I don't think there is much info out there about that from what I know, other than some frescoes showing Byzantine secular musicians.
In the recent years, Christodoulos Halaris attempted to reconstruct Byzantine secular music but his renditions have been criticised as more imaginative than based on real evidence. Here is what answers.com says about Halaris:
"Sometimes billed as "Chris Hallaris," Greek composer and scholar Christodoulos Halaris is a leading expert on the study and reconstruction of ancient Greek and Byzantine music. He turned to musicology and composing after studying mathematics in Paris. Taking his cues from religious iconography and traditional popular Greek music, Hallaris began reconstructing fragmentary (and sometimes nonexistent) old Greek music documents. His re-imagining of secular Byzantine music, with what Hallaris identifies as roots in Hellenic song, has met with skepticism from some scholars, but it is based on a serious study of a number of sources and centuries of related developments in Greek music. He has published more than fifty compact discs of this music, and helped create the Museum of Thessalonica, devoted to Greek music and now engaged in a significant project revolving around European medieval music. ~ James Reel, All Music Guide".
This is what wiki has to say. I can't find a bibliography or any reference to the sources from which this information was taken. Can anyone else?
The music of Greek Byzantium is also of major significance to the history and development of European music, as liturgical chants became the foundation and stepping stone for music of the Renaissance (see: Renaissance Music). It is also certain that Byzantine music included an extensive tradition of instrumental court music and dance; any other picture would be both incongruous with the historically and archaeologically documented opulence of the Eastern Roman Empire. There survive a few but explicit accounts of secular music. A characteristic example are the accounts of pneumatic organs, whose construction was furthest advanced in the eastern empire prior to their development in the west following the Renaissance.
To a certain degree we may look for remnants of Byzantine or early (Greek-speaking, Orthodox Christian) near eastern music in the music of the Ottoman Court. Examples such as that of the eminent composer and theorist Prince Kantemir of Romania learning music from the Greek musician Angelos indicate the continuing participation of Greek-speaking people in court culture. However, the sources are too scarce to permit any well-founded stipulations about what cultural musical changes took place when and under which influences during the long histories of the Byzantine and the Ottoman empires. Hypotheses that Turkish (Ottoman) music was influenced by Byzantine music, or the other way around, remain highly speculative. It seems more logical to consider that these influences were probably more manifold, considering the breadth and length of duration of these empires and the great number of ethnicities and major or minor cultures that they encompassed or came in touch with at each stage of their development.