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

[Ian Fritz]

With a careful reading of the Yamaha patent it is easy to understand how the FM signal of the DX7 is generated. The algo is quite simple:

1) A keypress produces a carrier wave with a frequency w (omega)

2) This frequency is multiplied (modulated) by a time-varying signal called a scale factor k. The resulting product is the instantaneous frequency of the system.

3) The instantaneous frequency values thus calculated are fed to an accumulator, which produces the time-integrated value of the instantaneous frequency. This is the phase of the output signal.

This is a calculation of a standard frequency-modulated signal. This is obviously FM, simply because the frequency is what is modulated (not the phase).

This algo is EXACTLY analagous to the analog circuitry we use for making FM modules:

1) A carrier frequency is generated via the V/Oct input and the usual exponential control current generator
 
2) This current is multiplied by the value of the signal fed to the Lin FM input

3) This product is fed to the integrater which is part of any VCO to produce the FM signal

Looks to me that Chowning and Yamaha are correct in saying the DX7 is an FM synth.

Ian




> On Nov 27, 2022, at 7:00 AM, René Schmitz <synth at schmitzbits.de> wrote:
> 
> Hi Ian and all,
> 
>> On 27.11.2022 00:30, Ian Fritz via Synth-diy wrote:
>> Many years ago on this list I asked why a distinction was made between PM and FM, as they are equivalent, phase being proportional to frequency (at fixed frequency, of course).
>> 
>> In response, Juergen Haible pointed out the difference only becomes relevant when considering what happens to the signal when you go up and down the keyboard. For FM the waveform stays the same. For PM it does not. This behavior can easily be seen in the standard textbook equations going back to early radio theory.
>> 
>> The book by Chowning and Bristol, “FM theory and applications” deals extensively with the DX7. It is specially noted more than once that the DX7 waveform does not change with keyboard pitch. So from this fact and the book title I conclude the DX7 does indeed produce FM signals.
>> 
>> So why is there this apparent disagreement? Does the DX7 waveform change with keyboard pitch or not? I’ve asked this question before but never got an answer. I do not have a DX7, but the waveforms of the plugin emulations I’ve seen are constant.
>> 
>> I’ve looked at a Yamaha patent and seen how the computational engine works. It does, of course, calculate in terms of changes in phase. But that does not necessarily mean that what is calculated is a standard PM signal, does it?
>> 
>> Ian
>> 
>> 
> 
> A PM waveform should stay the same too.
> 
> Provided you move both carrier and modulator in the same manner. If you turn off operator tracking on a DX7, or it's emulations then of course not...
> 
> Comparing output waveforms on one particular implementation, can not be considered definitive proof.
> 
> As there are too many other accidental influences . (Including operator error, firmware secret sauces, filters, EQs, bypass caps, distortion, what not).
> 
> 
> Sonically, both PM and FM can cover pretty much the same terrain.
> 
> In a nutshell the difference between PM and FM is what happens when the modulating operator has a DC offset.
> 
> With plain FM you get a net de-tuning (and your note is off), with PM you only get an inaudible phase difference.
> 
> This is what makes PM the mode that is musically more useful.
> 
> (For FM you integrate over this offset, and that DC creates the rising phase that detunes things.)
> 
> When you do complex patches with several cascaded operators, any integration error gets worse, as now your frequency ratios are off.
> 
> 
> 
> Best,
> 
>  René
> 
> 
>> 
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