Do you think is possible that this Electret Microphone https://www.sparkfun.com/products/9964 plus a DSPIC can recognize music frequencys with a FFT, or the electret only recognize the sound levels?
The electret will pick up sound just like any other microphone. There are a few draw backs though. You will be limited by the range of frequencies you can pick up with this type of microphone. I'm not sure what range you can expect but such information would be listed in the microphones datasheet.
Once you are able to get the analog stream from the microphone, you can analyze it using a suitable FFT algorithm, such as FFTW. It is from those, you'll be able to extract various peak frequencies within the music.
That microphone seems quite capable enough to pick up everything but the highest-frequency harmonics from tophat cymbals, and the amplifier's specs are better than those of the microphone. I can't think of any good reason why a DSPIC, in combination with that microphone couldn't be taught to recognize musical tones it "hears".
It can't do so as a plug-and-play unit, of course - it WILL take some considerable programming just to pick out primary monophonic tones, and considerably more to pick out polyphonic tones and harmonics.