FM synthesis - How does it work?

[jee_pack]

EXACTLY HOW DO YOU PREDICT OR UNDERSTAND THE OUTPUT RESULT OF FM SYNTHESIS?

FOR EXAMPLE:
IF I have a PULSE wave with variable width (the fm modulator) modulating a SQUARE WAVE (the carrier), and both oscilators are at the same pitch. How will the carrier wave be affected by the pulse width of the modulator wave...

Why am I'm asking?
According to a Reason patch, this combination of PWM and FM is supposed to create an OSS SYNC sound, and I'm simply trying to get the logic behind all this. The patch does create a unique sound, its called SyncedUp (in the polyphonic folder of the subtractor patches (factory soundbank), and the mod wheel controls the width of the pulse and consequently adds nice modulation to the final sound...

If you can help me with UNDERSTAND what the FM is doing here, than maybe you're good with understanding what's going on in a wave forms... and if you are, could you please help me figure out how "FM/PWM combination" and "TYPICAL OSS SYNC sounds" look in comparison...

Thanks in advance!

[tony tony chopper]

EXACTLY HOW DO YOU PREDICT OR UNDERSTAND THE OUTPUT RESULT OF FM SYNTHESIS?

in a lot of cases, you.. don't

especially when you're dealing with more than 2 or 3 operators

[mistertoast]

It's kind of nasty. Search Google for "FM Chowning" if you really want to know, but you probably don't.

It's a bit easier to take in if everything is a sine wave. Your example is nightmarish.

[Rusty Shackleford]

well, first, you realize it's not strictly speaking syncing the oscillators, it just sounds a bit like a sync effect. Why not record the output and look at the waveforms to see what the output actually looks like and compare to the initial waveforms?

[tony tony chopper]

and both oscilators are at the same pitch

note that with both at the same pitch, you will have a constant timbre, that's easier to understand

[afreshcupofjoe]

Rusty us right, It's not really a synced oscillator. It just sounds similar. There is a lot of complicated math involved in the resulting sound, so it is kind of hard to explain. Short answer: any time you fm modulate a waveform you are adding harmonics which are located mostly above, but sometimes also below the pitch of the carrier waveform. A modulator of the same pitch as the carrier adds certain even order (natural) harmonics to the sound. A modulator of a different pitch adds more odd ordered (unnatural) harmonics to the sound. The pitch and strength of these harmonics is dependent upon the shape of the carrier waveform. This is where it gets complicated and counterintuitive. Simplest example: If you modulate a sine wave with another sine wave of exactly the same pitch you get something with a very similar harmonic spectrum to a sawtooth waveform. I don't have much experience with modulating pulses, so you are on your own. Probably the best thing to do would be to look at the output of your synth through a scope like smexscope, but since you are in reason you will probably have to record the output and look at it in a wave editor.

[mistertoast]

Yeah, and note that osc sycn ALSO adds harmonics, so it's not unreasonable to expect that some osc sync sounds sound like some FM sounds.

[tamahome]

Does this help?

http://www.soundonsound.com/sos/apr00/a ... ecrets.htm

[jee_pack]

UHHHHH... lol, I get the point. Thanks a lot for explaining this though, perhaps I should take a different approach to it then... by the way, I already took at look at the spectrum, and its a very interresting looking wave form, perhaps, this will shed light on everything (without having to go through the math):





So forget the math, I know this seems to be nightmareish, but if you look at these pictures, would you be able to guess why this patch in particular is SyncedOss and not just any sound like SquareFM or something like that. A nightmare maybe, but I'm far from an expert in FM and synthetising, and the point of all this is to see what kind of sounds I can do with FM, I've read that FM should use SIN waves because other waves will create noise, but this patch doesn't use SIN WAVES and has quite a nice sound to it... so I'm lost and confused, should I just go by trial and error (cuse if you're experienced and that's how you think I should go about it, I'll gladly take the advice and apply it), but if you have anything ground rules, or FM tricks or tips you know, anything that will make me guess a bit less when I turn on the FM knob, that would be well satisfying.

thanks

[secret bass]

FM synth programming really isn't as hard as it's made out to be. There's only a few really key concepts.

One is realizing that the more one operator modulates another, the noisier the sound gets.
Another is just pairing off operators and having them do specific parts of a sound. For example, have operators 1 and 2 provide the initial attack of an e-piano sound, and operators 3 and 4 doing the more bell-like decay.
Remembering to use the envelopes is also another quite useful programming technique. Each operator has an ADSR envelope for a reason!
The ratio or tuning of the operators affects the timbre of the sound quite significantly. It's worth experimenting with it.
Finally, unless you really really really hate yourself, don't try and program FM on the TX81Z without an external editor.

[afreshcupofjoe]

Welcome to the world of FM synthesis. Get ready to have you mind blown to pieces. You are about to enter a very strange and wonderful world. That SOS is a really good starting place. Highly recommended.

That waveform is really strange because it has a random fragment of a heavily offset sin wave mixed with a pretty typical looking fm waveform. Looks something more like switching duty cycles like you'd see in maybe a phase distortion synth, but I really have no idea. It would be cool if you could post an audio clip, so we would have more of an idea of what's going on here.

If you want to explore FM synthesis, then a subtractive synth really isn't the best place to experiment. A real FM synth will have at least 4 osc with their own envelopes and special tuning and modulation features that are more suited to getting interesting FM sounds.

Sine waves are usually easier to work with for FM because the results are more predictable, and since you are adding harmonics every time you add a modulator it's good to start with something that doesn't already have a full harmonic spectrum. That doesn't mean that pulse waves can't produce interesting sounds too, but they start to get messy once you change their pitches, and the sounds you can produce are more limited before it starts to turn to noise.

The best tips I can give you for exploring FM is to think of it in terms of subtractive synthesis. In subtractive synthesis you are starting with a waveform with a lot of harmonics and then changing the harmonic spectrum by filtering some of those harmonics out. What harmonics get filtered out or added back in are controlled by an envelope or LFO connected to the filter. There can be much more involved, but this is the basic idea behind subtractive synthesis.

With FM synthesis you are doing something similar using a very different method. You're goal is still to alter the harmonic spectrum of a waveform over time, but instead of changing the harmonic spectrum with a variable filter you are changing the harmonic spectrum by varying the amplitude of various carrier waveforms. Slowly adding in a carrier waveform can be very similar to opening up a filter on a subtractive synth if the carrier and modulator have an even pitch relationship.

Once you start varying the pitch of the carrier waveforms you enter a whole new world of sound because you can drastically change how the harmonics relate to the fundamental and get all sorts of shifting sounds with harmonics that not only change in amplitude but change pitch in relation to the fundamental. Very cool stuff.

The only problem is that the results can be much more unpredictable than with subtractive synthesis, so it takes a lot more experimenting, but it can be very rewarding.

[tamahome]

'How to make a noise' has a pretty good non-math chapter on FM:

http://www.noisesculpture.com/index.php

[jee_pack]

thanks! your explanation afreshcupofjoe was pretty usefull. What I'm going to to do is examine how the wave looks without fm, and then I'm going to browse a few other subtractor patch to get a general idea, I think I guess how this works... You can see its almost like a sin wave with added harmonics that pulse... like a filter opens and closes real fast. It makes me think of something a read in the user manual: "in theory, a resonant filter can strip down the harmonics of any wave form and bring it down to a sin wave"... This is like an on/off switch to this filter going on and off at intense speed, giving this unique sound... I sort of get it... But out of curiousity, can this sound actually relate to oss sync in any way? and is oss sync something I can just push aside untill reason comes out with a better synth... I mean, does it realy create such a unique sound or is it just some random thing that can be replaced with fm? thanks again

[mistertoast]

osc sync is mostly interesting when the frequency is modulated or swept.

Do you need it?

No. After all, Skip James just had his guitar and his voice.

[jee_pack]

HA! toucher!