Hi looking for some help creating a modulation matrix for an fm synth similar to the one that's found on Native Instruments Fm8? Total pd noob and trying to create a basic fm synth with several operators for my uni course. I want to be able to set it up so any operator can modulate any other as well as feedback into itself or further back in the chain etc etc, like the matrix on the fm8. Struggling to get my head round how to set this up. Any help at all much appreciated.

Thanks in advance

Hi! I've done some fm with feedback lately for a Camomile plugin. If you don't mind doing archeology, the patches are here: https://patchstorage.com/pmer/

I think the best way to do multiple operators with feedback is something like this:

your matrix will need to be able to detect feedback paths and route them correctly through the single sample delay. it's possible if an oscillator is fed back into itself and also routed into an earlier oscillator that then feeds the first oscillator you will end up stacking delays? is this true?

Thanks I will have a look through those. As I said I am a pure data noob so pretty unsure about all this but if I get anywhere with it I'll report back.

This is what I have so far if anyone wants to have a look,
fm experimenting_3.pd

I basically have two operators in sub patches directly modulating the one carrier. I was thinking there might be some kind of magic that i could do with send~ and $ that would allow me to have them all modulate each other or/and themselves? I may be thinking far too simple but as I say im a bit of a noob so unsure on all this.
Thanks

@djpersonalspace This is what I have so far if anyone wants to have a look,
fm experimenting_3.pd

I basically have two operators in sub patches directly modulating the one carrier. I was thinking there might be some kind of magic that i could do with send~ and $ that would allow me to have them all modulate each other or/and themselves? I may be thinking far too simple but as I say im a bit of a noob so unsure on all this.
Thanks

the method weightless uses here is really good! https://forum.pdpatchrepo.info/topic/10745/3-op-fm-synth-with-mod-matrix/3

i opened up that patch and the crux of it is using tabsend~ and tabreceive~ with a block~ 1 1 1 to delay the outputs of each operator by one sample. (i am wondering now if this is a better method to get a one sample delay than using delwrite~ and delread~, i need to do some testing. at the very least, it's wasteful to use a delwrite~ with a buffer of an entire 7 ms)

the tables that tabsend~ and tabreceive~ use store only a single value each.

so each operator receives fm input one sample later than it arrives at the fm input. this is a totally negligible delay for normal fm, and feedback is only possible this way, because the phase can't be calculated and take feedback into account. the feedback must be from 1 sample in the past because otherwise it hasn't been calculated yet.

the $ arguments in the patch make it easier to make separate multiples of things. if you have time to go through the documentation about abstractions and arguments, that will be very useful for synth stuff generally.

i can draft up something that breaks down the tabsend/receive method this evening, but you should spend some time with the patch by weightless because it's great

Okay thanks. A lot of this is over my head so far to be honest but I'm pretty determined to understand it so I will spend some time on this patch and do some research to figure out how it works. Thanks for all the help !

Here's another take that might be lazy and dumb, but i have a suspicion that it is fine:
pmmatrix.pd

needs a lot of work before it will fit into a project. normal modulation from one operator to the other sounds fine to me. feedback sounds about right too. keeping the buffer on the delays down to 0.05 should be fine for sample rates down to 22050.

Awesome! I've been reading about this stuff all night but I'm clearly going to need to spend a good bit of time actually researching how PM synthesis works before I'm able to implement this successfully. Thanks for the patch its gonna help a lot

(I'll write here just to keep all the fm discussion in one place).

@LarsXI this is a great trick I hadn't thought of, sounds identical to the [tabsend~] method to me. I'm curious to experiment with it and see if it's cheaper on the cpu. Delay lines can get down to 1 sample delay without [block~] with the order of execution (G05.execution.order.pd). This won't work for feedback though.

hey! yep, i ran multiple instances of tabsend/recieves and then the delays, both in block~ 1 and it looked like the delays were slightly less cpu heavy, but i didn't check RAM. i'm still a little paranoid about cross modulation- like what if the fundamental gets negated if certain modulation is running 1 sample behind. but that's probably nonsense! especially since the phasor~s aren't phase synced anyway

i'm working on something now that i'm really excited about that has a simple 2op structure that feeds back into itself. I love fm feedback sounds so much.

the rzero~ -1 i copped from this thread, https://forum.pdpatchrepo.info/topic/6185/feedback-fm-algorithm/10

i wonder if there is an effect of putting that in front of the feedback delay

@LarsXI In the 3-op synth patch you mentioned there is an option the synch the phasors when you hit a new note, I don't know if that helps with what you are saying.

It's good to know that it's a little cheaper, anything helps as by the time you add polyphony things add up pretty quickly. I think that making a full-blown polyphonic 6-op synth with this method is pretty unrealistic, I think it's interesting to experiment with less operators and different waveforms. I did modify that 3-op synth with added waveforms like the TX81z, but then got carried away and added CZ-style oscillators too and that messed up the patch and I never had time to fix it.

I look forward to your 2-op patch, those camomile plugins you posted sound pretty sweet.

thank you!!

okay, yeah. actually now that i understand better how vline~ works i guess it would be possible to phase sync without using the sample and hold method. if i'm sending pitch with a vline~ i have time to send a phase 0 message to my phasors. i should revise some of my lfo designs that use sample and hold reset for no benefit.

i just need to make sure i'm not reseting phase on a stolen note to avoid clicks.

i used to have a tx81z and a dx11 and i have a strange suspicion. they let you set a ratio for operator pitch, as normal. then, they let you choose one of 7 options for oscillator detune. you do not select detune in cents. this could mean that each voice only has one phase accumulator/phasor-like osc. the ratios are set by multiplying and wrapping that ramp before a sine shape. when detune is selected, it's possible the synth uses one of six cheap low-frequency beating oscillators to send to the phase inputs of all the operators that are set to be detuned.

yep, this creates two sine tones, 2 Hz apart...

the phasor~ 2 would be common to all voices

in polyphonic material it might be fine, as long as each voice received an arbitrary dc offset. but it would spoil per-voice pitch envelopes. the dx11 has pitch envelope, but it definitely targets the pitch of all operators at once.

on second thought, i'm pretty sure i'm wrong about this one, because of the fixed ratio operators in the tx81z/dx11

txdxdetune.pd

this patch is still kind of interesting and you would save a good bit of processing. on a 4 op 8 voice synth, you would save 23 phase accumulators total, but have reduced control over individual operator pitch.