Nonlinear Oscillators?

Dan Slater dslater at
Thu Jul 9 02:41:06 CEST 1998

Sean Costello wrote:
> Hi all:
> Has anyone out there tried to construct a nonlinear oscillator?  By
> "nonlinear" I mean an oscillator that behaves like the nonlinear
> elements in a traditional musical instrument (like an overblown reed, a
> bowed string, etc.).  I would love to have a musical instrument that
> could jump octaves like a wind instrument (i.e. with the same sort of
> noisy transition, not just clean octave jumps), or generate chaotic
> subharmonics like a Gyuto monk, or growl like a sax, or create
> multiphonics like an oboe.
> Any ideas?  I was thinking that perhaps linear feedback FM could be
> used, where the output is fed back through a nonlinear element (like a
> full-wave rectifier, or any of the Serge waveshapers, or perhaps
> something like the Dual Slope Generator) before going back to the FM
> input.  Ideally, the oscillator would be able to track through a
> reasonable range under voltage control, and have the nonlinearities
> under voltage control to a reasonable degree.

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.

	Anyway it is quite simple to do. You can use the classic chaotic
circuits such as the Ueda Attractor or Chua circuit.

	The mandatory requirement of a chaotic system is a non linear feedback
path. Any system with non linear feedback can go chaotic if there is
sufficient gain. Therefore, the ideas that you proposed above are quite
capable of producing chaotic signals. 

	A simple approach that sounds even better than the classical chaos
circuits is just to cross couple a pair of FM modulated sine wave
oscillators. Simply take oscillator 1 output and FM modulate oscillator
2, similarily take oscillator 2 output and FM modulate oscillator 1.
Make sure that you have adequate gain in the FM paths, if not you will
not be able to get the full spectrum of sounds. You may need to add
amplifiers in the FM paths. The FM inputs are inherently non-linear as
the transfer function is dependent upon the instantaneous oscillator
phase angle. You can get anything from pure sine waves to pure white
noise from this patch. Likewise, "overblown" sounds and octave jumps are
quite easy to get.

	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

Good luck;

Dan Slater (dslater at

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