BLDC motor's frequency
I think you might be misunderstanding the underlying principle of BLDC commutation. The equation t = L/R I believe is used to determine the minimum PWM frequency necessary, but in practice you will want your PWM frequency to be higher than this to increase power efficiency. Often a frequency that is above audible (>20kHz) is used so that you can't hear an annoying whine from the coils, but this varies depending on the control technique used and the hardware it is being implemented on.

If you're building your own BLDC solution, I recommend starting with learning how trapezoidal control works. There are many great documents online from major companies such as TI, NXP, etc. that describe it.