Dear Dejan,
I believe I have the article somewhere, but I'm not sure if I'll be able to fish it out for you any time soon. If I recall (it's been quite a long time since I've read it) there are four or five weak 'proofs' put forward, trying to argue for the use of chromatic and enharmonic intervals as being later (I believe he uses the term) 'oriental' borrowings or influences on post-Byzantine modes.
This is something Tillyard expresses in many of his articles; take this quote as an example:
Chromatic Passages
Anyone who has listened to Modern Greek Church music must have been struck by the frequency of its chromatic passages; but in Middle Byzantine music we never find a whole hymn in the chromatic species, but only a short passage here and there. Further, the introduction of the chromatic sign seems usually, if not always, to be due to a later hand than the thirteenth century and may be regarded, in the main (1), as a fifteenth century development. Until the reform of Chrysanthus in 1821, Greek Church Music had only one properly chromatic sign, called Nenano (nenano [in Greek]) [sign], which might be used (so far as can be seen) in any mode and on any part of the scale, where the augmented tone was desired. This sign has survived in the modern system
The effect of the sign only lasted to the end of the versicle.
In the Late Byzantine system we often find, not only Mode I Plagal, but also II Plagal using the Chromatic species
Furthermore it is possible that the Late Byzantine notation where it used the Chromatic modulation-sign, may have recorded an older, though unwritten, practice of some singers, who had come under Oriental influence.(H. J. W. Tillyard, HANDBOOK OF THE MIDDLE BYZANTINE MUSICAL NOTATION (Copenhague: Levin & Munksgaard, 1935), pp. 35-6.)
Dejan, this is something you can find in Wellesz articles and many others. There was a clear 'line' held by all MMB people that Byzantine Music was a purely diatonic music. If I recall correctly, Tillyard begins his article that you mention above with the premise that both the enharmonic and chromatic genera witnessed to in ancient Greek music theory had long ceased to exist before Byzantine music makes its appearance. Chrysanthos is usually blamed (along with the other two Teachers of the New Method, Gregorios Protopsaltes and Chourmuzios Chartophylax) for introducing such intervals into Greek Church music, always, through 'oriental' influence; the line usually goes: they were forced to by their Ottoman lords.
The big weakness (other than the fact that the premise is not founded on any pure data, but simply speculation) is that if the introduction of chromatic (and enharmonic) intervals was such a late development, how is it that (1) there are no records of any protest and (2) when we have Konstantinos Byzantios chanting from the right analogion with the old notation and his lambadarios Stephanos chanting from the new notation on the left analogion, how is it that there is no difference in performance expressed, in fact, specific witnesses exist explicitly stating that "no difference in performance was detected"!?
As far as the most Greek Byzantine musicologists are concerned, there's no issue. Chromaticism and enharmonic intervals were always on the scene and did not 'disappear'. The only person I know of in the 'western camp' (if such a thing exists) who dared stand up for chromaticism in Byzantine music from the beginning was J. Raasted:
"Chromaticism in Medieval Byzantine Chant" CIMAGL 15 (1986) 15-36
Prof. Stathis has often told us of his joy when he heard Raasted speak on this topic in Wien at the Egon Wellesz Symposium (1985). The consequences of accepting such a premise (that chromaticism existed in Medieval Byzantine chant), however, are quite far-reaching for those 'scholars' who do transcriptions from Byzantine music manuscripts using the guidelines established by the MMB founders.
That's about all I have time for just now. If I can be of any other assistance, don't hesitate to contact me privately, too.