The system byzantine notation was derived from is, according to some suppositions, not only verbal-musical but also choreographic, partaining to a very old (ancient) tradition of artistic dancing-singing (choral poetry). After some point, the singing dancer(s) it was designed for could be taken as fictional ones, keeping the voices in fact and dancing in theory. Dancing could also be more with hands than with feet. The use of "fictional" characters is a very ancient practice, attested in Sumeria, for example on clay tablets. So one could compose, write down and perform a dancing choral ode without any real dancing taking part, pretty much like in the western oratorium, where acting is imagined but not performed (the Eastern Church never reached the composition of oratoria, mostly , it seems, because it was out of its philosophy-theology). Now, the level of concretiness - i.e., how much the byzantine notation system is detailed and precise, comparing it to the western one - in its pitch, style and/or body moment description - can be debatable - I have heard, for example, that it can be much more precise than western notation,in denoting very small pitch changes. In Chrysanthos's book one has the impression that what the writer admits is that the old byzantine system is not so good for the description of rhythm - comparing to western notation, or to the Otoman practice. But, one must bear in mind that since ancient times and, according to Baud-Bovy, since Aristoxenus, popular i.e. symmetric and repetitive dance patterns, like the ones reflected in western notation (4/4, 9/8 etc.) are considered non-appropriate for poetic music. PS. - To put it briefly - it seems that the two systems are incompatible, and cannot be transcribed to one onother, only (perhaps) be combined.