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".