[LAD] Re: Calculating logarithmic curve for controller automation

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).

Best wishes,

Jeanette
>
> Note that this is a exponential mapping from bars or beats to
> tempo, not from time to tempo (because as the tempo is changing,
> so does the duration of a bars or beat).
>
> Ciao,
>
> -- 
> FA
>
>

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