Slope functions?

[Chris-S]

Hi,
can someone point me some good hints or links for slope functions?

So, there is a slope parameter (e.g. -1 .. 1) which makes a segment linear (s=0), concave (s=1) or convex (s=-1).

Chris

[hugoderwolf]

Here's a simple one with a parabol segment in the range 0 <= x <= 1:
y = -s x^2 + (1+s)x

However that's not symmetric with respect to the linear version. To get something symmetric you'll probably need to have two versions for positive and negative s, where one would need to include a sqrt. What is this for?

[Chris-S]

For purposes like envelope generator and key velocity scaling.

[stw]

For purposes like envelope generator and key velocity scaling.

If you've normalized values you could do some kind of rational mapping:

Code: Select all

// m is your value at 0.5

b = (m-0.5)/(0.5-0.5*m);
scaledval = (1+b)*x/(1 + b*x);

e.g. m = 0.25 ; m = 0.75 yields to

rationalmap.png

EDIT: fixed typo

[Chris-S]

Thanks that looks good.

[xoxos]

two "cheapies" ... functionality is often inferior for many apps compared to pow/exp style transforms, but "if you can't run them, it doesn't matter.."

inverse "curve" to x*x [0,1]
x*(2-x)

s-curve in same range
x*x*(3-2x)

don't talk about these or ppl will say you're not real dsp

[hugoderwolf]

inverse "curve" to x*x [0,1]
x*(2-x)

That's the same as mine (without the parameter), but unfortunately, it's not at all inverse. Should work fine for most cases though, as long as there aren't any constraints to the derivative at the 0,1 points.

[Chris-S]

Wrote a JS plugin which uses the slope function.

I'm not sure about the best sequence.

I have:

1) Slope
2) Scale (* factor)
3) Offset (+ offset)
4) Limit

slope01.png