Quadtrature Osc / Shepard Function Generator
1999-09-09 by Tkacs, Ken
>> ...any interest/plans for a quadrature oscillator, or better yet, aShepard function generator?
> Since you brought these up, I will ask you (and others) to offer up someobservations on what these two modules can do and why we would want them in
our MOTM system. I am still quite modular stupid myself since MOTM is my
first modular experience. Larry H.
Sure, I'd be glad to elaborate. Forgive me if I drone... these two devices,
and their uses, are difficult to explain, even simply. This is one of those
cases where, if you heard the effects, you would understand them almost
immediately, but to explain them (without diagrams) is a bit of a chore....
First, for those that don't know what a quadrature oscillator is: Picture
the Sine output of an oscillator, and then tap off that and run it through
an inverter. You now have two locked Sines-one with "0-degree shift" (the
original Sine) and a "180-degree shifted" (inverted) Sine output.
Now, picture shifting the original Sine only 90-degrees, and then taking an
inverted tap off that. You now have four, 'phase-locked' Sines 90-degrees
apart (thus, quadrature).
This arrangement is normally used in LFOs, rather than audio oscillators,
because it can produce some wild stereo/quad panning effects. It can also be
used to drive the modulator input of a frequency shifter (too big a nut to
attempt here). I was first introduced to the effect way back in my college
days when a Teaching Assistant showed me how to take an LFO's Sine, put it
through a passive Lowpass Filter (using it more as a lag integrator) to
squeeze the Sine to a 90-degree shift... Then he balanced levels and used
the 90-degree shifted Sines to feed the modulator inputs of two Ring
Modulators. The effect, as I remember it, was indescribable! There was a
strange auto-panning between the two speakers, and the very slight spectral
shift from the two Ring Mods, mixed back with the original signal, produced
a very subtle, unearthly shimmer.
This is only one application of an LFO in quadrature-anywhere you can think
of using an LFO, let your mind wander as to how you could supplement the
effect with a different phase of the same modulation source. The TA in my
story above used a very carefully tuned integrator to create the phase
shift, but for any real work (and for voltage control of the LFO's
frequency) you need to have the oscillator provide you with the quadrature
outputs.
I have only ever heard quadrature outputs as Sines (or triangles), and only
from LFOs, not audio oscillators. Perhaps getting this to work in the audio
range is too difficult, or perhaps someone discovered along the way that it
was useless!? I can imagine, though, that, having an audio oscillator with
multiple waveshape outputs, and some of them in quadrature, would allow one
to mix the phase-shifted outputs back into a richer waveform to alter
specific harmonics. I'm thinking of this only on paper; as I said, I've
never heard the effect.
Now, *Shepard functions* are very difficult to explain without a pencil, but
the concept is related to the mess I just typed, above. To understand the
Shepard Function, you have to really understand the quadrature oscillator
concept--four sine (or triangle, whatever) waveforms, 90-degrees apart. Now,
fill in another phase between each of those, giving you eight 45-degree
shifted phases of the same Sine wave (you can use more, but eight
["octature"?] is a functional minimum for this effect to properly work).
Okay, NOW... for each of those eight Sines, you need a Sawtooth wave that
shares the exact phase. So you have 8 Sines 45-degrees apart, and 8 Saws
45-degrees apart.
What can you do with this?
The most famous use is the "barberpole" effect. If you're new to Shepard
functions, you really have to bear with me here and visualize this.
Send a signal (in your mind) to eight filters (phase shifters are a classic,
but anything voltage-controllable may be used). The outputs of these filters
each goes to a VCA, and the eight outputs of these are mixed together (they
don't have to be, but let's keep it simple).
Now, take the output of each of the Sawtooths from your SFG and use that to
control the frequency of each of the filters. Then, take the Sines and run
them to each of the VCAs, making sure that the Sine/Sawtooth phase pairs go
to the associated VCF/VCA pairs.
What happens? As the Sawtooth rises (or falls), for each filter, the
associated VCA for each brings the gain up from zero, to full, and then
gently back down again. The overall gain is constant, because the outputs
from all of the VCAs are driven by the "same" control signal spaced evenly
apart (45-degrees). Each VCA reveals a gently timed window on its own
filter, letting the signal pass only as the sawtooth rises (falls,
whatever). By the time the Sawtooth wants to 'snap' back to its lowest
point, that particular VCA has shut off the output completely, and the other
7 VCAs are revealing their own swept filters at some point on the Sawtooth
OTHER than the hard 'vertical.'
What this sounds like is an 'infinite' effect, a 'barberpole' effect, where
the effect is swept in one direction forever-it never seems to cycle around
the way a normal phaser/flanger does when swept by a Sine or Triangle.
I first heard this in the Seventies where eight VCO/VCA pairs were used. The
effect that this created was that of an infinitely rising tone. It just
seemed to go up & up & up in pitch and never go supersonic, never 'fall,'
and never end. A very strange sonic illusion.
I know that this is pretty bizarre if you've never heard of it before-it may
take several reads through. I also realize that it is VERY module intensive
(but weren't we all going to buy 20 of each MOTM module anyway...? :-) ).
But it is a VERY cool effect. Plus, you don't need to use all of the Shepard
outputs all of the time-every other output is a quadrature output, for
instance. Odd combinations of outputs can create very bizarre effects. What
happens if you rig something like the above, but scramble the associations
between the Saws & Sines? I don't know! I want to find out!