Hardware based MIDI decoding / synthesizing
Start with, say, a guide to the protocol.

Given that you've decided to use an Arduino, you can just speak MIDI more or less directly. There's even a handy tutorial on the Arduino website for MIDI out! MIDI input is slightly more electrically complex as you're supposed to have an optoisolator in there to avoid ground loops.

It's almost entirely a software project, but if you're willing to pick up code from the internet should be reasonably straightforward.

Edit: a bit more googling has found someone who's actually done this, in 40xx CMOS rather than 74: http://www.pykett.org.uk/a_midi_pedalboard_encoder.htm

That's MIDI output rather than input. I still maintain there's no point doing it by halves: if you're going to do MIDI decode in hardware, do all the audio in hardware too, don't just put an Arduino in there as a PWM generator. And if you do have the Arduino, let it do the protocol bit and consider moving the audio side to analog.