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
Dear Galina Alekse'eva
Thank you for informing us about your newest publications relevant to the topic.
Why do I get error messages in all the links you offered to us?
In your case academia.edu could be an option...
Ah, there it is:
https://dvgu.academia.edu/%D0%93%D0%B0%D0%BB%D0%B8%D0%BD%D0%B0%D0%9...
"Anspaßungsschlüssel" (fun key) is a very nice typo!
When I was in Paris last February, I was told about Church Slavonic (Glagolithic) papyrus with the tropologion repertoire which are earlier than the well-known translation projects during and after the Studites reform as in Ohrid and in Veliky Novgorod. I got very interested.
Can you tell us about their evidence concerning the oktoechos signatures?
In my opinion especially Owen Wright's article "The sight of sound" (2004) must be attractive for scholars of medieval chant, since early Greek sources dating before the 13th century are rare, while the Papadikai are full of wheels which resemble wheels we can find in Arabic sources.
The introduction, I admit, is hard to read, the missing gap the author was looking for was the art of memory, according to Mary Carruthers' an immaterial systematic representation organised in a geometrical imagination or an imagination of a building, which served a musician during his orientation within a tone system. The Western keyboard already can be regarded as such an immaterial representation, at least this is one aspect beyond the instrument and its mechanic to produce sound.
In the Papadikai we have the small wheel as a parallage diagramme, but there is a big wheel with for small peripheral ones which are all organised in a different way with respect to the small one. Since I realised the same as a three-dimensional spiral, it would look the same, if we regard it from the top.
Al-Kindi's spiral or braid (now an imagination) also builds a pentachord, and if the braid is continued on each step it organises a tetraphonic tone system (similar to the Dasia system).
The difference between Schola and Musica enchiriades is that Al-Kindi's reference to an Arabic translation of Greek terms is more evident. But unlike Owen Wright, Eckhard Neubauer (1998) insisted that al-Kindi could not profit from Arabic translations of ancient Greek harmonics treatises (as did later al-Farabi), it was rather an enthusiastic exchange with the contemporary Byzantine oktoechos as a tonal system. As evidence he quoted this passage of al-Kindi's treatise (pp. 378-79):
Now al-Kindi's braid is different from the systema teleion he described on the Ud's keyboard, and it is not necessarily a Byzantine invention in its progressions, but it can be read as a contemporary evidence, that tetraphonia was used by Byzantine psaltes and connected with his adoration of tone system, where each element has an own modal tonality within the oktoechos system.
The "correspondence" between Wright and Neubauer was, that the particular braid was not earlier continued than by Safi al-Din al-Urmawi (13th century), while al-Farabi and Ibn Sina were rather under influence of an Arabo-Persian harmonics reception.
Dear Colleagues! Sorry for the long absence. Your discussion is very timely. I believe that the names of the musical formulas, their musical content very closely connected with the system Ihos (Mode, Glas) both of Byzantine and Russian medieval music.
Talk about Echos should start with the actual Byzantine sources. Only such an approach will be true in terms of methodology. And if the works of Byzantine scholars the XI-XIV centuries, Michael Psellus, George Pahime Mr., Nicola Gregory, Manuel Bryennios still poorly understood in terms of the positions of the last Echos - the treatise of the first half of the XIV century "Hagiopolit» [The Hagiopolites. 1983] gives quite a clear picture of the perceptions of the medieval singers this category of thinking. It becomes clear that Echos - is a set of concepts that are related to:
ethos of Echos (Phrygian terms, Dorian, etc. related to the category of "Eidos", translated as "kind of melody» (¢eidoV thV melwdiaV); here it is necessary to also take into account three main Byzantine singing stile- irmologichesky, papadichesky and stihirarichesky.
system of melodic formulas, depending on the composition of their functions: (paragraphs 3 and 45 "Hagiopolit") - enihima ((hnhchma) -begining and the base of Echos, epihima (ephchma) (ejp - hcevw - to answer an echo-Butler, 1958 m I, p 598) - enihime addition, downward-yuscheesya and adapts to the melody that is sung in psalmody;.. apihima (aphchma) be the initial intonation formula entirely; cadential formula - apodidontai apoqeseiV (paragraph 48 "Check cadence of the second Echos as well as the second plagal");
melodic specificity of the Echos, resulting from the form of his apihim (pas section we 32: "Four major ihosa - the most popular type of muse for locally-tension apihim» - «mousikwn cordwn aphchmata eidoteV»;
the concept of the tropes as a musical formula at all (paragraph 33: "self-sufficiency tropes have four plagal and four medial Echos ", paragraph 47: "The first Echos takes place on tropes from the second and plagal first"; paragraph 55: "If anyone more carefully consider these Problems, he will find thousands of tropes of Echos ";
system of Phtora changing -forming composition of a singing Echos in accordance with the modulation displacements of specified Phtora;
the nature and volume of melodic movement of Echos (the steps up or down during the transition from one Echos into another Echos) shown in paragraphs 38-44 and schemes to "wheel."
Thus, Echos has a variety of ensuring internal function parameters - An initial formula (ihimy, enihimy, epihimy, apihimy), the formula at all (tropes), cadential formula (apofeseis), with their melodic specificity, referred to as the ethos by Echos, and also has options to ensure that its external properties - melodic motion with the Phtora system [The Hagiopolites. 1983, c. 43-44]. See about
3.3 part from monograf by Alekseeva Galina.doc
Discussing al-Kindi we cannot get closer to him as with the "Hagiopolites" which is supposed to be the theoretical introduction of the 9th-century tropologion, the collection of stichera and the heirmologion without musical notation, even if Raasted's edition was based on a late copy of the 14th century, today preserved in Paris. Of course, you are right if you suppose that the corresponding introduction used for the book sticherarion was the early Papadike or the earlier corpus of dialogue treatises (erotapokriseis). The relevance of the Hagiopolites is obvious, since the theoretical explanations of the Papadikai still paraphrase and interprete extracts taken from the Hagiopolites.
The question about the synthesis which goes farer than the simple assumption that the Carolingian Oktoechos was based on the synthesis made by the Hagiopolites and its Oktoechos (see Harold Powers' part of the article "mode"), is the discussion, when the double octave of the systema teleion and its fixed degrees (estotes) have moved from A to Γ. The other open question is what was the role of the systema teleion within the Hagiopolitan Oktoechos whose four octaves establish another tetraphonic tone system.
The closest correspondence might be Gabriel Hieromonachos who also mentions the Ud starting with middle string as μέση (Arabic mathnā), since he finds the elements of the tone system by ascending and descending from the middle string in heptaphonia. Now, the mesē is usually regarded as kyrios prōtos on a or κε (if you allow me to refer to the monosyllabic solfège of the New Method which can be misleading), the exo and not the eso of echos protos (see chart 7b in Erevnides, taken from Constantin Floros), while Al-Kindi's mathnā is tuned on G or δι. Hence, there is a certain role that heptaphonia still plays within the later Papadic reception of the Hagiopolitan Oktoechos.
Unfortunately, I found no explanation about the particular role that the systema teleion plays within the Byzantine practice of Octoechos, but maybe you are right to point at the term εἴδος, since it can mean what was translated as "species" into Latin, be it the tetrachord, the pentachord, or octave (oktōchordon), as well as formulas to the melos, when the name of the tropes were used as name for the eight modes as ecclesiastic church tones.
By the way, if you speak of the Slavic reception do you mean the earlier of Ohrid which did more care about the Byzantine system of avtomela and their prosomoia, but not so much about a correct translation of the hymns, or do you mean the later Russian translations, which cared about the hymn texts, so that the prosomoia had to be recomposed?
Now the first problem is, what is meant by Gabriel Hieromonachos, if he goes seven steps (phonai) up and seven down? Do they construct the systema teleion like on the ud keyboard discussed by Al-Kindi who started from the first finger fret, one tonus over G (in that case what I did call heptaphonia)?
The usual system of building connections between the modes is the parallage. The easiest description for a parallage diagramme are four columns, each one represents a descending step (by the use of the plagios enechima at the bottom) or an ascending one (by the use of the kyrios enechima at the top of each column). Hence, if I use four columns with α᾽, β᾽, γ᾽, and δ᾽ on the top (ascending from left to right) I have πλδ᾽, πλα᾽, πλβ᾽, and υαρ on the bottom (descending from right to left). You used the images taken from two manuscripts with these wheels.
If organise these four columns as diameters in a wheel, I have an ascending (clockwise) and descending (counterclockwise) hemisphere as tetrachords. The difference to the big wheel is that the latter is organised as a pentachord with the kyrios at 12 o'clock and with the plagios at 6 o'clock, the simple form works clockwise, the big in th middle with five rings in both directions.
But it could be as well realised as a simple spiral.
Actually the combination of this tetraphonia with heptaphonia can also be found in Papadike of the Mone Megistis Lavras (Ioannes Koukouzeles' escaped here from the court), one of the older sources which can be dated back to 1436 (Ms. E. 173, as introduction to an Anthology which also includes extracts of a sticherarion kalophonikon). It resembles very much to this illumination in a much later manuscript.
Christian Troelsgård and Maria Alexandru (2013) mentioned this "heptaphonia" which is in fact based on tetraphonic parallage, but there was no place and time to offer any explanation. Instead they pointed at the paradox, that the seven steps downwards from the phthongos of kyrios devteros (b for instance) leads to the phthongos of varys which is an augmented octave below (B flat in this case). Was it a strategy to modulate (μεταβολὴ κατὰ τὸν ἤχον) from devteros to tritos echoi?
Finally I have to emphasise that there is no use for eight tropoi as far as the Hagiopolitan oktoechos is concerned, since it consists of the four octaves species which are C—c for tetartos echoi, D—d for protos echoi, E—e (with low intonation) for devteros echoi and F for tritos echoi. For my correction of Oliver Strunk's imagination of the Byzantine tonal system see the second chapter of my doctoral thesis.
In any case Al-Kindi's treatise and his concept of spirals, cords or braids on the ud keyboard could show the way, how tetraphonia was established within the systema teleion.
Dear Oliver!
I do not see any contradiction in my and your reasoning. I look at every Echos not as a range, and as the Echos of the melodies filling by system of musical formulas. With even the same name, these formulas from the Echos to the Echos got changes. And these changes are deep inside, fret due to the content of the Echos. for example, I send you some illustrations.
Схема 3.18. Структура системы ихоса-гласа
ИХОС
«ГНОРИСТИКИ» ИДЕИ
«ДИЛОТИКИ» ИДЕИ
опорно-звукорядная
подсистема
формульная подсистема
подсистема ладовых наклонений
месос, тетрафония, наос в ихосе
ихиматос (ихимы, енихимы +епихимы=
апихимы), апофесеис
натяжение вида апихим,
дорийские, фригийские и т.д. тропы
ГЛАС
объем звукоряда, устои, побочные опоры, неустои в гласе
попевки, фиты, лица согласно композиционным функциям
большие, малые или укосненные лады согласно теории С. Смоленского
See also the scheme 5.
G. Amargianakis, Nanna Shiodt, B. Karastoyanov and others studed the formulas as Byzantine as Russian. I send You the different melodic fulling of the same formulas from different Echoses (табл.5.4).
I can do translation later, if You need.
5 from monography.pdf
5.4. из 5. 1 раздела.pdf
I was not talking about differences between you and me, but between different theoretical and practical approaches towards the subject (their language and their period in history).
The question of the range or ambitus (be it a tetrachord or the octave species of a certain echos) is the question about the difference between the meloi (which requires the organisation in tetraphonia) and being within one melos (I do not expect an augmented octave within the melos of echos devteros, not even if it is diatonic, nevertheless, there is an augmented octave between the finalis of the echos varys in a low register and the diatonic echos devteros on b natural). The question is, what was the role between the three tone systems used by composers of Byzantine chant.
Oliver Strunk was wrong, when he assumed there is a B natural. This was a later adaptation to the ṭanbur frets as a common musical reference during the Ottoman empire (many varys meloi of the current tradition adapted to formulas which had not been part of Orthodox chant during earlier periods). They were integrated, as well as the sticherarion notation integrated other Byzantine chant books like Asmatikon and Kontakarion since the 13th century (it already happened in the Asmatika and Kontakaria written in Italy, because the notators used the monastic oktoechos notation).
The tropus (transposition octave) or tonus in ancient harmonics on the other hand was not defined as a terminology concerned with modal tonality, it was a new meaning after the synthesis between the science and the Byzantine practice of composition and chant was done. I do not know about the synthesis in Russia, when the new translations sacrificed the Byzantine melodies for a better translation. I inserted an essay by Irina and Marina Školnik about the heirmologic repertoire. I have no questions concerning your Russian text, although I do not know Russian (just some Polish), I believe that I can understand it.
I translate my scheme:
The structure of the Echos-Glas system includes 2 parts on opinion Hagiopolit:
Gnoristike Ideas(from gnosis - knowledge) has 2 parts:
Delotike (explaining) ideas has
subsystem of the range of supports (scale)
subsystem of musical formulas
subsystem of modal moods
mesos, tetraphonia, naos
echematos(apechem), apopheseis
tension of the apechem tipe
Russian glas
volume of scale, steady tones, side supports, unstable tones in the Glas
popevki, feats, according to the composite entity functions
large, small or ukosnennye tetrachords according to the theory of S. Smolensky
Irina and Marina Skolnik wrote about formulas from the different Glas, they do not difference between them. Their results are correct, but not detailed.
Bibliography:
Гексаих — древнерусская ладовая система http://www.kholopov.ru/hexa.html
Cт. Смоленский. О древнерусских певческих нотациях. Памятники древней письменности и искусства. т. 145, 1901, http://ibook-edu.ru/books/9600
You seem to agree that the result of this reception was a certain preference for the triphonic tone system (connected tetrachords), similar to the one described by Ioannes Plousiadenos as the one ruling the phthora nana.
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