Nonlinear Oscillators?

[Dan Slater]

Sean Costello wrote:
> 
> Dan Slater wrote:
> 
> > Hi Sean;
> >
> >         I have done quite a bit of this type of stuff. I wrote an article on
> > this topic that is coming out in the next issue of the Computer Music
> > Journal that you might find interesting. The article is heavily oriented
> > toward analog techniques and includes a number of chaotic patches for
> > analog modular synthesizers.
> 
> Wow!  When does the next issue come out?  I should probably just get a
> subscription (I always put off buying the issues, then get them a few
> months after they come out).  By the time the issue is out, I should
> have my Nord Modular; hopefully the sort of chaotic patches you describe
> can be implemented (I fear that the Nord might err on the tame side, in
> order to minimize aliasing).
> 

	My understanding is that the CMJ issue should be out any day. I did try
to implement a chaotic FM patch in Kyma during a demo of the system and
found that I was fighting the system. Digital technology is just as
capable of chaos as analog is. Almost all designers of digital systems
have put restrictions in their systems that prevent or limit the use of
chaotic techniques. I do not know if the Nord people put these
restrictions in the system. I did try the same chaotic FM patch on a
Buchla analog modular instrument and in a digital computer and got quite
similar results. This is some of what is written up in the CMJ paper.


> >         An even simpler variation is just to take a VCO output and run it back
> > into the FM input. This approach was used in the Yamaha DX-7 as a noise
> > generator.
> 
> I know that Bernie Hutchins had a circuit that used this technique in
> Electronotes - I believe that it was VCO Option 3 in the ENS-76 series -
> but that it was discovered that it caused pitch bends that were
> unsatisfactory, due to the DC component that developed in the feedback
> signal. Still, this is what I had in mind for the TB-303 type circuit:
> VCO with linear feedback FM, with feedback running through a non-linear
> circuit.  It might be difficult to make the circuit simple and still
> retain good pitch accuracy with high amounts of feedback; on the other
> hand, who's to say what would sound good in the given application?


	What you say would likely work. I have found that the 2 oscillator
chaotic FM patch works quite well and have concentrated on that. I have
added various items into the feedback paths including filters, frequency
shifters, reverbs, etc. These devices all change the character of the
sounds in a variety of ways, some boring, some quite interesting. One of
the most interesting patches occured when I took 4 oscillators and
routed them through a quadraphonic sound swirler. Instead of listening
to the sounds in quad I used the rotator to dynamically route the VCO
outputs to the FM inputs. The result was a set of chaotic dynamically
changing feedback loops.

> 
> Hmm...isn't Yamaha FM based on phase modulation, as opposed to strict
> frequency modulation?  If so, are there any analog oscillator designs
> that allow phase to be controlled directly? 

	Phase and frequency modulation are closely interrelated, essentially
equivalent. Frequency is the time derivative of phase. So a phase
modulated oscillator can be made by passing the FM control signal
through a differentiator (a form of high pass filter) and then into a
standard frequency modulated oscillator.

Good luck;

Dan Slater (dslater at ix.netcom.com)