>
> A very simple parametric curve is
> y = (1 - x) / (1 + a*x)
> With a = 0, you get a line thru 0,1 and 1,0
> With increasing a, you bend the line to almost a sharp angle.



Hello Stefan.

Indeed, that's a simple parametric, but for generating envelopes we have
the freedom to depend on the previous sample's output.  So, while an
exponential curve parametric-style requires a pow(), the iterative solution
is simply current = previous * multiplier.

Adding a range of curves can be done by adding a delta, as Andre/Werner and
I have independently discovered (along with probably many others).

And "current = previous * multiplier + delta" is going to be fewer
calculations than a parametric formula such as yours.  So I suggest the
Andre/Werner/my method seems faster for the specific application of
envelopes, as well as offering true exponential curves.

My synthesizer is a programming language, not a graphic synth, and includes
curve and s-curve functions that are parametric, and indeed use the exact
function you mention!

http://moselle-synth.com/

Thanks, Frank
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