What is ring modulation?

Ring modulation in plain English

A ring modulator multiplies your sound by a second signal, the carrier, which is usually a sine wave from an oscillator inside the effect, and multiplying two waves together makes frequencies that weren't in either of them.

Feed it a 220 Hz tone with a 300 Hz carrier and you get 80 Hz and 520 Hz out: the carrier minus the tone, and the carrier plus the tone. The 220 Hz you put in is gone, and so is the 300 Hz carrier. A real instrument has many harmonics, and each one gets the same treatment, so a single note comes out as a cluster of new frequencies.

Because those new frequencies are spaced by adding and subtracting hertz, they hardly ever land on the neat multiples that make a note sound like a note. That's the clang ring mod is known for, and it's what turned actors' voices into Daleks in Doctor Who.

How ring modulation works

At every sample, the ring modulator takes the level of your sound and multiplies it by the level of the carrier. When the carrier is at its peak, your sound passes through at full level. When the carrier crosses zero, the output is silent for that instant, and when the carrier swings negative your sound comes out upside down, with its polarity flipped.

Do that thousands of times a second and the result can be worked out exactly. Multiplying a sine at frequency A by a full-height sine at frequency B gives two sines, one at A + B and one at A − B, each half the height of the original. There is nothing left at A or at B.

Here are the numbers for a 440 Hz note, the A that tuners use, with a 100 Hz carrier:

The input was 440, 880 and 1,320 Hz, all multiples of 440. The output is 340, 540, 780, 980, 1,220 and 1,420 Hz. Those are all multiples of 20 Hz, but the lowest of them is the 17th, which is too far up the series for your ear to hear 20 Hz as the pitch. So it hears a chord of unrelated tones, which is what inharmonic means.

The lower frequency can move the opposite way to the knob. While the carrier is below a frequency in your sound, the difference is that frequency minus the carrier, so it falls as you turn the carrier up. Turn a 150 Hz carrier up towards 220 Hz on a 220 Hz tone and the lower frequency falls from 70 Hz to almost nothing; past 220 Hz the difference becomes the carrier minus the tone, and it rises again.

The output also comes out quieter. Each new frequency is half the height of the one that made it, and together they're about 3 dB below the dry sound, which is why the lab matches the loudness before you compare.

Reading the lab

The top screen is a spectrum, with frequency running from 20 Hz on the left to 20 kHz on the right. The dashed line is the dry sound and the pink line is what comes out of the ring modulator. With the test tone, each peak has its frequency printed above it, and hovering over one tells you which sum or difference it is.

Under it on the left is a scope, a picture of the waveform across a few cycles of the carrier. The pale shape is the dry sound, the dashed teal line is the carrier and the pink is the output, which is the two multiplied together. Watch the pink pinch to nothing every time the teal line crosses the middle: that's the moment the carrier passes through zero.

The Right now panel describes what the current settings are doing, using numbers measured from the processed sound. The lab runs the same ring modulator offline to draw both screens, so the peaks you see are the ones you're hearing. Press A/B to hear the dry sound at the same loudness as the processed one.

Test tone is the clearest way to learn what the effect does, because with one frequency going in you can see exactly where each new one comes from. Switch to a loop, or upload your own sound, to hear it on music.

The controls

Carrier frequency

This is the main control on any ring modulator, and it's usually labelled Frequency or Carrier. It sets how many hertz every frequency in your sound gets moved up and down. Low settings, under about 100 Hz, keep the new frequencies close to the old ones, so the source is still recognisable with a rough, buzzy edge. Settings in the hundreds of hertz scatter the frequencies far enough apart that a voice or a chord turns into metal.

Small moves make a big difference, because the relationship between the carrier and the notes decides whether the result sounds pitched or clangy. Sweep the carrier slowly with the test tone playing and you'll hear the two new tones slide in opposite directions while the carrier is under the note.

Carrier wave

A sine carrier is the cleanest choice, because a sine has no harmonics of its own and so each frequency in your sound makes exactly one sum and one difference. A square wave has harmonics at 3, 5, 7 times its frequency and up, and every one of them does its own ring modulation. With the test tone and a square carrier, the spectrum fills with peaks: the note plus and minus the carrier, plus and minus three times the carrier, and so on up. It sounds harsher and buzzier, which is sometimes what you want.

Mix

At 100% you hear only the ring modulated sound. Bring it down and the dry sound comes back underneath. On anything that has to stay in tune, full strength is usually too strange, so try 20 to 50%: the ring modulator adds a metallic layer and the dry sound keeps the pitch and weight.

Very low carrier speeds

Below about 20 Hz the carrier is too slow to hear as a pitch, and the effect turns into a rhythmic pulse. It's twice as fast as you might expect. A sine passes through zero twice per cycle, so a 4 Hz carrier silences the sound 8 times a second, and every other pulse comes out upside down. A square carrier behaves differently down here, because it jumps between full and full upside down without passing through the middle: the level never dips, and you hear a click at each flip. The LFO that some ring modulators have does a different job, sweeping the carrier frequency up and down.

Why ring modulation sounds metallic

A note from a voice, a string or a synth has a fundamental plus harmonics at whole-number multiples of it. That neat spacing is what your ear uses to hear one pitch. Bells and struck metal plates don't work that way: their frequencies sit at uneven ratios, which is why a bell's pitch can be hard to name.

Ring modulation moves every harmonic by the same number of hertz, so the multiples stop being multiples. Say a note has harmonics at 200, 400 and 600 Hz and the carrier is 70 Hz. The output is 130, 270, 330, 470, 530 and 670 Hz. Those are all multiples of 10 Hz, but the lowest is the 13th, so your ear can't find a low note they all belong to, and it hears metal.

It stays musical when the carrier is a simple ratio of the note. If the carrier is a whole-number multiple of the note, every sum and difference is a multiple of the note too, so the pitch survives and only the tone colour changes. If the carrier is half the note, everything lands on odd multiples of half the note, and you hear a hollow tone an octave down.

The 0 Hz part in the second row is a fixed shift of the whole waveform above or below the centre line, called a DC offset. You can't hear it, and the lab filters it out so it doesn't throw off the screens.

A fixed carrier can only match one note at a time. Play a melody through it and every note lands on a different ratio, so a few come out close to in tune and the rest clang. That's why synths with ring modulation usually build it between two oscillators that both follow the keyboard: the ratio stays the same on every note, so the sound is consistent from the bottom of the keyboard to the top. The ARP Odyssey and the Korg MS-20 both have a ring modulator wired up this way.

Ring modulation vs amplitude modulation

Amplitude modulation, or AM, also multiplies your sound by a carrier, but first it lifts the carrier so it never drops below zero. In the lab, AM multiplies by 0.5 plus half the carrier, so the level swings between full and nothing and the wave never flips over. Work through the maths and the output is the original at half its height, plus the same sum and difference that ring modulation makes at a quarter of the height each, so they sit 6 dB below the original.

Because AM keeps the original pitch, a carrier in the hundreds of hertz still leaves the melody audible under the new tones. At low carrier speeds AM is what a tremolo does, and it pulses once per cycle where ring modulation pulses twice. The tremolo lesson covers slow AM in detail.

A frequency shifter is the other close relative. It keeps only one of the two new frequencies, the sum or the difference, so everything moves in one direction by the same number of hertz. The comparison in ring modulation vs frequency shifting goes through how they differ.

How to make a robot voice with ring modulation

The BBC Radiophonic Workshop made the original Dalek voices in Doctor Who by ring modulating the actors' voices with a 30 Hz oscillator. A low carrier keeps the words intelligible, because nothing moves far from where it started, while the shifted harmonics take away the natural pitch of the voice and leave a buzz.

1. Put a ring modulator on the vocal as an insertLogic Pro's Ringshifter or the Ring mode in Ableton Live's Shifter both work, and so does any ring mod plug-in with a sine carrier.
2. Set the carrier between 30 and 60 HzLower is more intelligible and more buzzy. Higher starts to turn the voice into metal.
3. Set the mix to 100%Any dry voice underneath brings the human pitch back and spoils the effect.
4. Add some distortion after itA small amount of saturation or overdrive roughens the buzz and makes it sound more like an old speaker.
5. Cut the low endThe difference tones land below the voice's normal range, and in the lab they make the vocal about 6 dB heavier under 150 Hz. A high-pass filter around 150 Hz clears them out and gives the thin sound of a small speaker.

Where ring modulation works in a mix

Drums and percussion

Most drums have no clear pitch to lose, so ring modulation can't put them out of tune, which makes them the easiest place to start. A carrier between about 300 Hz and 1 kHz turns a snare or a hi-hat into something like a struck pipe. Mix it in at 30 to 50% and the hits keep their weight while picking up a metallic ring on top.

Synths and sound design

For bells, gongs and sci-fi tones, ring modulate one oscillator with another that follows the keyboard at a fixed ratio. Slowly sweeping the carrier on a held chord makes a shifting, alien texture that suits film and game sound design. It's been used on acoustic instruments for a long time too: in Mantra, written in 1970, Karlheinz Stockhausen has the sound of both pianos ring modulated by sine waves.

Bass

Ring modulation moves the fundamental of a bass note away from where it was, so a 55 Hz bass through a 400 Hz carrier comes out at 345 and 455 Hz, and the low end disappears. If you want a metallic edge on a bass, run the ring modulator on a copy, high-pass it, and keep the original underneath for the weight.

Ring modulator plug-ins and hardware

Logic Pro has Ringshifter, which switches between ring modulation and frequency shifting. Ableton Live's Shifter has a Ring mode alongside its pitch and frequency shifting modes. In hardware, the Moog Moogerfooger MF-102 is a ring modulator with its own carrier oscillator and an LFO to move it. Plenty of synths include one as well, either as an effect or as a mixer source between two oscillators.

The controls are much the same everywhere: a carrier frequency, sometimes a choice of carrier wave, a dry/wet mix, and on some units an LFO for the carrier. A few let you use another track as the carrier instead of an oscillator, which multiplies two sounds together and gets unpredictable quickly. Analogue ring modulators rarely cancel perfectly, so a little of the carrier and the dry sound leaks through, and that leak is part of how they sound.

Common ring modulation mistakes

Expecting a melody to stay in tune

A fixed carrier only lines up with notes that sit at a simple ratio to it. On a melody, either accept the clang, keep the mix low, or automate the carrier to follow the notes.

Putting it on the whole bass or the whole mix

Everything under the carrier frequency gets moved up and away, so a full-strength ring modulator takes out the low end of whatever it touches. Use it on a send or a copy and keep the dry signal for the weight.

Treating a slow carrier like a tremolo

At low speeds ring modulation pulses at twice the carrier rate, and the wave flips over at every dip. If you set it to 2 Hz expecting a quarter-note pulse at 120 BPM, you'll get eighth notes. Use AM, or a tremolo, when you want one pulse per cycle.

High carriers on bright sounds

Cymbals and breathy vocals have energy up to 15 kHz and beyond, so a carrier of 7 kHz or more pushes their sums past 22.05 kHz, the highest frequency a 44.1 kHz session can hold. They fold back down as aliasing, a gritty layer that isn't in the music. The aliasing and oversampling lesson explains how that happens and how to hear it.

Train your ears

The quiz under the lab plays ring modulation or AM with a hidden carrier between 180 and 620 Hz, on the test tone or on a loop, and covers the screens while you listen. Both are matched in loudness, so the only clue is whether the original pitch is still there. Eight rounds take two or three minutes, and your best score is kept in your browser.

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