Using an FFT is not going to do what the OP asked for. Yes it will give you a nice display but it will not pick out a single note and allow you to light an LED. It will light LEDs according to the spectrum of the waveform. That is you will get a different display from the same note, depending on the not's harmonic content.
If you look closely, you will find that most keyboard players have 10 fingers, typically 5 on each hand. If you don't allow for polyphony, then you are not making something that practical to use in the Real World.