All of the pieces are there, it will just take some work to put them all together. You will need hardware to connect to MIDI IN and OUT...we offer the Flexible MIDI Shield
for this purpose, though there are other similar shields available from Sparkfun.
You will need some place to store the data. The Arduino has built-in EEPROM (2kbytes) but this will fill up quickly and it takes a "long" time to write to it relative to how fast some MIDI messages can come in. You can use a data logging card, or use the built-in NAND FLASH on our BeatVox
Finally, there is a MIDI Library
for Arduino that can help with the software.
The rest is all fun: pulling it all together and making it work
: compatible with Arduino UNO, 24V operation, all I/O's fused and protected