Allpass stage tuning, & allpass-based vibratos

[Sean Costello]

Hi all:

As part of the ensemble discussing that has been going on recently, Harry
Bissell asked me a very interesting question:

> The Nat Semi design uses stagger tuned stages for the all-pass (I think univibe
> also) but most use equal values... Any Idea why ????

I have a paper somewhere by W.M. Hartmann (from a 1977 or 1978 JAES) that
explains why equally-tuned stages are the most useful for phasing effects.
However, what if you are trying to obtain a vibrato from phase shifting? Would
equally-tuned stages work best, or are staggered values more useful? Also, how
many stages would be needed for a good vibrato sound? 

I guess the big question would be: Does an allpass-based vibrato system preserve
the relationship between the input frequencies, or are the input frequencies
shifted out of harmonic relationship during the vibrato excursion? I know that a
frequency shifter can implement vibrato, but I also know that these frequencies
are not maintaining their proper harmonic relationship. Does the same thing
happen in a phase shifter-based vibrato? The answer might be a simple one, but
it is too much for my tired mind to figure out tonight - I am trying to put up
web pages for all of my Csound compositions & instuments, and it is rather
draining.

I will be implementing a few new allpass-based ugens in Csound this week, that
should be more useful than my first one. I found a nice paper by Julius Smith,
that describes using cascaded second-order allpass sections to have direct
control over notch frequency, width and depth in the standard phaser
configuration. I should be able to conduct a few more fruitful allpass
experiments once I have these ugens in place.

Thanks,

Sean Costello