[sdiy] Generating acyclic waveforms?

[Magnus Danielson]

cheater cheater wrote:
> Magnus,
> How does the effect you describe work? Does it have a name? Do you
> think that it can be used for audio-rate oscillators, even if not
> necessarily with voltage controlled frequency?
I think you need to look into physical modeling.

The issue is that the phase-delay or for that matter group delay at the 
end of the resonant cavity isn't perfectly matching up, such that the 
effective resonant length is somewhat different or for that matter the 
resonant period.

The impedance error at the end of an open cavity and the way the 
effective reflection
behaves in the time-plane shifts over frequency. The shape of the mouth 
is of interest in the acoustical sense.

Physical modeling using two delays (to simulate the two directions of 
the wave) and then analogue networks for reflection impedance simulation 
would pull it off. It is however not very near out normal VCOs in 
architecture.

Scott Gravenhorst have look at similar things:
http://home1.gte.net/res0658s/FPGA_synth/
http://www.fpga.synth.net/pmwiki/pmwiki.php?n=FPGASynth.DigitalWaveguide

https://ccrma.stanford.edu/~jos/swgt/swgt.html
https://ccrma.stanford.edu/~jos/swgt/Wind_Instruments.html

If you want to go in deep:
https://ccrma.stanford.edu/STANM/stanms/stanm39/
(185 pages, acoustical impedances and all)

In essence, for the fundamental and for instance the 3rd overtone to be 
perfectly harmonic to each other, their round-trip delay needs to be the 
same. If the group delay is different (relevant for noise input when 
blowing), they will not be perfectly in tune but somewhat shifted.

Cheers,
Magnus