exponential rising (was Re: definition of Syncing)

[Don Tillman]

   Date: Tue, 26 Nov 1996 16:18:45 -0600 (CST)
   From: DJMaytag <djmaytag at terracom.net>

   curious question (possibly stupid, but who knows?): what would it sound like
   if you had an exponentially rising voltage across that same cap? interesting
   sounding waveform or no?

First off, it won't happen directly in a VCO implementation as the
linear rise is entirely important in determining the frequency.  A
comparator waits for that voltage to hit a certain point to reset
things and if the rise isn't linear the pitch will be way off.

But no matter... you're really asking about the waveform.  

It'll be somewhat sawtooth-like, containing all harmonics, but they'll
decay off more slowly than a sawtooth, so it'll be brighter.

If you are interested in the exact harmonic content it makes a nice
little exercise to work out the Fourier transform of this waveform.

In general, any given waveform won't be all that exciting; it's just
going to be a harmonic series.  Exceptions happen when there's
something really blatent, like all the even harmonics missing as
with a square wave.  Or when you can impart a change to the harmonic
series in an interesting way.

   Date: Wed, 27 Nov 1996 00:26:38 +0100
   From: Patrik Erikson <me95pen at ing.umu.se>

   An exponentially rising waveform across a cap.???  That's the inverse
   function to the caps' normal behaviour, isn't it? 

I have no idea what you mean by "inverse", but a capacitor with a
resistive load will naturally do an exponential decay.  And since
waveforms sound alike whether they're going forwards or backwards, a
single cycle of Mr. Maytag's suggestion will sound like a capacitor
decaying.  But how do you repeat the cycle?  See below...

   From: chordman at concentric.net (Synthaholic AKA sPEW)
   Date: Wed, 27 Nov 1996 03:45:46 GMT

   Assuming the commonly available linear sawtooth whose wave form rises
   from zero to some positive voltage and quicky returns to zero, this
   could be applied to both sides of a two (or four) quadrant multiplier,
   (ring modulator).  The output would represent the square of the input.

That's a similiar shape, but different.  It would be a nice exercise
to derrive the harmonic series of that one too.

   Date: Wed, 27 Nov 1996 10:21:12 +0200 (EET)
   From: Mikko Helin <MHELIN at tne01.tele.nokia.fi>

   I think it would sound like tb-303, which has actually
   exponentially _falling_  sawtooth. Interesting? 

Someone paid you off to bring the 303 into this discussion, didn't
they?  

   From: Mark Smart <smart at nn.com>
   Date: Wed, 27 Nov 1996 11:21:41 -0600 (CST)

   Well the ARP Omni's (here I go again with the Omnis) tone generation
   circuitry uses exponentially decaying sawtooth waves. 

Exponential over half the cycle, yeah.  That's done as a poor-man's
sawtooth -- when you need a whole bunch of roughly sawtooth waves and
your TOG/divider-chain only puts out squares, it's a very reasonable
solution.
							The RC circuits
   are crudely tuned to each square wave's frequency (in some cases by
   chopping off part of the ceramic disc cap and covering up the exposed
   electrolyte with fingernail polish!).

This is a joke, right?  You're kidding, right?

  -- Don