We know using one oscillator to frequency modulate another is a lot of fun…but just what is the difference between the different types of FM? I finally got my hands on a module – the Endorphin.es Furthrrrr Generator complex oscillator – that is capable of being switched (with some behind-the-faceplate fiddling) between exponential, linear, and linear through zero FM, and created the movie below showing off all three:

(If you’re interested in learning more about the Furthrrrr Generator, click here for an overview of the entire module.)

The short answers to the differences between FM types are:

  • exponential FM goes out of tune as soon as you start increasing the modulation depth (fortunately, once you stop changing the depth, it stays in tune)
  • linear FM stays in tune for shallow modulation depths (tip: the higher the carrier is tuned, the deeper you can modulate before it starts detuning)
  • through-zero FM (TZFM) stays in tune regardless of modulation depth (as long as you don’t bump up against the tuning limits of the carrier oscillator)

Here are the details why:

Endorphin.es Furthrrrr Generator with deep exponential FMExponential FM (starting at 02:06 in the video above) typically uses a 1 volt/octave input to modulate the frequency of a VCO. Say you’ve tuned the VCO to 440Hz, and send it a perfectly symmetrical* modulation waveform that goes + and – 1 volt. That means its pitch will go up to 880Hz and down to 220Hz: 1 octave up and down. The problem is, the average between those frequencies is 880 + 220 ÷ 2 = 550 Hz, not 440, so you will get a pitch shift. If you keep the modulation voltage level steady, the pitch will remain steady, and you can re-tune the VCO. But if you envelope the modulation depth (a cool effect), the pitch will bend during the envelope.

* What if the modulation waveform was not perfectly symmetrical? Say it was a pulse wave that was 90% wide, meaning it spent 90% of its time at +1v and 10% of its time at –1v. This means it will spend more time shifting the pitch of the VCO up rather than down, causing further pitch shifts and errors. This problem exists with all forms of frequency modulation, and is why the linear FM input on some oscillators is AC-coupled – to try to remove this offset.

Endorphin.es Furthrrrr Generator stalling with linear FMLinear FM (starting at 10:03 in the video above) typically uses a separate input for a VCO where its frequency is offset by a certain number of Hertz (instead of octaves) per volt. Let’s say we turned down the attenuator often found on FM inputs to where its response was 100Hz/V. In our example with a +/–1v modulation signal, the VCO would be shifted up to 540Hz and down to 340Hz, still averaging 440Hz – so it should keep the same pitch (as long as the modulating waveform was perfectly symmetrical*, with no DC offset). No re-tuning! Even better, it stays in tune while you envelope the modulation depth, so you can create some really cool “plucked” sounds.

So what’s the downside? Linear FM is often implemented in a way that it does not go as deep as exponential FM. It could be, but then you start running into the Through Zero problem.

Let’s say we turned up the attenuator on our linear FM input to where its range was now 500Hz per volt. Send it a +/–1v modulation signal, and its pitch would be shifted up to 440 + 500 = 940 Hz, and down to 440 – 500 = …what? Math would tell you -60Hz, but most analog VCOs won’t go below (through) 0Hz, flat-lining at any attempts to drive them lower. So now our VCO is going between 940 and 0Hz, averaging 470Hz – meaning we have a pitch shift issue again. (There is a popular video out there demonstrating a VCO making horrible noises when asked to go negative; fortunately, that’s not how most of them actually sound.)

There are a few potential workarounds: Either tune the carrier oscillator to a higher initial pitch, or reduce the modulation depth so you don’t drive it below 0Hz.

Endorphin.es Furthrrrr Generator going through zeroOr…find an oscillator that supports TZFM (starting at 16:11 in the video above) and can indeed go through 0Hz and into the negative frequency range. This means turning around and running backwards when asked. Using our example above, that means turning around going back up to 60Hz, but backwards, yielding the same result as running at -60Hz. Average together 940 and -60Hz, and we’re back to 440Hz. Yay!

Running backwards is not the easiest thing for an analog VCO to do, although more and more modules are appearing that can. For example, the classic 3340 VCO chip – which several companies have recently cloned or re-issued, and which is at the core of numerous new VCOs and semi-modular synths announced in the past few months – is capable of doing both linear and exponential FM. It can even do through-zero FM with some additional components. Alas, very few manufacturers are adding those components to enable this feature (which I think is a mistake).

It’s easier to program a digital VCO to run backwards and therefore support through-zero FM. The linear FM mode in the Expert Sleepers Disting, for example, has supported this since day one. Some of you know I was one of the more vocal users lobbying for the Synthesis Technology E352 to support TZFM, and I’m thrilled to say it now does with a recent update.

But as always, there’s a potential catch. VCOs – digital ones in particular – often have frequency limits that they won’t go beyond. So there is a chance, for example, that with a high carrier pitch and a high modulation depth, a VCO might hit a frequency ceiling (rather than the 0Hz floor) and not modulate as high as it can low, again causing a pitch shift. So if you hear a pitch shift when modulating a VCO that supports TZFM, this is what’s going on. (That, or your modulation waveform is not perfectly symmetrical – see * above.)

My personal bottom lines are:

  • If I’m creating percussion sounds, I like exponential FM as it includes a pitch shift as I modulate the carrier. This recreates an exaggerated version of how many acoustic percussion instruments work.
  • If I’m creating tonal sounds I expect to play from a sequencer or keyboard, I prefer linear FM, so I don’t have to deal with the carrier oscillator detuning when I start to turn up the FM depth.
  • If an oscillator supports linear FM, I strongly prefer it supports TZFM, so I can crank up or envelope the FM depth as much as I want without worrying about detuning. At the end of the day, Through Zero FM is linear FM “that just works.”
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