Ring modulation vs frequency shifting

At a glance

What's the difference between ring modulation and frequency shifting?

Both effects take a second signal, a sine wave called the carrier, and use it to move every frequency in your sound by the carrier's frequency, measured in hertz. On a ring modulator the control is usually called Frequency or Carrier. On a frequency shifter it's usually called Shift. Either way, the number on the dial is how many hertz everything moves.

A ring modulator multiplies your sound by the carrier. When you multiply two sine waves together you get two new ones, at the sum of their frequencies and at the difference. So every frequency in your sound turns into a pair, one above where it was and one below, and the frequency it started at disappears. Radio engineers call those two copies sidebands, the upper sideband and the lower sideband.

A frequency shifter does that multiplication twice. It puts two copies of your sound a quarter of a cycle out of step with each other, multiplies them by two copies of the carrier that are also a quarter of a cycle apart, and then adds or subtracts the results. One sideband cancels out and the other doubles. What's left is a single copy of the sound with every frequency moved up, or every frequency moved down. In radio terms, ring modulation is double sideband and frequency shifting is single sideband.

The simplest way to remember it is that a ring modulator is a frequency shifter going both ways at once. The table shows what each one does to a note with harmonics at 440, 880 and 1,320 Hz, with the dial set to 100 Hz.

The ring modulated column is the other two columns put together. Three frequencies went in and six came out, where the shifter gives you three.

People often mistake both effects for a pitch shifter, and both differ from one in the same way. A pitch shifter multiplies every frequency by one number, which keeps the harmonics in proportion. These two add or subtract a fixed number of hertz, which doesn't. The frequency shifting lesson goes through that difference harmonic by harmonic.

One sine wave through both

A sine wave has no harmonics, so it's the clearest way to see what each effect does. The lab starts in ring mode at 50 Hz. The spectrum shows two lines, at 60 Hz and 160 Hz, and nothing at 110 Hz.

Switch to Shift up and the 60 Hz line goes, leaving 160 Hz. That's 110 plus 50, a jump of about 6.5 semitones for this note. Switch to Shift down and you get 60 Hz on its own, about 10.5 semitones lower than the original. Flip between the three with the 1, 2 and 3 keys and you can watch ring mode light up both of the lines the shifter gives you one at a time.

On a single sine both results still sound like a plain tone, because one or two sines can't clash much. The difference gets bigger as soon as the sound has harmonics.

On chords and voices: bells against sour notes

A note from a voice or a synth is a fundamental plus harmonics at whole-number multiples of it. Your ear uses that even spacing to hear a single pitch. Move every harmonic by the same number of hertz and the spacing stays even, but the multiples stop being multiples, so the note stops sounding like one note. That's called inharmonic, and it's why both effects sound metallic.

The amount of metal is where they part. A ring modulator gives every harmonic two copies, so a chord with dozens of harmonics comes out with twice as many unrelated lines. They fill the spectrum from below the original notes to above them, and the chord turns into something closer to a gong or a set of bells, with the original harmony hard to pick out.

A frequency shifter moves everything one way. The lines are just as inharmonic, but there are half as many of them and they keep their order, so the chord changes are still easy to follow. Shifted up, a part sounds thinner and sour. Shifted down, it gets darker and the low notes growl. It sounds like the same music played on a broken instrument, where the ring modulated version sounds like a different instrument.

The last lesson step puts a voice through both. Ring modulation at 30 Hz turns it into a buzzing robot, and the Daleks in Doctor Who speak through a ring modulator. A 30 Hz frequency shift leaves it sounding like a voice, just a strange and out of tune one.

Direction, and what happens below 0 Hz

A frequency shifter has a direction and a ring modulator doesn't. Up and down sound different: up thins a sound out, and down makes it heavier and murkier, so a shifter gives you a choice the ring modulator can't.

Both effects can try to push a frequency below 0 Hz, and both deal with it the same way. Suppose you put a 110 Hz sine through a 150 Hz setting. The ring modulator's lower sideband should be 110 minus 150, which is −40 Hz. In a real sound, −40 Hz is the same as 40 Hz with its phase flipped, so it comes out at 40 Hz, folded back up past zero. A frequency shifter set to shift down 150 Hz does exactly the same thing and also gives you 40 Hz.

That's why the lower tone stops falling and starts rising again once you turn a ring modulator's carrier up past the note. On bass, the folded parts land among the real low notes and muddy them. A high-pass filter before either effect, set near the carrier or shift frequency, leaves the fold very little to work with.

Settings that keep a note in tune

There are settings where both effects keep the harmonics lined up, and they're the same settings for both. If the carrier or shift is a whole-number multiple of the note, every new frequency is a multiple of the note too.

Take a 110 Hz sawtooth, which has harmonics at 110, 220, 330 Hz and up. Shift it up by 110 Hz and every harmonic moves up one place, so you get the same series with the bottom one missing. Your ear still hears 110 Hz as the pitch, because it fills in the missing note from the spacing. Ring modulate it with a 110 Hz carrier and you get those same sums plus the differences, which start at 0 Hz and climb in 110 Hz steps, so the whole series comes back with a different balance.

Half the note is the other useful setting. Shift the 110 Hz sawtooth up 55 Hz and the harmonics land at 165, 275 and 385 Hz, the odd multiples of 55 Hz. The waveform now repeats 55 times a second, an octave down, and having only odd multiples gives it the hollow sound of a square wave. Ring modulating with a 55 Hz carrier gives odd multiples of 55 Hz as well.

The catch for both is that a fixed setting only fits one note. Play a melody through either effect and each note lands on a different ratio. Synths get round this by ring modulating two oscillators that both follow the keyboard, so the ratio stays the same on every note.

At slow speeds they behave nothing alike

Below about 20 Hz the carrier is too slow to hear as a pitch, and this is where the two effects sound least alike.

A slow ring modulator makes the level pulse. The two copies sit only a few hertz apart, and two frequencies that close together beat against each other, rising and falling in level. A sine carrier passes through zero twice per cycle, so an 8 Hz carrier silences the sound 16 times a second, and each time the sound comes back after a dip, its waveform is flipped upside down compared with the time before. That's a choppy, hard-edged effect, twice the speed you'd expect from the number on the dial.

Mix a slow ring modulator 50/50 with the original and the choppiness goes. Half the original plus half the ring modulated sound is the same as the original multiplied by a carrier that's been lifted so it never goes below zero. That's amplitude modulation, the effect inside a tremolo, and it dips once per cycle.

A slow frequency shifter on its own does very little. Moving everything up by half a hertz changes the pitch by a tiny fraction of a semitone, too little to hear. Mix it with the original, though, and the two copies drift slowly in and out of step. Wherever they're out of step they cancel, so notches sweep through the sound like a phaser. A phaser's sweep goes back and forth, while the shifter's keeps going in one direction and wraps round, which is called a barber-pole effect.

Inside each one

A ring modulator is a multiplier: your sound times the carrier. In a plug-in that's one line of code. The analogue version takes its name from its circuit, four diodes wired in a loop between two transformers. The Moog Moogerfooger MF-102 is one hardware ring modulator you might come across.

With a sine carrier, each frequency is split into two copies at half its height. Two half-height copies carry half as much power as the original, so a ring modulated sound comes out about 3 dB quieter. The lab matches the loudness of everything you compare, so you won't hear that drop there, but you will in a DAW.

A frequency shifter needs more parts. First it splits your sound into two copies whose phase differs by 90° at every frequency, which is done with a pair of allpass filter chains (the lab uses four filter stages in each chain). Then it ring modulates one copy with a cosine and the other with a sine at the shift frequency. Adding the two results cancels the lower sideband; subtracting them cancels the upper one. Because the frequency shifter works out both sidebands on the way, switching it to ring modulation only means skipping the cancelling step, and that's why many shifters include a ring mode. Logic Pro's Ringshifter is one plug-in that does both.

The 90° networks only hold their accuracy over a range of frequencies. The one in the lab stays within about a degree of 90° from 20 Hz to the top of the audio range. Below 20 Hz the unwanted sideband doesn't cancel completely, and a faint copy of it leaks through.

Which one to use

If you can only have one, get the frequency shifter. If it has a ring mode, it's a ring modulator as well, and a ring modulator can't do the reverse. Reach for a dedicated ring modulator when you want its extras, like a square-wave carrier or an analogue circuit's grit. The ring modulation lesson covers those.

How to choose between them on a sound

1. Start with the shifter at 0 HzPut a frequency shifter on the track, set to shift up with the mix at 100%, and slowly raise the shift. Under 10 Hz you'll hear the part go slightly sour; by 50 to 100 Hz it starts to clang.
2. Try the other directionFlip to shift down at the same setting. If the low end turns to mud, add a high-pass filter before the shifter set near the shift amount.
3. Switch to ring modeAt the same setting, switch to ring modulation, or put a ring modulator in its place with the carrier at the same frequency. If you wanted the sound to become something else, this is usually it.
4. Bring the original backLower the mix to between 20 and 50% to layer the effect under the original instead of replacing it. This keeps the pitch and weight of the part.
5. Match the levelsRing modulation comes out about 3 dB quieter, so turn its output up before you compare, or the shifter will win for being louder.

Common mistakes

Expecting either one to change the key

Neither effect transposes a sample. An 8 Hz shift moves a 110 Hz note about 1.2 semitones but a 1,760 Hz harmonic only about 0.08 semitones, so the parts of the sound end up out of tune with each other. Use a pitch shifter for that; the pitch shifting lesson explains how.

Reading a slow ring modulator's rate wrong

A 4 Hz carrier gives 8 dips a second. If you're trying to lock the pulse to a tempo, set the carrier to half the rate you want.

Using a frequency shifter slowly at 100% wet

Below a few hertz a frequency shifter on its own is close to inaudible, so people assume it's broken. The sweep only appears when the original is mixed back in, so bring the mix down to about 50%.

Ring modulating a whole mix

Every sound in the mix gets its own pair of sidebands and the bass folds into the low mids, so the result is usually a mess. Put it on one part, or on a send so the dry mix plays underneath.

Training your ears

To tell the two apart by ear, listen for direction and density. A frequency shifter keeps the sound moving one way, so the part still has a shape you can follow. A ring modulator fills in above and below at the same time, and a slow one chops the sound into pulses.

The quiz under the lab asks that question. Each round plays a sound through either a ring modulator or a frequency shifter, set between 100 and 300 Hz, with the screens covered and the loudness matched, and you say which one it is. The shifter rounds sound thin or dark and out of tune with themselves, while the ring modulator rounds sound crowded, because every frequency comes out twice. Hear the chords ring modulated and then shifted by the same amount to set the difference in your ear before you start.

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