[sdiy] Good Expo curve for VCA use..

[rburnett at richieburnett.co.uk]

> It's of course easy to justify an exponential decay, but I think it's
> a little harder to evaluate "naturalness" of attacks...

I think the attack shape produced by analogue ADSR envelope generators 
sounds natural to us because the "inverted exponential attack" shape 
does closely mimic what is seen in nature.

We know that the amplitude of oscillation in a high-Q resonant system 
will decay away exponentially when the excitation is abruptly removed, 
but a similar behaviour occurs in the attack phase.  The amplitude of a 
high-Q resonant system will also "ring-up" with the inverted exponential 
shape when excitation is abruptly applied.  (...both of these curves 
theoretically taking forever to reach their steady-state settling 
points!)

In the general case, whenever excitation is abruptly changed a linear 
system's existing response will decay away exponentially, and the new 
steady-state response will grow with an inverted exponential attack.  
The response at any given point in time is a weighted superposition of 
the old steady-state response and the new steady-state response, and 
sweeps exponentially from old to new.

-Richie,