The calculation you would want to do is not simple. Higher permeability results in higher inductance, but only up to a point, using short cores and an "open" magnetic circuit as pickups do. Note that steel is a lot higher permeability than any Alnico, but the difference in inductance is only about a factor of two.
Measurement is the easiest thing to do. There are some things to watch out for. You need a meter that works well with low Q coils. Using a low frequency, say 120 Hz, gets you a measurement very close to the coil inductance unaffected by eddy current losses. Using 1 KHz will result in a measurement a bit lower when using steel cores because of these currents.