Value scaling for midi mapped Time/Rate Knobs

aaron.br

Does anyone here happen to know how time/rate values are scaled when mapped to MIDI CC values 0-127. For example the phaser 9's "rate" knob when sync is turned off goes from .03hz to 9.76hz, but its not linear. It also doesn't seem to fit any basic exponential or logarithmic curves.

For some context why Im asking: I've been working on a touch interface so I can control certain parameters from my ipad and have midi mapped a number of fader controls to guitar rig knobs. For most of them I don't really need to see the exact value is, but for time/rate knobs it can be helpful. With milliseconds this is pretty straight forward and I can just map the MIDI CC value from 0-127 to whatever the MS range is like 5-2000ms for Phaser 9 so that I can show the value directly on my ipad as Im changing it. For HZ and fractional note lengths this has been a lot trickier. I can kind of approximate it by sampling a bunch of values and using linear extrapolation, but its not quite right and kind of a pain to do for each component since each component with HZ rate controls has a slightly different range too. Im sure there is some function that defines this but I just haven't been able to figure out what that might be.

I know it's kind of an obscure technical question but if anyone has any insight I'd be very grateful! TIA!