[sdiy] Re: Spiral Waveforms

[Ian Fritz]

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.

   Ian