I am working in Fruity Loops studio, and funnily enough, I need to solve something with math. I want a way to calculate the track tempo I get based on an arbitrary value.
I know the following values give these tempos:
60 BPM = 0.09765625
150 BPM = 0.27343
180 BPM = 0.33203125
So say I want figure out a method of finding an arbitrary number, and I already know those three values. What would the formula look like? My math skills could really use some work, but that's not important here.
On
Because this is a linear function (it's shaped like a line), the first thing to do is find the slope:
$m = {{y_2 - y_1} \over {x_2 - x_1}}$
$m ={ {.33203125 - .09765625} \over {180 BPM - 60 BPM}} = 0.001953125 $
Since we also have a point, using the point-slope formula is most convenient here.
$y-y_1 = m (x-x_1)$
$y - 0.09765625 = 0.001953125(x - 60)$
$y = 0.001953125 x - 0.01953125$
In this equation, x is the BPM, and y is your output. You'll find that this holds for other points, and the method of finding the answer used here will work for any line.
If we suppose that the relationship between the tempo and the output value is linear, then we can easily determine an equation for the line. I used a WolframAlpha to find the equation, rather than breaking out 'ye olde calculator. Letting the $x$-axis represent BPM and the $y$-axis represent your parameter, it gave me $y=0.00195313x-0.019313$. So you can evaluate this equation for $x=150$ BPM to get $y=0.2734382$.
Now, this only holds if the relation is a straight line. If you have any information about whether the relationship is linear or not (for example, a third ordered pair), you should add it in, and we might be able to give you a better approximation.
ETA: looks like you got the same answer as me for the parameter corresponding to 150 BMP. I would say that's pretty good evidence that your relationship is linear. Therefore, you can use the above equation to calculate the parameter (percentage?) for any tempo.