What is frequency shifting?

Frequency shifting in plain English

Every pitched sound is a stack of frequencies. Play an A at 110 Hz on a synth and you get 110 Hz, plus harmonics at 220, 330, 440 Hz and on up, each one a whole-number multiple of the lowest. Your ear hears that neat stack as a single note with a pitch of 110 Hz.

A frequency shifter slides the whole stack by a fixed amount. Shift it up by 100 Hz and 110 becomes 210, 220 becomes 320 and 330 becomes 430, so every line in the spectrum moves the same distance, counted in hertz.

That sounds harmless until you look at the new numbers. 320 isn't twice 210, and 430 isn't three times it, so the stack is no longer a harmonic series and your ear can't hear it as one clean note. What comes out sounds like a bell, a struck metal bar or a synth that has gone badly out of tune with itself, and that clang is the reason people reach for a frequency shifter.

Frequency shifting vs pitch shifting

A pitch shifter does something different with the same stack. It multiplies every frequency by one number, so moving 110 Hz up to 210 Hz means multiplying by about 1.91, which puts the 2nd harmonic at 420 Hz and the 3rd at 630 Hz. The ratios survive and the note stays a note, only higher. A frequency shifter adds where a pitch shifter multiplies, and adding the same number to every harmonic is exactly what breaks the ratios.

Every figure in the right-hand column is a multiple of 210. In the middle column only the first one is.

There's a second difference, and it explains why a frequency shifter can't transpose a song. The same number of hertz is a huge musical step at the bottom of the spectrum and a tiny one at the top. Going from 110 Hz to 210 Hz is 11.2 semitones, nearly an octave, while a harmonic at 1,760 Hz that moves to 1,860 Hz goes up less than one semitone. A bass line and a hi-hat put through the same shifter end up moved by completely different musical amounts. The harmonics screen in the lab draws all three rows, so you can watch the middle one drift away from the dashed one as you turn the Shift knob.

Why does frequency shifting sound metallic?

Bells, gongs, cymbals and struck metal bars have overtones that aren't whole-number multiples of each other, which is why none of them sounds quite like a single clear note. When a frequency shifter pushes a normal note's harmonics off their multiples, it gives that note the same kind of spectrum, and your ear files it with the metal things.

How metallic depends on the size of the shift. A few hertz is too small to hear as a pitch change at all. Push it to tens of hertz and the note starts to sound sour, as if it's out of tune with itself, and once the shift is a big fraction of the note's own frequency (50 Hz or more on a 110 Hz bass) it stops sounding like a note and turns into a clang.

Sounds that were never harmonic react differently. Drums, cymbals, noise and most sound effects don't have a neat row of harmonics to break, so shifting them sounds more like retuning: down makes a snare deeper and darker, and up makes it thinner and more papery. That's why percussion is one of the most forgiving things to put through a frequency shifter.

How does a frequency shifter work?

The trick comes from radio. Multiply a sound by a sine wave and you get two copies of it, one moved up by the sine's frequency and one moved down, called the upper and lower sidebands. That multiplication on its own is a ring modulator, and it's why ring modulation is so clangy: you get both copies at once and lose the original.

A frequency shifter cancels one of the two copies. It uses a chain of allpass filters to split the sound into two versions a quarter of a cycle (90 degrees) apart at every frequency, then multiplies one by a cosine and the other by a sine at the shift frequency. Add the two results and the lower sideband cancels, leaving only the copy that moved up; subtract them and the upper one cancels instead. The 90 degree split is called a Hilbert transform, and the result is single-sideband modulation, which radio transmitters use because it needs half the bandwidth.

The lab on this page is built exactly that way. Its two filter chains stay within about a degree of 90 degrees apart from 20 Hz to 20 kHz, which leaves the unwanted sideband roughly 40 dB or more below the one you keep. Choose Both sidebands and you hear the ring modulator that sits inside every frequency shifter. Harald Bode built a frequency shifter for the composer Vladimir Ussachevsky, and Moog later turned the design into a module, the 1630 Bode Frequency Shifter. The ring modulation vs frequency shifting comparison goes through the difference between the two side by side.

Shifting down and the fold at 0 Hz

Shifting down has a problem that shifting up doesn't: there's nothing below 0 Hz. When a frequency is lower than the shift, it goes past zero and comes back up the other side, mirrored.

Say you shift a 110 Hz note down by 150 Hz. The note itself would land at −40 Hz, which can't exist, so it comes out at 40 Hz. The 2nd harmonic at 220 Hz lands at 70 Hz, the 3rd at 180 Hz and the 4th at 290 Hz. The two lowest are now only 30 Hz apart and beat against each other, so the bottom of the sound becomes a rough, muddy growl.

That growl can be great on a sound-design hit and terrible on a bass line you need in tune. A high-pass filter before the shifter, set close to the shift amount, removes most of it, because whatever sits below the shift is exactly the part that folds. In the lab, the Right now panel tells you how much of the current sound's energy sits below the shift when you switch to Shift down.

Small shifts: tremolo and endless sweeps

Below about 5 Hz a frequency shifter stops sounding like a pitch effect, and on its own it sounds almost like the original. Mix the original back in and the sound starts to move.

Take a single sine. With the shift at 2 Hz and the mix at 50% you have two tones, 110 Hz and 112 Hz, which drift in and out of step twice a second. When they line up they add together and when they're opposite they cancel, so what you hear is a tremolo. The loop screen in the lab draws the level rising and falling.

On chords or a pad the same thing happens to every frequency at once, with one twist. The allpass filters inside the shifter have already moved the phase of each frequency by a different amount, so the places where the two copies cancel are spread across the spectrum as a row of notches. As time passes the notches slide along in one direction and never turn round. It sounds like a phaser whose sweep has no end, and it's often called a barber-pole effect, after the stripes that seem to climb a barber's pole for ever. Shifting up sends the sweep one way and shifting down sends it the other. The chorus vs flanger vs phaser comparison covers the more familiar sweeping effects.

Small shifts have a practical use outside music too. A shift of a few hertz in a public address system makes it less likely to howl, because each trip from the speaker back into the microphone moves the sound a little further from the frequency that wants to ring. Manfred Schroeder described the idea in a 1964 paper in the Journal of the Acoustical Society of America.

Feedback and spiralling echoes

Many shifters put a delay after the shift and send the output back to the input, and Valhalla FreqEcho is built around that idea. Each echo goes through the shifter again, so it comes out one more step away from the original. Shift up 120 Hz with feedback on, and a 110 Hz note comes out at 230 Hz, with echoes following at 350, 470 and 590 Hz.

Feedback sets how fast the repeats fade. At 60%, each echo is 60% of the level of the one before, about 4.4 dB quieter, so the fifth repeat is around 22 dB down. With delays of 100 ms or more you hear separate repeats climbing like a staircase; under about 20 ms they blur into one continuous swirl. The delay feedback lesson covers the delay side of this in more depth.

Reading the lab

The top screen is the spectrum of the whole loop, from 20 Hz on the left to 20 kHz on the right. The pale shape is the original and the coloured shape is what comes out of the shifter, played at the same loudness so you're comparing where the energy sits and nothing else. On the sine, the lab prints the frequency each line has landed on. While the loop plays, a thin white line shows the spectrum moment by moment, which is the only way to see the barber-pole notches move.

Under it, the loop screen shows the sound over time. A frequency shifter at 100% mix hardly changes this picture, so watch it when you bring the original back in or turn up the feedback.

The harmonics screen is a diagram of a 110 Hz note with its first ten harmonics. The top row is the note as it is, the middle row is where the shifter puts each harmonic, and the dashed bottom row is where a pitch shifter would put them for comparison. Hollow dots mark harmonics that went below zero and folded back. Next to it, the Right now panel explains what your settings are doing, using figures measured from the sound that's loaded.

You can use any sound. Upload a file, or press Record and play something for eight seconds, and it loops through the lab in place of ours. Nothing leaves your device.

The controls

Frequency shifters keep to a small set of controls. Ableton Live and Logic Pro both include one (Logic's is called Ringshifter, and does ring modulation as well), and Valhalla FreqEcho is a free plug-in built around one.

Shift

How many hertz every frequency moves, usually from a fraction of a hertz up to a few kilohertz. In the lab it runs from 0.1 Hz to 2 kHz. Some shifters use a single knob that goes negative for down and positive for up, and others pair a shift knob with a direction switch.

Direction

Up adds the shift and down takes it away. Both sidebands keeps the two copies and drops the original, which makes it a ring modulator. Some hardware shifters give you the up and down versions on separate outputs at the same time, so you can pan them apart.

Mix

The balance between the shifted sound and the original. Leave it at 100% for the clang. Bring it down towards 50% with a shift of a few hertz or less for tremolo and sweeps; at bigger shifts, a partial mix plays two versions of the part that clash with each other.

Feedback and delay

Feedback sends the shifted sound back into the shifter after the delay time, so every echo is shifted again. In the lab feedback stops at 90%, and the Delay knob does nothing while Feedback is at 0%.

LFO and stereo

Plenty of shifters add an LFO to move the shift amount up and down for you, and some shift the left and right channels in opposite directions to widen the sound. The lab leaves those out, so the shift itself is all you hear.

How to use a frequency shifter, step by step

1. Pick a sound that can take itPercussion, pads, sound effects and vocal throws are forgiving. A bass line or lead melody that has to stay in key isn't.
2. Start smallSet 10 to 30 Hz and listen to how sour the sound gets before you go further.
3. Choose the directionUp sounds thinner and clangier, and down sounds darker. If you go down, put a high-pass filter before the shifter at roughly the shift amount so the low end doesn't fold into mud.
4. Set the mixUse 100% for metallic tones, or 30 to 50% with under 5 Hz of shift for tremolo and endless sweeps.
5. Add feedback lastWith the delay at an eighth note (250 ms at 120 BPM), raise the feedback until the echoes climb as far as you want.
6. Compare at matched loudnessSwitch the shifter off and on at the same level, which the A/B button in the lab does for you.

Starting settings for common uses

These are places to begin. The ranges are wide because the right amount depends so much on the pitch of the sound you're shifting.

Common frequency shifting mistakes

Using it to change key

A frequency shifter moves low notes much further than high ones, so a shifted sample ends up out of tune with itself. To transpose, use a pitch shifter; the pitch shifting and time stretching lesson explains how they work.

Shifting bass down with nothing below it filtered

Everything under the shift amount folds back up past 0 Hz and lands among the real bass notes. A high-pass filter before the shifter, set near the shift, fixes most of it.

Putting it across a whole mix

On a full mix, every part moves by the same hertz and ends up out of tune with every other part. Put the shifter on one sound, or on a send so you can blend in as much as you want.

Running the feedback too high

Near 100% the echoes never fade, and in plug-ins that go past it the level keeps building. Keep feedback under about 80% unless you're riding it by hand, and put a limiter after the shifter while you experiment.

Train your ears to hear the direction

The quiz under the lab shifts a sound up or down by 80 to 250 Hz, covers the screens and matches the loudness, then asks which way it went. Up tends to sound thinner and brighter, while down sounds darker and leaves the low notes hollow. Eight rounds take a couple of minutes, and your best score is saved in your browser.

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