While the synthesis between harmonikai and Carolingian chant theory can be studied between Boethius as a Carolingian source (we have no earlier manuscripts) and Hucbald, there has not really survived an early source which testified about the synthesis between the Byzantine octoechos and the Ancient Greek tropes, I mean how the Dorian mode on E—e became that of D—d. Harold Powers (Grove article "mode") wrote:
From the 6th century to the early 9th, when the repertory of Western plainchant achieved its basic forms, there is no record of descriptive or theoretical sources, and of course no notated music. Towards the end of this period a system of eight modal categories, for which there was no genuine precedent in Hellenistic theory, came to be associated with the rapidly stabilizing repertory of Gregorian chant. This system was proximately of medieval Byzantine origin, as indicated by the non-Hellenistic Greek names of the modes in the earliest Western sources from about 800.
The origins of the Eastern Christian system of eight modes – usually called Oktōēchos – are not entirely clear; but it seems more than probable that it was not delimited purely or even primarily by musical criteria. In any case, the octenary property of the modal system of Latin chant in the West was of non-Latin origin
Then he abruptly switched back to the Western synthesis and the reception of the Hagiopolites in Carolingian tonaries. In my imagination, the synthesis can probably explained, that Dorian as the main trope was defined by the fixed degrees of the tone system, the frame of the tetrachords had been B—E—a—b—e—aa, and it must have changed somewhen to A—D—G—a—d—g—aa. But so far, no source had been found which could offer any evidence. Concerning Carolingian theory, this could simply have been a misreading of Boethius, but please read the very original opinion in Pavlos' article.
Please bear in mind some slight modifications suggested by the author. If Pavlos agrees, I can also upload a pdf with the modifications added as a commentary, or Pavlos might upload an updated version of the text as pdf.
The happy meeting between Epitrope and Aristoxenos
While Chrysanthos linear description of the tetrachord α'—δ' (12:11 x 88:81 x 9:8 = 4:3, 151’ + 143’ + 204' = 498’ cents) was based on corrupted arithmetics (108/96/88/81 = 12 + 8 + 7: 8 + 7 + 12 turned into 9 + 7 + 12, which count the fourth into 28 and therefore into 4 minor tones, but not 5 half tones of 6 units), a patriarchal synode in 1883 decided for an equal tempered representation which counted the fourth in 30 units (10 + 8 + 12, 166' + 133' + 200' = 500' cents). Aristoxenos divided the tetrachord into 60 parts. The exact method of division is still a controversial matter.
- Ἡ Ἐπιτροπή: Στοιχεώδης Διδασκαλία τῆς Ἐκκλησιαστικῆς Μουσικῆς Ἐκπονηθεῖσα ἐπὶ τῇ βάσει τοῦ Ψαλτηρίου ὑπὸ τῆς Ἐπιτροπῆς τοῦ Οἱκουμενικοῦ Πατριαρχείου ἐν Ἔτει 1883, Istanbul 1888, Reprint: Athens 1978.
A 24 mode system mentioned in the Alchemy compilation
The reconstruction of the hardly readable paraechoi was easily done, because they are mentioned later:
Ὥσπερ δὲ τεσσάρων μουσικῶν γενικωτάτων στοιχείων, αον, βον, γον, δον, γίνονται παρ῾ αὐτῶν τῷ εἴδει διάφορα στοιχεῖα κδ῾, κέντροι καὶ ἶσοι καὶ πλάγιοι, καθαροί τε καὶ ἄηχοι [καὶ παράηχοι]· καὶ ἀδύνατον ἄλλως ὑφανθῦναι τὰς κατὰ μέρος ἀπείρους μελωδίας τῶν ὕμνων ἣ θεραπείων ἣ ἄποκαλύψεων ἣ ἄλλον σκέλους τῆς ἱερᾶς ἐπιστήμης, καὶ οἷον ῥεύσεως ἣ φθορᾶς ἄλλον μουσικῶν παθῶν ἐλευθέρας,
My translation as an alternative to Gombosi's one (1940, 40):
As there are 4 basic elements, there are also four musical ways, the πρῶτος, the δεύτερος, the τρίτος, and the τέταρτος, and by their formulas the same generate 24 different elements: the [4] κέντροι (central), [4] ἶσοι (basic), and [4] πλάγιοι (plagal), the [4] καθαροί (kathartic), [4] ἄηχοι (aphonic), and [4 παράηχοι (paraphonic)]. Hence, it is impossible to create something outside those infinite melodies of hymns, treatments, revelations, and of other parts of the Holy Wisdom, which is free from the irregularities and spoilages of other musical passions (πάθη).
The text according to Marcellin Berthelot's edition (1888, ii:219):
Ὥσπερ δὲ δ´ ὄντων τῶν μουσικῶν γενικωτάτων στοχῶν, α´, β´, γ´, δ´, γίνονται παρ῾ αὐτοῖς τῷ εἴδει διάφοροι στοχοὶ κδ´, κέντροι καὶ ἶσοι καὶ πλάγιοι καθαροί τε καὶ ἄηχοι · καὶ ἀδύνατον ἄλλως ὑφανθῦναι τὰς κατὰ μέρος ἀπείρους μελῳδίας τῶν ὕμνων, ἣ θεραπειῶν ἣ ἄποκαλύψεων, ἣ ἄλλου σκέλους τῆς ἱερᾶς ἐπιστήμης, καὶ οἷον ῥεύσεως, ἣ φθορᾶς, ἢ ἄλλων μουσικῶν παθῶν ἐλευθέρας ·
Here another version clearly in the context of the book ceremonies which is closer to Gombosi's quotation (1888, iii:434):
Ὥσπερ δὲ τεσσάρων ὄντων μουσικῶν γενικωτάτων στοχῶν, Α Β Γ Δ, γίνονται παρ῾ αὐτῶν τῷ εἴδει διάφοροι στοχοὶ κδ´, κέντροι καὶ ἶσοι καὶ πλάγιοι, καθαροί τε καὶ ἄηχοι <καὶ παράηχοι> · καὶ ἀδύνατον ἄλλως ὑφανθῆναι τὰς κατὰ μέρος ἀπείρους μελῳδίας τῶν ὕμνων ἣ θεραπειῶν, ἤ ἄποκαλύψεων, ἤ ἄλλου σκέλους τῆς ἱερᾶς ἐπιστήμης, καὶ οἷον ῥεύσεως ἤ φθορᾶς ἤ ἄλλων μουσικῶν παθῶν ἐλευθέρας, τοῦτο κἀνταῦθα ἔστιν εύρεῖν τὸν δυνατὸν ἐπὶ τῆς μιᾶς καὶ ἀληθοῦς κυριωτάτης ὕλης, τῆς ὀρνιθογονίας.
translated as follows (1888, ii:212):
De même que les lignes musicales les plus générales étant au nombre de quatre, Α, Β, Γ, Δ, on forme avec elles 24 lignes d'espèces diverses ; et qu'il y a aussi des centres et des lignes obliques, selon qu'il a été dit à propos des sons, et attendu qu'il est impossible de composer autrement les mélodies innombrables des hymnes, pour le service (du culte ?), la révélation, ou quelque autre partie de la science sacré... (Phrase inintelligible.)
Alia musica compilations
Some of the sources have been already published online, see my list of tonaries. There you will also find links to two corresponding editions. There is a third edition by Karl-Werner Gümpel of the "Nova expositio" part as he found it in a manuscript of the Catalonian monastery Ripoll.
Bibliography
Replies
May be, You are wright. I must think about this question. large - this is CDEF, small - DEFG, ukosnenny tetrachord - EFGA
The "Byzantine tonal system" was certainly not just the systema teleion (as some might understand by reading the summary written by the sisters Školnik), but this was probably also my contribution to the subject since I recommended to reconsider the role of the three tone systems (after Chrysanthos it became even four due to his concept of diphonia ruling the current melos of echos devteros). Such a view would also prove that a Al-Kindi's reception of the Byzantine tradition was sufficient, even if he could not have access to the later translations of Ancient Greek treatises of science as did Al-Farabi.
Plousiadenos' triphonic parallage worked surprisingly well for its integration of all genos combinations used in psaltic art:
It might be possible that these modes were not that "primitive" as Jean Claire was tempted to believe...
Dear Oliver! Thank You for Your information. It is very important. I am sorry, I can not open this article by Claire, I read only abstract about the author. I hope, in Russian chant adaptation of Byzantine system of singing was realy. I am sorry, I dont know about Al-Kindi and Al-Farabi theories. Write me please several works about these scientists. I will be read. I think about the adaptation problems all time, but I have not full information about these questions. And I have not enough time, because I am teacher for my students and aspirants, who study different problems, not only palaeography.
Achilles not only spoke about this, but invited the orchestra of arabic musik.
draft_programme_icmp2015.pdf
Ἀχιλλεὺς Χαλδαιάκης, νεομεθοδικὲς συνθετικὲς πρακτικές: ἰδέα, διαμόρφωση καὶ ἐπέκεινα προ- οπτικές - this is report.
My Greek colleagues told me about it last year, when we met before in Sofia. Despite of his traditionalist approach, they are some musicians like Kyriakos Kalaitzides in Thessaloniki and Evgenios Voulgares in Patras who both teach the instruments of "the Polis" to young musicians since 2005, see for instance the concert of November 2008 with a rather radical approach (simply understanding makam segah as ἦχος λἐγετος). Now, they become more relaxed about the Ottoman history which is important. On the other hand, I appreciate that Greeks have such a profound understanding of history, since Plovdiv became "European capital of world heritage" many just call the Ottoman architecture of the historical centre "Old Bulgarian," the ony exception is the beautiful mosque which is 100 years older than all the mosques of Istanbul!
But the exchange is much older than the history of the Ottoman Empire and Al-Kindi is one of the earlier sources we have...
Please do not worry about Jean Claire, it is probably not so relevant for you. I just would like to tell you that there is also Western theory of primitive modes based on DO, RE and MI. Only the formalist consequence (à la Todorov or Shklovskiy) is missing that its tone system could be organised in triphonia. But as a Russian reception of Byzantine music this is very interesting!
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