The point of the comparison with the Turkish model is that there have been modal systems which fit secular modal music quite informatively. But nobody seems to have felt it mattered in the Christian Middle Ages (Grocheio said something to the effect that it was a waste of time trying) - except for the handful of tunes like "L'Homme Armé" that crossed over into liturgical use, so you'd need to know what contexts they'd fit into, why bother?

Reading back a bit, there were precedents for this. Ancient Greek music theoreticians had many subtle references to the music they couldn't analyze and didn't want to talk about. Quite likely this undocumented stuff (like aulos tunes) was the bulk of what ancient Greeks actually listened to.