Please have a look on the discussion of the videos made by a performance of Capella romana in a virtual reconstruction of the Constantinopolitan Hagia Sophia.
There have been numerous studies of the rite which belongs to this cathedral, and the very unspecific name "Byzantine rite" had been often used for this very particular rite. One of the most remarkable studies is certainly that by Oliver Strunk, because it revealed, that the turn to a mixed rite and the reform by the school of the maistores like Ioannes Glykys and Ioannes Koukouzeles as a synthesis of the former cathedral rite with the notation of the Stoudites reform had been never accepted in other corners of the Byzantine Empire like for instance the Hagia Sophia of Thessaloniki, where the former tradition had been continued until the Turkish conquest in 1430.
Neil Moran contributed to the earlier tradition by treating a rather unpopular aspect, the role of Eunochs as castrato singers during the celebrations of the cathedral rite. I studied myself the cherouvika in the Italian choir books (asmatika) and found out, that the celebrations of the Greek rite in Norman and Svevian Italy had a certain orientation to contemporary Constantinople, but they still used the old books (asmatikon and kontakarion), and not the "order of services" (Gr. τάξις τῶν ἀκολουθίων), the book of Ioannes Koukouzeles' reform. Nevertheless, they integrated certain elements of the kalophonic style, but never expanded the cherouvika in such a way as we find it transcribed as "cherouvikon asmatikon". Nevertheless, the Constantinopolitan sources are very important, because they combine 3 different books: the typikon, the asmatikon, and the psaltikon.
Please listen to Konstantinos Terzopoulos' paper which was dedicated to Konstantinos Byzantios' studies of the cathedral rite after the reform, a Phanariot who systematically refused Chrysanthine notation and continued to write manuscripts in Late Byzantine notation. His typikon had also be translated into Bulgarian by Neofit of Rila, an important protagonist of the Bulgarian Orthodox continuation of monodic chant. During his presentation Konstantinos Terzopoulos showed an Akolouthiai manuscripts (Athens, National Library of Greece (EBE), Ms. gr. 2406) which transcribed the cherouvikon asmatikon as an echos devteros, while the Italian asmatika, whose notators already used the notation of the Stoudites reform, use a main intonation of plagios devteros. This is probably an indication that the diatonic plagios devteros had presumably been intoned on a rather high pitch, because its ambitus ranges far under its finalis down to Γ (here understood as a Guidonian letter which had been probably intoned in parallage as a plagios protos). Please note that the Hagiopolites mentions that devteros melodies tend to use the plagios as finalis.
So far, I never met singers who are able to perform such a long piece than the elaborated or calophonic version of the cherouvikon asmatikon which contains several pages of teretismata and nenanismata of the domestikos (the choir leaders), while large part of the text had been performed by a soloist (monophonares, probably the lampadarios) from the height of the Ambo. The cherouvikon performed by Capella romana uses the oldest source of the Papadic cherouvikon, which replaced the cherouvikon asmatikon by an abridged version to be performed in the echos of the week according to the Hagiopolite oktoechos cycle. The akolouthiai of 1458, which has been preserved as Ms. 1120 of the library of the Iviron Monastery on Mount Athos, has not the cherouvikon asmatikon, but an oktoechos cycle made of the old model by Manouel Chrysaphes, a Lampadarios and famous composer of Constantinople. In the video of Capella romana you can listen to the echos prôtos version, as it has been reconstructed by Ioannis Arvanitis.
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