, because then the index sounds like what it is: a different way of getting brightness.

The oscillators and waveforms lesson is the place to start if saw, square and triangle are new to you, and the ADSR envelopes lesson covers the envelope that shapes the volume of every note in all three methods.

How to choose a synthesis method for a sound

1. Listen to how the sound changes over one noteIf it gets duller as it goes, like a plucked string, a filter is closing, so start subtractive. If it strikes bright and rings, start with FM. If its character shifts, like a voice going from “ooh” to “aah”, start with a wavetable.
2. Check whether it has a clear pitchHum along. If you can't find the note, or it sounds metallic, its partials are probably off the harmonic series, and FM is the method that gets there most directly.
3. Pick the closest raw shapeOn a subtractive or wavetable synth, choose the oscillator wave or table frame nearest to the sound with the filter open. On an FM synth, pick the ratio first and set the index low.
4. Add the movementPut an envelope on whatever controls the tone: the cutoff, the index or the position. A lot of plucks and bells that sound complicated are one shape and one envelope.
5. Compare at the same levelBrighter versions sound louder, and louder versions sound better at first. Match the volume before you decide one method beat another.

Common mistakes

Expecting a filter to add brightness

A low-pass filter can only remove harmonics. If the raw oscillator sounds dull, opening the filter won't help, and resonance only lifts what's already there. Pick a brighter oscillator wave or wavetable frame instead, or add some FM between oscillators.

Landing on an in-between FM ratio by accident

A ratio of 2.03 instead of 2 makes the sidebands beat slowly against the harmonics, and anything further off starts to clang. If an FM patch won't sit with the rest of the track, check that every ratio is a whole number, or 0.5, unless you wanted the clang.

Leaving the wavetable position still

A wavetable parked on one frame is a fixed waveform, and you've given up the one thing wavetables do best. Even a small, slow LFO on the position makes every note shift a little as it plays.

Running everything bright

All three methods can make a sound with partials up past 15 kHz, and several of those stacked in a mix gets harsh fast. High FM indexes can also push sidebands past half the sample rate, where they fold back down as aliasing. Keep the brightest settings for the sound that's meant to stand out.

Training your ears to tell them apart

The quiz under the lab plays the riff through one of the three engines with a typical patch, at the same level, and covers every screen and knob. Your job is to name the engine. Listen to the first half-second of each note, where the giveaway is a closing filter, a clang or a shape that slides. The closest pair is wavetable against a resonant subtractive patch, because both move a peak through the harmonics.

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