I have scanned and uploaded the article "The Survival of Byzantine Chant in the Monophonic Music of the Modern Greek Church" by Markos Dragoumis. In it he identifies a number of Byzantine melodies from mediaeval mss transcribed according to the short exegesis method that have close parallels with transcriptions in the New Method done in the 19th c. Since Dragoumis follows the MMB methodology in his transcriptions to the staff notation, I would very much be interested to learn what Ioannis Arvanitis' approach gives for these same melodies.
I'm not at home and cannot see this article (the file you uploaded appears damaged to me), so I cannot give details now. In general, my rhythmic interpretation makes the old chants (some of them at least) to sound more similar to the present-day ones. One should not expect to find complete similarity, of course, but the direct relation is more apparent. To give some examples, I can mention the old "H parthenos shmeron", "Epephanhs shmeron", the "Theotoke h elpis" (which I have uploaded in the discussion on my transcriptions sung by the Romeiko ensemble). There is also the automelon "W tou paradoxou thaumatos", which is very close to the one sung today, as well us other automela. The similarity appears much more close when examining the form of chants found mainly from the 14th-15th c and not so much the form they had earlier. Nevertheless, there is a close relation of the forms of 14th-15th c to the earlier forms. So, despite of the differences there is a continuity of the tradition. What is written down in the Mss are "snapshots" of a history. When one sees successive snapshots, one realizes this continuity. When comparing only the very old form to the present-day one, the difference appears, of course, greater. In some cases, and from what I have investigated till now, this history can be described in some detail, as eg. the transition from the older form of the Protos heirmoi or automela to their present-day one. This transition could be apparent in purely melodic terms (that is, without any reference to a specific rhythmic interpretation) but my rhythmic transcription gives the continuity also for the rhythmic part, as well as the transition to the longer forms of interpretation (short melismatic, like Katavasiai, etc). I cannot elaborate on this here and I 'd need a lot of time and to describe many examples to do this.
I cannot give specific examples now. Maybe when I come back home.
