[LAD] Re: Calculating logarithmic curve for controller automation

Il giorno ven 24 feb 2023 alle ore 00:59 Jeanette C.
<julien-3g/[email protected]> ha scritto:
>
> Feb 23 2023, Fons Adriaensen has written:
> ...
> > So if the start and end values are A and B, you would make a linear
> > function from log (A) to log (B), and then use exp () on that to
> > find the tempo at any point.
> ...
> Thanks! This is fascinating. Starting with an exponential curve i.e.
> first get exp(a) and exp(b),, get the linear function and calculate the
> values by log(a + inc), it makes a huge change in the curve shape when I
> scale in input arguments a and b. So starting with exp(120) to exp(150)
> is a very steep curve, whereas exp(1.2) to exp(1.5) and a rescaling post
> all other calculations gives a much gentler slope. Whereas the same
> exercise beginning with log makes no difference going from log(1.2) to
> log(1.5) and scaling up the final values to 120 to 150 is no different,
> at least to three or four places after the decimal point, to starting
> with log(120) to log(150).

Given any three points (x1, y1), (x2, (y1+y3)/2), (x3, y3) where
y1>y2>y3 or y1<y2<y3 you can find an exponential function passing
through them as explained here:
https://www.orastron.com/blog/potentiometers-parameter-mapping-part-1
(+ "output scaling").

In other words, you can choose a midpoint of your liking and build an
exponential function passing through it and the extremes.

-- 
Stefano D'Angelo
https://www.orastron.com/ - https://dangelo.audio/
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