c. 400-1400 (There is sometimes listed a time period before this one taking up the 400-800 called the Antiquity Period)
This will be the shortest history lesson for the time periods, because music notation as we know it did not start to develop until about 1100 A.D. which is toward the end of this time period. There was indeed a great deal of music being performed and composed, it was largely not written down. We can only guess about what most of it would sound like.
With that being said, the Catholic Church did start music notation. The myth is that Pope Gregory "The Great" received word from God through a bird of the idea of notating music. It's quite likely that he was not even the one to initiate the invention of music notation, though. The first notated music was Gregorian Chant, named after Pope Gregory. The notation was not completely the same as we have today since the notes were squarish and there was no set number of lines, among other differences. I've posted an handwritten example below (everything was transcribed by monks).
The lute was the "guitar" of the day. Here's is a little video of what it sounded like.