Kind of.

We have surviving notations from that time. Western music notation was different from what we have now, but in principle deals with things that can give us an idea of what people were working with. We also have some texts that deal with theoretical matters. So we have tried to solved the puzzle based on those things (plus the experience of performers).

For the 12th century in Europe we can talk about Perotin the Great. Here, listen to this. You can see some notation in that video. Those signs tell us about the notes, but are not super specific about rhythm.

Do we really know how this all sounded exactly? Not exactly. Let's take some music by Guillaume de Machaut, from the 14th century, as an example. Listen to this interpretation by the Oxford Camerata. Nice, clean, precise smooth lines... Now listen to what Marcel Pérès proposes. A rather different way to sing, and added ornaments that remind us of eastern music.

We obviously don't have recordings from back then. At best we have problematic notations, theory books, and descriptions in texts.

hi! there's lots of room for the music historians to contribute more examples, and especially answer the question "how do we know", but meanwhile, you can get started on examples in these previous posts on music from Medieval Europe (I'm taking a guess that that's where you were thinking.. ?)

• Do we know what music sounded like in Ancient Rome, Ancient Greece and Medieval Europe?

• How accurate is the music that we hear in "medieval" television shows and movies?

• Resources for Medieval Church/Choir Music

• In medieval Europe, did Arab musicians ever perform at court? Would European monarchs have been exposed to non-European music?

• How was music taught to musicians and scholars from the Middle Ages up to the 20th century (western civilization)?

• What sort of music did royalty listen to in the middle ages?

• What music people listened in Middle Age that could be considered "heavy" nowadays, in the particular standards of culture and musical history)