Linear versus exponential FM and FM questions

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8 posts since 9 Feb, 2011

Post Wed Feb 09, 2011 10:16 am

Why does linear, Chowning FM sound better than octave/note based FM?

Most synthesizers use linear FM, in other words the modulator changes the frequency by the same number above and below the the operator level, for example 440hz +/- 200hz.

it would seem like it makes more sense to modulate the operator by the same amount of notes above and below its set frequency, for example 440 +440/-220(+12 notes/-12 notes)

both versions have stable side bands, except exponential frequency sounds like the octave timber climbs exponentially -too high and too fast- even though the notes stay on tune.

As far as I understand, if you see a linear FM wave in an oscilloscope, the waveform changes slowly on each note, so logically it should not scale well across the keyboard, but if you use exponential, then the waveform stays the same all the way across the keyboard, just getting faster and faster, so why does it not sound better?

It would make sense to me that linear FM would be less stable because the amount of frequency modulation relative to the ratio of the notes does not follow the scale of the octave. In other words, at the low notes 200hz is the same as one octave, and on the high notes it's the same as one semi-tone.

Maybe I didn't understand it right-if you use a ratio of 1/2, that means that the modulator is always one octave different to the operator.

I have been told that the human ear interprets higher sounds as being louder than the ones, and that is related to balancing FM.

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3426 posts since 15 Nov, 2006 from Pacific NW

Post Thu Feb 10, 2011 12:27 am

Many analog synthesizers used exponential FM: Minimoog, Prophet-5, Octave Cat, ARP Odyssey, most modular synths. The main problem with exponential FM is, as you increase the FM index, the perceived fundamental of the pitch shifts. Bernie Hutchins wrote a good explanation of why this happens in Electronotes, but I forget what it is. So, if you set up a simple 2-oscillator carrier/modulator pair with exponential FM oscillators, the pitch of the note would change as the index varies. It's a cool sound, but it doesn't get you that classic FM sound.

For a monosynth, exponential FM can be fun, assuming you have enough time to tweak the patch to your liking. Changing the waveshape of the modulator will change the perceived fundamental pitch. The Minimoog used the modulation wheel to control FM, so any jostling of this would change the pitch. As far as poly synths, the slight differences between the VCAs used for oscillator levels for FM would result in pitch differences between voices. On my (long since departed) Prophet-5, it was near impossible to create a patch with high FM indices and be able to play a chord that was in tune.

As far as your question about the ratio between carrier and oscillator in linear FM, it is usually represented as a pitch ratio. So, if you have a 2:1 ratio between modulator and carrier, the modulator will always be 1 octave above the carrier. This is how you get stable pitches for different notes.

Sean Costello


Topic Starter

8 posts since 9 Feb, 2011

Post Thu Feb 10, 2011 2:05 am

Very interesting, I didn't realize that many old school synths used exponential FM.

Hey-I have found out why linear FM is more stable and why it goes across the keyboard so well.

When you modulate a waveform by the same amount of added frequency as subtracted frequency, the waveform gets a fun shape and it always coincides back in phase at the end of every period. In other words, it is still 100% in tune.

When exponential, the waveform changes its zero crossing every time so basically it turns into a different frequency.

The reason why linear FM sounds the right frequency across all the scales even though it changes waveform -is the same reason that people prefer triangle baselines than sinewaves. Every time a linear FM waveform goes up one octave, it has half as many wiggles in it, and strangely, the sound stays perfectly balanced if it does that... So if the base waveform has 16 sine type wiggles, the top note has only wiggle, then then the human ear thinks that sound is perfect, because if it also had 16 wigles at the high notes then it would sound many octaves higher than it was, and also the sidebands become clearer at the top so the timbre changes and sounds less tonal.

6657 posts since 10 Oct, 2005 from Toronto, Canada

Post Thu Feb 10, 2011 8:39 am

"Old school" synths used "exponential FM" because FM was primarily for vibrato. And you typically want the note bending up by the same interval it's bending down. This does fall apart when the FM modulator reaches audio rates however.

Try modulating the oscillator's phase rather than its frequency directly. You'll find your "Operator FM" sounds work nicely then. Poly-Ana does this, if you need a demo. (See the "PM:" presets, 085 and 086.)

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3426 posts since 15 Nov, 2006 from Pacific NW

Post Fri Feb 11, 2011 10:38 am

AdmiralQuality wrote:"Old school" synths used "exponential FM" because FM was primarily for vibrato. And you typically want the note bending up by the same interval it's bending down. This does fall apart when the FM modulator reaches audio rates however.
Most of the old school VCOs only had exponential frequency inputs. This worked best for keyboard traffic and vibrato, and it took a lot of work to get the oscillator to track over different octaves. FM synthesis was popular in academic computer music circles in the 1970's, but didn't really enter the wider public consciousness until the DX7. So the only analog oscillators that made use of FM tended to be in more academic (Electronotes) or experimental (Buchla) circles.

As far as I know, none of the integrated oscillators from CEM or SSM featured linear FM. This might be because linear FM on an analog oscillator can sound more subtle than its digital counterpart, unless the oscillator is specifically designed to have "through-zero" modulation. I think that at least one of the CEM system-on-a-chips, the CEM 3396, had linear filter FM.

Sean Costello

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