# Calculating an exponential curve

I'm developing a synthesiser and have finished the LFO's. I'm wanting to provide a knob on the UI for setting the rate. The minimum value of the LFO will be .01 Hz and the maximum value will be 3000 hz. I'll have 100 increments in the knob and I want to apply an exponential curve to the values (Lfo rate).

What is the formula/function for calculating this?

• When asking for library questions of the type... how to convert from linear to exponential frequency, how to convert from pitch to frequency, and so on, it's always faster to search online. when i build synths i normally do 1*1 or 1*1*1 it's a very fast way of making an exponential curve from 0 to 1, albeit not a pitch to frequency exponential, just a customizeable one for control inputs, because the resulting values from .01 to 3000 will be oddly spaced atonal values, you can try different stuff. for FM it should be tonal modulator operator frequency for balance, i.e. 5ths and 12ths. – com.prehensible Mar 19 '16 at 11:27

Set $\Delta=\frac{1}{99}\log_{10}\left(\frac{3000}{0.01}\right)$
Then the $n_{th}$ knob position should be
$p_n=10^{n\Delta-2}$
Where $n$ runs between 0 and 99 in integer step.