I am also interested in something along these lines. I am not sure if it is possible, but I may give it a go to see how far I get. I'm going to start by getting some GraphTech GHOST saddles for my Strat at some point in the next few months.
This post discusses the same thing.http://arduino.cc/forum/index.php/topic,10982.0.html
These are my thoughts:
The first problem seems to be that the Arduino actually only has one ADC, and uses an internal multiplexer to switch between its analogue inputs. It can only sample one at a time. I guess that this may not be fast enough for our purpose.
I wonder if there is a cheap-ish chip that has eight separate ADCs. That might be more suitable. The first couple that I have found seem to have the same problem -- one actual ADC, multiplexing between the inputs. Maybe the answer is to use six separate ADCs external to the Arduino.
Next, comes the properly difficult part. Working out the mathematics and algorithms that will convert the pitch voltages to note data. I suspect that the microcontroller on an Arduino might not be fast enough, or might not have enough memory for this. Still, I'm interested enough to give it a go. It may be that one of the upgraded Arduino models might be more suitable.
A Fast Fourier Transform should pick out the frequencies of the main harmonics in the note being played. The fundamental frequency (which is what we are interested in) should be the biggest one.
I gather that (to avoid latency problems when picking up the lowest notes) some of the commercial MIDI guitar arrangements analyse the attack of the waveform envelope instead in some way.