[ardour-dev] slider_postion2gain analysis

[gerard van dongen]

My math hobby strikes again :)

Hope somebody finds this useful, otherwise I had fun figuring it out  
anyway.


The slider_postion_to_gain function used in ardour =

pow (2.0,(sqrt(sqrt(sqrt(pos)))*198.0-192.0)/6.0)

which is really (ascii math)

           1/8
   (198 * p     - 192)/6
2

equals



                1/8
   ((32+1) n * p   -  32* n) / n
2

where n = 6
hmm, divide out n
this is actually just pow(2,sqrt(sqrt(sqrt(pos)))*33 - 32)

well there is one little bit of code optimization anyway.

and this gives unity gain at 0.78178675, 2 at p=1 and pow(2, -32) at 0  
which is nice because we work with 32 bits

So the problem is I want my midi controller to give me gain G at position  
P (where G is allready translated to [0,2] and P to [0,1]

so now the formula is
             1/8
      (x+1)*P    - x
G = 2

solve for x gives:
                     1/8       1/8
x= ( (logG/log2) - P   ) / ( P    - 1)

_and_ we want x >= 32 (or can it be smaller ? , say 24, I don't know)

which constrains the possibilities
f.e. I want at P=0.6 G to be 0.8 that requires x to be 20.37061 so that is  
not good enough.

Obviously (or I should have seen it before starting this mail) you can  
only adjust downwards then, if you want 0 to remain 0
What that means is that if you want your controller to behave similarly to  
ardour's faders, and you can only set G at a lower value than the current  
slider_position_to_gain function returns.
Practically that means CC value 99 is about the lowest controller value  
for unity gain, and clearly 127 will give you division by zero.