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

Ian Fritz ijfritz at comcast.net
Fri Dec 2 09:54:50 CET 2022

For standard FM, you write the instantaneous frequency as an initial frequency plus a sinusoidal modulation. To get the phase you integrate the instantaneous frequency. This results in w_init t + Integral(Acos w_m t), where the second term is (A/w_m)sin w_m t . The difference between PM and FM is just the factor of 1/w_m .

I’m out of the country for a few weeks, but I’ll try to keep up some with this discussion.

Ian

> On Dec 2, 2022, at 6:38 AM, Donald Tillman <don at till.com> wrote:
>
> ﻿
>> On Nov 29, 2022, at 5:29 PM, Ian Fritz <ijfritz at comcast.net> wrote:
>>
>>
>> Oh, you should look at the Chowning/Bristol book again.  They go step-by-step teaching how to understand FM.  And as mentioned before they treat the DX7 as an FM synth.  Their DX7 exercises and examples would not work for a PM synth.
>
> Okay, let's check it out...
>
> The book is called "FM Theory & Applications, By Musicians for Musicians" by Dr. John Chowning and David Bristow.  A pdf scan is easy to find on the interwebs.
>
> Oh dear, this is very badly written.  No matter...
>
> So let's try an experiment.  I've got a DX7II-FD here.  It's been a long time; dusty, presets rotted away, 'forgot how to use the thing...
>
> Okay, Alg 3.
> Op2, 2x frequency, level 70
> Op1, 1x frequency.
>
> And this is how you make a DX-7 square wave:
>
>
>
> One of the cool things you can do with PM is to use an audio signal to modulate a low frequency oscillator.  (Huh?  That sounds so backwards.)  This creates a phase shifty chorus sound, so it's a sweet trick for Hammond patches.
>
> If the DX-7 used frequency modulation, that would integrate the above square wave into a triangle, while phase modulation would preserve the square wave.
>
> Move Ops 1,2 up to 2,3 and set Op1 to 1Hz.
>
> Groovy:
>
>
>
> And this works across the keyboard.
>
>   -- Don
> --
> Donald Tillman, Palo Alto, California
> https://www.till.com
>
>
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