Could be they do, but I'm looking for a MIDI. MIDI's can be heard, downloaded, edited and played by me and my friends.

One title that came up a lot when I googled 15th century music was 'Missa de l'homme armee.' Ogckegem, Dufay, de Prez... I've seen references to that more than once in books of music history.

Odd that the idea was so widespread but I cannot hear even one piece from those masses on the Internet.
========
If you are curious and wish to hear something beautiful and interesting, actually haunting from about 1200, check out the music of Perotin, of Notre Dame Cathedral. He would have been old-fashioned by the time of the painting of the angels, however.