[sdiy] Re: Spiral Waveforms

[Magnus Danielson]

From: Scott Gravenhorst <music.maker at gte.net>
Subject: [sdiy] Re: Spiral Waveforms
Date: Sun, 11 Apr 2004 07:49:58 -0700
Message-ID: <200404111449.i3BEnwg13072 at linux6.lan>

Hi Scott,

> First, I think that everyone was caught off guard by Steven.  No one knew
> until days later why he responded the way he did.  After reading about AS,
> his posts make more psychological sense.  I doubt the group reaction would
> have been as it was had we known, I don't believe that anyone here is
> intentionally cruel.

Now you've got me off track here. This thread has been so full of feelings that
I've stayed out of it so far. What am I missing?

(BTW. I'm sad to see so much reactions here, this used to be a quite little
heaven but if people are going to continue like this... no, now.. behave!)

> That said, here are my random synapse firings...
> 
> Ian's description notes that a constant angular velocity yeilds a constant
> output frequency,

Which in my mind is really the definition of frequency. Given the phase-state
you can get all other aspects of time-variance from derivations of more or less
complex style.

> which is a good thing for tonal music.  But this doesn't
> seem all that easy to do in analog electronics.  Sawtooth and triangle
> oscillators try to do this by using a linear current to charge a capacitor.
>  The sawtooth has the nasty reset time that perturbs constant angular
> velocity.

Well, we try to compensate that out.

>  I'm not sure, but triangle oscillators may also exhibit this to
> a lesser degree at ramp direction reversal time due to the finite amount of
> time it takes to switch the current source's polarity.

Yes, but usually you should be able to balance the positve and negative
reversal times fairly well. It is now the difference between them which is
important for outgoing frequency, so the first-degree error is by default
compensated out.

> Once we get away from linear ramps, things get difficult.  Someone correct me
> if I am wrong, but sinewave oscillators don't operate by following a dot as
> it goes around a circle with constant angular velocity. 

You really *SHOULD* take a look at how a sine/cosine oscillator built around
a state-variable works, since it actually does exactly that, follow the dot
around. Here there is an error, and that error is in the difference of gain in
the first and second integrator. Also, the integrators isn't perfect
integrators but has some leakage. This causes the circle to be slightly
elliptic and slightly titled.

> Of the difficulties involved, it seems to me that there are two main
> requirements: 1) a circuit to establish and maintain the spiral and
> 2) a circuit that can provide a projection of the spiral placing a "light
> source" at a given angle.  One way to approach this might be the use of
> quadrature, would simple panning provide the projection?  If one distorts the
> quadrature outputs, the angular velocity is maintained, but would panning
> still give a (variable) projection?  It seems that this idea might be more
> easily implemented using DSP or other digitally computed methods.  I can't
> envision how much different this would be from what we already do with
> oscillators and waveshapers.

I have an old article on how to make oscilloscope art using Paia modules.
In essence you hook up the scope at the different outputs of a Paia filter
module (a state-variable). Creating a spiral waveform isn't very difficult,
since you just send in a tick and then the high-Q setting allows the filter to
ring and the two out of phase outputs will provide the X and Y waveforms and
forming a spiral.

The higher Q, the less energy the ringing loses per cycle, and thus the denser
will the spirals be.

You don't need any DSP to do this, I could have my SEMs do it for me! Or for
that matter, the ASM-1. If you have an ARP 2500 standing in a corner collecting
dust I'm sure you can do it with that too, since it too has a SVF filter.

Is this what you guys have been fighting about or what?

Cheers,
Magnus - puzzled