technicalities of analog fm vs digital fm

[thesnow]

I'm interested in the technicalities that have to with why oscillator to oscillator audio frequency modulation is harder to achieve in the architecture of analog oscillators/synthesis, and it seems to be easier achieved with the use of digital oscillators/synthesis.

I'm really into complex harmonics and am familiar with the mathematics related to frequency modulation and sideband pairs. So I'm really interested in finding out some more information on this topic from those of you with more experience than me and knowledge on this topic.

btw, I'm not interested in the common snarky, smart ass, unnecessary, condescending comments that appear on this forum. If you think this question is silly and you're not interested in helping with this discussion than just save it and don't waste your time please. hopefully this can be an interesting discussion.

[chamomileshark]

I never quite followed the digital FM comment that for example DX7 was not FM but something else and Yamaha used that term to put others off the scent. Also I never quite understood the statement that Chowning patented FM (and the term) when it must have been knocking around really early in electronic music.

If the DX7 thing is FM I thought the reason given why it could do more was about the purity of the sine waves and possibly the phase relationships.

I remember Cynthia talking about some people who were into FM that used only filters rather than Oscillators to generate sine waves.

I look forward to other more concrete replies than mine - I spent some time going through frequency relationships and making a note of the timbres created but I didn't really find some of the obvious ones, I forget now but there are FM relationships to create sort of saw, pulse and square waves. One thing is that I probably now have a frequency counter and it's better to use that than a tuner that reads off notes - I would find often I'd need to tweak the tuning of the modulation oscillator from the note.

[bubbajaxx]

I'd like to know more about this as well. Always been well into FM - Yamaha DX, FM8, Operator. When doing FM on the modular I'm not really getting the results I was hoping for... all I know is FMing with analog oscillators isn't through zero FMing - but I don't really get that either.

[thesnow]

it's interesting for example that the DSI Poly Evolver can cross fm using the digital oscillators and not the analog oscillators, the Prophet 12 can cross fm, but the Prophet '08 and Mopho keyboards can not. In a youtube video Dave Smith says he used digital oscillators on the Prophet 12 because you could cross fm the oscillators, which you can't do with analog, he said.

[Mungo]

Plenty of discussions if you search the forums:
viewtopic.php?t=88072
viewtopic.php?p=1323571

[Opus110]

And another:

viewtopic.php?t=65119&start=all&postday ... torder=asc

[thesnow]

Plenty of discussions if you search the forums:
viewtopic.php?t=88072
viewtopic.php?p=1323571

And another:

viewtopic.php?t=65119&start=all&postday ... torder=asc

Thanks.

Not sure if I see anything explaining why fm is achieved more accurately digitally than analog.

Don't think it's a crime to post a new topic similar to past topics either. Or is it a crime on this forum?

Does my topic sound like it's asking whether fm is overrated or not?

Good info in those threads though Mungo. Thanks.

[flashheart]

In answer to the OPs why digital over analogue, this from one of the linked threads answers it well.

If you want really clean FM sounds like the examples on this page:
http://www.modcan.com/emodules/fmvdo.html
you probably need something dedicated that's digital.
In those examples the osc's are locked in absolute math-pefect frequency ratios and that's mostly what makes the difference. Of course you can approximate that in analog or make general clangorous sounds of course. But if you're wanting clean bell-like FM that tracks across 2-3 octaves I'd recommend something like the Modcan.

(my emphasis) Analogue by it's nature isn't precise, digital is. Even very minor changes in relative frequency/phase will change the end result.

[thesnow]

In answer to the OPs why digital over analogue, this from one of the linked threads answers it well.

If you want really clean FM sounds like the examples on this page:
http://www.modcan.com/emodules/fmvdo.html
you probably need something dedicated that's digital.
In those examples the osc's are locked in absolute math-pefect frequency ratios and that's mostly what makes the difference. Of course you can approximate that in analog or make general clangorous sounds of course. But if you're wanting clean bell-like FM that tracks across 2-3 octaves I'd recommend something like the Modcan.

(my emphasis) Analogue by it's nature isn't precise, digital is. Even very minor changes in relative frequency/phase will change the end result.

I didn't see that one! So, basically it's because analog oscillators are continuous and digital is discrete. I guess that makes sense. Am interested in if accurate fm is ever achieved in the analog domain still ever or is it just simply partially inaccurate every time?

[flashheart]

So, basically it's because analog oscillators are continuous and digital is discrete.

I really don't get what you mean by this. The audio output from any decent DAC is just as 'continuous' as any analogue source. Pure accuracy is easier in digital - that's the point.

[thesnow]

um don't really see where digital to analog converters became the conversation here but okay I guess

so "Pure accuracy is easier in digital - that's the point." because "Analogue by it's nature isn't precise, digital is."

okay.

[mskala]

Am interested in if accurate fm is ever achieved in the analog domain still ever or is it just simply partially inaccurate every time?

You can get perfect frequency ratios in analog using PLLs, or fake it in a moderately dirty way with hard-sync. But for the classic phase-locked linear-FM effect you will also need your carrier and modulator to be very clean sine waves without harmonics of their own - which is possible, but tricky. All in all, digital is going to be a cheaper way to achieve this effect.

Edited to add: to be clear, hard sync gives you perfect frequency ratios, but is harmonically dirty. You'd need to filter the result agressively.

[thesnow]

Am interested in if accurate fm is ever achieved in the analog domain still ever or is it just simply partially inaccurate every time?

You can get perfect frequency ratios in analog using PLLs, or fake it in a moderately dirty way with hard-sync. But for the classic phase-locked linear-FM effect you will also need your carrier and modulator to be very clean sine waves without harmonics of their own - which is possible, but tricky. All in all, digital is going to be a cheaper way to achieve this effect.

Edited to add: to be clear, hard sync gives you perfect frequency ratios, but is harmonically dirty. You'd need to filter the result agressively.

THANK YOU.

[Opus110]

Plenty of discussions if you search the forums:
viewtopic.php?t=88072
viewtopic.php?p=1323571

And another:

viewtopic.php?t=65119&start=all&postday ... torder=asc

Thanks.

Not sure if I see anything explaining why fm is achieved more accurately digitally than analog.

Don't think it's a crime to post a new topic similar to past topics either. Or is it a crime on this forum?

Does my topic sound like it's asking whether fm is overrated or not?

Good info in those threads though Mungo. Thanks.

No crime, and I do think it's a great question. Just pointing out for everybody's sake that there is a lot of other good threads on the subject.

People should get defensive when other people make reference to other threads. It doesn't mean "just do a search you lazy bum!", but rather "I'm sure many people will give you great answers on your question but if the subject interests you please note that there are also the following threads you might be interested in".

[thesnow]

No crime, and I do think it's a great question. Just pointing out for everybody's sake that there is a lot of other good threads on the subject.

People should get defensive when other people make reference to other threads. It doesn't mean "just do a search you lazy bum!", but rather "I'm sure many people will give you great answers on your question but if the subject interests you please note that there are also the following threads you might be interested in".

got it, cool, thanks

[Mungo]

Good info in those threads though Mungo. Thanks.

No worries, they're some good background on FM/PM.

In answer to the OPs why digital over analogue, this from one of the linked threads answers it well.

If you want really clean FM sounds like the examples on this page:
http://www.modcan.com/emodules/fmvdo.html
you probably need something dedicated that's digital.
In those examples the osc's are locked in absolute math-pefect frequency ratios and that's mostly what makes the difference. Of course you can approximate that in analog or make general clangorous sounds of course. But if you're wanting clean bell-like FM that tracks across 2-3 octaves I'd recommend something like the Modcan.

(my emphasis) Analogue by it's nature isn't precise, digital is. Even very minor changes in relative frequency/phase will change the end result.

Keep reading that thread because the perfect ratios with FM/PM is largely a myth, the maths behind PM creates harmonic and enharmonic additions with perfect ratios while other ratios will create only enharmonic additions. But both situations are musically useful as the attached audio sample shows.

The stability and tracking accuracy of the oscillators used in FM/PM is the critical parameter for playable FM/PM sounds. Digital oscillators can track more accurately over much wider ranges than analog oscillators and can have much better stability.

[frijitz]

... to be clear, hard sync gives you perfect frequency ratios, but is harmonically dirty. You'd need to filter the result agressively.

Not all that bad, really. My Teezer unit has variable level sync and can lock over a wide range with very little distortion. Documented with sound clips and sonograms here:
http://www.electro-music.com/forum/topi ... torder=asc

Also, please tell us how you would "filter the results".

Ian

[mskala]

I wouldn't. I would use a digital oscillator, or a circuit like yours specifically intended for this kind of thing. But when I wrote that I had in mind someone trying to make do with very basic analog modules that maybe aren't quite so cleverly built. Such a person might do something like this:



Left to right I call these the master, the modulator, the filter, and the carrier.

The common CV drives the oscillators close to a 1:3:5 frequency ratio (or whatever you like), but close isn't enough, the question was about exact locking. So the master syncs the other two VCOs. But then you get spikes in the modulation, which will be noticeable in the final output. (Soft-sync might help reduce this, at the cost of demanding better tracking from the oscillators.) So you run the modulator's output (which, bear in mind, is just a sine wave) through a VCF tuned a little above its frequency. That kills the spikes, as well as improving its sineyness if maybe it wasn't so great to begin with. If the tracking of the oscillators isn't great, you get some distortion in the phases, but much less than if they weren't synced at all. And if the tracking of the filter isn't great, it's no big deal, because it only needs to be accurate enough to stay a little above the modulator.

[MitchXI]

I didn't check to see if it was covered in the threads folks linked to,

but the reason digital fm is so easy to implement is this -

in a yamaha style set-up, an oscillator is simply a ramp that goes from zero to one for every cycle - a phase accumulator - that gets fed into a lookup table that converts zero to one values into a sine wave

if you add a second oscillator's sine output to the ramp wave before the sine wave function, you get an fm equivalent

so each oscillator is a dirt simple ramp wave and a sine wave function. all the oscillators use the same lookup table for sine vales, and in order to have an fm modulation relationship, you simply add the output of one oscillator into the other oscillator's sine wave function.

the only digital computations that need to happen are addition, multiplication(for mod index/amount), and a table lookup. All real simple stuff to do.

Then it's stable because all the digital ramp waves are being generated by a single computer that's running at a certain speed, etc.

The ramps are reset each time a new note is generated and the pitches of each can be exact ratios of the master clock...

[Mefistophelees]

In a youtube video Dave Smith says he used digital oscillators on the Prophet 12 because you could cross fm the oscillators, which you can't do with analog, he said.

Haven't seen that exact quote but DSI usually say it's because they're more precise and you can do more with them.

Analogue FM is great but if it goes out slightly it doesn't really matter because it's usually monophonic.

It's a different story for polyphony where it all goes horribly wrong if the oscillators drift even a tiny fraction. The Alesis Andromeda can provide a very good example.

[thesnow]

this is all awesome information

[timmcg]

From my experience, the FM synthesis being referred to by the OP is linear FM a.k.a Phase modulation. Most, but not all, analogue oscillators have exponential FM inputs which will not give the same kinds of timbres. Using a Doepfer A111-1 for example will get you what you're looking for and I'm sure there are many others out there. Also, my guess to why it's mostly done in the digital domain is the stability and accuracy of digital. If you take most digital synths with multiple oscillators you'll find that there's no phasing... they're all locked together so when you start modulating one with another using different ratios it's going to be predictable. With analogue oscillators there's always going to be some phasing and harder to get reliable results. Try taking the Nord G2 demo software for a spin; it's free and has some oscillators with linear FM input as well as Exponential. Here's a patch that replaces the FM operator Yamaha style of modules they didn't include in the demo. It was easy to do because they included the tools to build what they removed which I really don't understand. PS It's only monophonic but it will give you what you're looking for. Cheers.

[rjungemann]

linear FM a.k.a Phase modulation.

Although phase and frequency are dependent on each other, phase modulation and frequency modulation are mathematically distinct. If you are not changing the rate of modulation, you may not be able to tell the difference, but if you are actively changing the ratio or index, the way the resulting waveform changes is different. "In PM we change the phase, in FM we change the phase increment, and to go from FM to PM, integrate the FM modulating signal. But you can't tell which is in use from the output waveform; you have to know what the modulating signal is."—from "An Introduction to FM"

Update: Here is a more thorough explanation of the relationship between PM and FM: http://moinsound.wordpress.com/2011/03/ ... hnologies/

[thesnow]

awesome, insightful information again and continues.

I guess sometimes it takes a couple days for all of the good ones to join.

[flo]

In a youtube video Dave Smith says he used digital oscillators on the Prophet 12 because you could cross fm the oscillators, which you can't do with analog, he said.

Haven't seen that exact quote but DSI usually say it's because they're more precise and you can do more with them.

Analogue FM is great but if it goes out slightly it doesn't really matter because it's usually monophonic.

It's a different story for polyphony where it all goes horribly wrong if the oscillators drift even a tiny fraction. The Alesis Andromeda can provide a very good example.

The A6 does very nice FM patches. Of course nothing like a DX7, but beautiful on its own.

As has been mentioned by now, I always attributed the differences to a) PM on the DX instead of FM and b) stability of the oscs and c) perfect sines...