[sdiy] Re: Spiral Waveforms

[Magnus Danielson]

From: Scott Gravenhorst <music.maker at gte.net>
Subject: Re: [sdiy] Re: Spiral Waveforms
Date: Mon, 12 Apr 2004 08:20:56 -0700
Message-ID: <200404121520.i3CFKug21021 at linux6.lan>

> Ian Fritz <ijfritz at earthlink.net> wrote:
> >Hi Scott --
> >
> >At 08:49 AM 4/11/2004, Scott Gravenhorst wrote:
> >>Ian's description notes that a constant angular velocity yeilds a constant
> >>output frequency, 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.  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.  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.  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.
> >
> >Thinking in terms of directly generating spiral waveforms I agree with 
> >you.  It would be tricky.  But using the waveshaper approach -- starting 
> >with a sine and distorting it with various algebraic manipulations -- isn't 
> >difficult in principle.  I would say that the important question is whether 
> >a simple circuit could give a useful range of dynamic waveforms.  It seems 
> >worth thinking about a bit.
> 
> I don't see this as conceptually different from what people already do with
> modulars, i.e., sine wave to waveshaper, or any-wave to waveshaper for that
> matter.  If the output is to be a single waveform, generated from a single
> waveform, how does the spiral come into play?

I've yeat to understand how a "spiral waveform" behaves if it is substantially
different from a decaying sine (or for that matter accelerating). Given a sine,
you need an exponential increase/decrease generator (really just a single-pole
diff-system) and a VCA to control the amplitude of the sine.

Is anyone able to draw one? Are we chasing bigfoot or could somebody please
explain what this "spiral" aspect is indicating.

Cheers,
Magnus