Feedback in FM synthesis

[Martin Czech]

great! Thanx for the information, Don.

The through zero PM modulator I proposed some time ago
was simply a piecewise linear network, with tri or saw osc
input as phase pointer.  Saw is obvious to do:


Network input: x
        output: y
        



                /\  y 
                |
                |
             /\ |      /\
     \      /  \|     /  \
------\----/a---\----/b---\------>  x
       \  /     |\  /      \
        \/      | \/        \/
                |
         
As long as your saw stays between a and b, we have
a saw->tri shaper. Now a some dc to your saw.
->phase shift! Amalog phase modulation.
>From tri to saw is obvious...

Saw will give glitches in the waveform, of course.
I guess there is a clever way for doing this with a tri
wave.

Otherwise a slew rate limiter (may be only in the region
where the saw skips back) will do the job.

I'd be very interested if someone trys an actual
implementation.

Don?

You already have such circuits, think of the Haible/Tillman
interpolator.

m.c.



:::Date: Wed, 9 Aug 2000 07:53:22 -0700 (PDT)
:::To: czech at Micronas.Com
:::CC: synth-diy at node12b53.a2000.nl
:::Subject: Re: Feedback  in FM synthesis
:::From: Don Tillman <don at till.com>
:::Web-page: http://www.till.com/
:::
:::   Date: Tue, 8 Aug 2000 09:29:55 +0200 (MET DST)
:::   From: Martin Czech <czech at Micronas.Com>
:::
:::   :::John Chowning's original patent is FM.  US patent 4,018,121:
:::   :::http://www.patents.ibm.com/details?pn=US04018121__
:::
:::   In this patent I see the formula:
:::   e=A*sin(wc*t+I*sin(wm*t))
:::
:::   I think I is intended as modulation parameter independend from wm.
:::   If this is the case, this formula describes PM and not FM.
:::
:::Sure enough.
:::
:::The Chowning patent shares a lot with his article "The Synthesis of
:::Complex Audio Spectra by Means of Frequency Modulation", Journal of
:::the Audio Engineering Society, 1973.  It was republished as chapter 1
:::of the book "Foundations of Computer Music" edited by Curtis Roads.
:::
:::In all cases his equation is, as you note, PM.  
:::
:::But his block diagram ("Music V" notation) in both the article and
:::the patent is clearly real FM.
:::
:::So I just asked Julius Smith about this.  Julius is a professor at
:::Stanford's CCRMA, worked on FM and currently works on a lot of
:::physical modeling stuff, and he used to play in my rock band.  He said
:::that at CCRMA they used both FM and PM implementations.
:::
:::He also said that PM has an advantage because you can use feedback
:::without it degenerating. 
:::
:::I get the feeling that at CCRMA they used the phrase "FM" in a generic
:::way to mean any situation where one digital oscillator is driving
:::another.  But I'm really suprised that none of the papers that I've
:::seen mention the difference between FM and PM.
:::
:::Of course you know what this means; us analog oscillator builders now
:::have to come up with a linear through-zero PM input.  Juergen?
:::
:::  -- Don
:::
:::-- 
:::Don Tillman
:::Palo Alto, California, USA
:::don at till.com
:::http://www.till.com