[sdiy] PM vs FM was: Re: Buchla 295 10-band comb filter topology

[Donald Tillman]

> On Nov 28, 2022, at 9:42 AM, Ian Fritz via Synth-diy <synth-diy at synth-diy.org> wrote:
> 
> OK, I've figured out what the FM/PM disagreement most likely stems from.
> 
> On Fig 8 of the patent the DX7 output is given by the expression
> 
> Sin{kwt + f(w_m t)}
> 
> From fundamental theory, this expression is THE SAME for FM and PM. The difference between the two is in the function f().


Phase Modulation is:
  out = sin(kwt + f(w_m t))

Frequency Modulation would be:
  out = sin((kw + f(w_m t)) t)

Where:
  k is the carrier frequency ratio, 1 in the regular case
  w is the carrier frequency
  w_m is the modulator frequency
  f is the modulator's enveloped sine operation


But what are the implications?

* If you have FM, you can fake PM by taking the derivative of the modulation input.

* Likewise if you have PM, you can fake FM by taking the integral of the modulation input.

* PM naturally goes from sine wave to really bright.  The crisp acoustic-like sounds of the DX-7 are due to PM.  And that was a big deal because nothing like that had been heard from a synth before, 

* The concept of FM isn't helpful in designing voices.  We don't have a feel for what FM variations sound like.  Explanations like "vibrato, only faster" are useless.

* The concept of PM, which I described as "warping the waveform along the time axis", is much simpler.  If you know this, everything makes sense.  And it's a lot easier to design voices.

* With PM you can literally sketch out what the waveform will look like.  Much more difficult with FM.

* In the simple example case (modulator feeding carrier, same frequency) does the phase of the modulator wrt the carrier make a difference?  PM tells you exactly.  FM is actually deceptive; Bessel functions assume a 90 degree difference between the modulator and carrier, but that's never mentioned.

Why am I so insistent about this?  Because the *mechanism* is important.  If you understand the mechanism, you are empowered to use it to do innovative things.

And the "FM Synthesis" mechanism has a weird history of being hidden.  Not intentionally.  But here we are almost 40 years later and there's still a crazy amount of confusion about the basics.

  -- Don
--
Donald Tillman, Palo Alto, California
https://www.till.com