Neil Moran wrote:
Incidentally Svetlana Kumjudjieva mentioned that Troelsgard recently presented many sources dating from the 4th/5th centuries on with modal designations in the oldest papyri. From her research she concludes that the book of the Oktoechos was compiled for the first time during the 8th century in the Georgian Iadgari. This was the time of John Damascene.
Re: papyrus music mss cf. Christian Troelsgård, University of Copenhagen, ‘A New Source for the Early Octoechos? Papyrus Vindobonensis G 19.934 and its musical implications’, in: Proceedings of the 1st International Conference of the ASBMH (2007), p. 668. Abstract: On the basis of palaeographical analysis, the first editors, Kurt Treu and Johannes Diethart, dated the hymnological codex Pap. Vind. G 19.934 to the sixth century. Enough modal ascriptions are found in this fragmentary source to make an analysis of its musical structure and to compare it with other early sources for the Octoechos system.
By the way, you can read all the papers of the 2007 conference here:
http://www.asbmh.pitt.edu/page9/page10/page11/page11.html
and see the video documentation of the speeches held there:
http://www.asbmh.pitt.edu/page9/page10/page10.html
If you would like to read Christian Troelsgård's paper, and see some facsimilia of the papyri:
Replies
It is right, that the Georgian and Armenian translations of the Greek hymns which were later transmitted by the book octoechos are the earliest sources, and they don't follow the 9th century redaction of the Greek tropologion which favor compositions by John of Damascus and his circle at the Mar Saba.