I don't understand exactly what you are trying to do, but a [u]MIDI[/u] keyboard with MIDI software is probably the best solution.
With MIDI, you are just capturing (and/or saving/sending) the keypresses or the notes, so there is very little processing required and it's very efficient. With some additional hardware, the Arduino can handle that if you don't want to use your computer.
There is audio-to-MIDI software that can take a signal from a microphone and determine the notes & timing and create a MIDI file, but I'm not sure how well that works with chords. That kind of processing (especially analyzing chords) probably takes more processing power than the Arduino.