Shota
Παλαιό Μέλος
Of course, Zaal Tsereteli's statistic method needs to be questioned,
I wouldn’t call his method “statistic”. What it relies upon is that Tsereteli tries to identify similar formulae in different neumated heirmoi. Then, if the staff notation transcriptions also contain similar or identical melodies in the same places, he concludes the melodic passages in the staff notation transcriptions stayed stable over centuries and they should be related to medieval versions. On basis of this he tries to figure out how the individual signs function. But all such “coincidences” seem to be restricted to smaller parts of the heirmoi, not the entire melodies, and usually are based on two-three occurrences of formulae. In the end he arrives at the table like the one you showed, which to me is too rigid and simplistic to be true. If his method were correct, he must have been able to transcribe heirmoi in the neumatic notation that were not used in his analysis, compared transcriptions to the notated versions from the 19th c., and validated his results. But as far as I know he has no example like that.
I don’t claim I can or will ever be able to “decipher” (?) the Georgian notation (this is an impossible task given its imprecise, mnemonic character), but its strucural implications are in so many ways linked to the melodies passed in the classical Byzantine heirmologion / sticherarion that it would be strange to ignore it. This concerns both the minute details, such as occurrence of melismatic passages, or more global features like repetition of certain neumatic patterns, or even entire structures of the hymns as we know them from the middle Byzantine sources.
There is a huge corpus of Georgian heirmoi / automela that mimic the metrical structure of the Greek originals (at the expense of exactness of translation). Now from the Slavonic or Melchite sources we know a similar approach was used by other nations too to retain Greek melodies for translated texts. This is something the Georgian philologists were preaching already long ago, but it didn’t fall on a very fertile ground in Georgian musicology.