Musicologie Médiévale

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The Klara Mechkova's books on Tetraphonia and Triphonia

Dear friends, I would like to present to you two books by Bulgarian researcher musicologist and professor of music history Klara Mechkova.

Over the last decade, she has published two books on Tetraphonia and Triphonia as the major systems of the Byzantine music.

The Oktaechon System of the Byzantine Music in the Theoretical Text...

Мечкова, Клара. Осмогласната система на византийската музика в изворовите теоретични текстове. Тетрафонията. - В. Търново: АБАГАР, 2009, 230 с. ISBN 978-954-427-850-2 COBISS.BG-ID 1231216868

1. The Oktaechon System of the Byzantine Music in the Theoretical Text Sources. The Tetraphonia (2009). The book follows strictly the medieval Byzantine sources. The researcher examines in detail key issues of Byzantine music theory, makes a detailed and in-depth analysis of the St. John Koukouzeli's wheel (Τροχός). Klara Mechkova pays special attention to terms and issues such as φωνή, ήχος (functional theory of the echoi), the discrepancy between the order and naming of the Ancient Greek scales and Byzantine scales, the relation between music and theology in the medieval Byzantium.

Main Topics:

  • The theological background related to the specifics, contents and time of appearance of the Byzantine theoretical texts
  • The idea of phone in the Byzantine music system and medieval treatises
  • Phone and the accompanying terms in the texts sources
  • Phone - the definition
  • The quality of the note and phone
  • Phone and Tetraphonia
  • The melos of the note
  • The melos of the note and the polysyllabic naming of the notes
  • The melos of the note and the interval matter of phone
  • Tetraphonia and genus
  • Metrophonia and parallage
  • The functionality of tetraphonia. The Oktaechia.
  • The tetraphonia features: 1) the tetraphonia as a hypostatic union; 2) the principle of the corresponding pair phone-tetraphonia; 3) the principle of the circular motion-tetraphonia; 4) the common operations ot the both principles
  • The tetraphonia and mastering of the acoustic space
  • The Oktaechia: 1) the principle of the corresponding pairs; 2) the tetraphonia and the filling of scales of the echoi
  • The principle of the circular motion in the Oktaechia
  • The Wheel of the St. John Koukouzelis: 1) the meaning of the small circles; 2) the meaning of the Tree; 3) the optimal variant of the circular motion in the Wheel and the small circles of the Wheel; 4) the second element of the Wheel; 5) the maximal variant of the circular motion in the Tree and the Wheel; 6) the spiral motion in the Tree; 7) the central body of the Wheel; 8) about the Wheel as a musical incarnation of the theological idea about the "saved space"
  • The Ancient naming of the scales and Byzantine echoi in the treatise of Agiopolitis. The principle of the circular motion. The treatise Vaticanus Graecus 871. The principle of the corresponding pairs echoi in to the Koukouzeli's Wheel.
  • A functional theory of the echoi: the historical and theological background; the meaning of the term ήχος; the theological aspect of the terms κύριος and πλάγιος.
  • The main ideas in to the treatise of the Monk Gabriel (Codex Lavra 610): γνωριστική and δηλωτική idea; mesos, diplasmos, naos.

The Triphonia in the Tetraphonic Musical System and in the Life of ...

Мечкова, Клара. Трифонията в тетрафоничната музикална система и в живота на византийското осмогласие. - Пловдив: Астарта, 2018, 291 с. ISBN 978 – 954 - 350-265-3 COBISS.BG-ID 1288298724


2. The Triphonia in the Tetraphonic Musical System and in the Life of the Byzantine Oktaechon (2018). The book is a continuation of the first with an emphasis on the Triphonia as a subsystem of the Byzantine music. The author makes a detailed analysis on the graphic of John Plusiadinos (Η σωφοτάτη παραλλαγή). Also, in this book she translates and analyzes the δοξαστικό Θεαρχίω νεύματι by various Byzantine sources. She pays special attention to terms such as φθορά, νανά, λέγετος, νενανώ and others key concepts. The question about the tonal system is also addressed in this book. She mentions the testimony of Chrysanthos about the three types of tonal intervals and traces the connection with the sources of Arabic music in the Middle Ages. It suggests that Arab musicians may have borrowed the idea of the intervals from the medieval Byzantium (there is no direct evidence, so this remains only a scientific assumption and hypothesis).

The Klara Mechkova's research focus is on the musical systems, functional analysis and the way these major components of music work, following strictly Byzantine music sources. In addition, she has deep knowledge and gives credit to the Three Teachers' reform. On one hand, she traces the continuity between medieval Byzantine music and the music of The Modern Times (the Three teachers' reform). On the other hand, she does not make the mistake of fully identifying or completely negating any connection between the Middle Ages and Modern Times (as many Western researchers make).

Main Topics:

  • The Triphonia in to the contemporary science and the medieval text sources
  • The basics of Triphonia: 1) definition; 2) the functionality of the triphonia and tetraphonia; 3) a functional relationships between the triphonia and tetraphonia; 4) the melodic "holdingness" and "unholdingness" as a prerequisite for a functional "holdingness" and "unholdingness"
  • The Triphonia as a phtora: 1) different kind of modulations in the echoi; 2) the double parallage
  • The "turnover" of the Triphonia: 1) the monophonia; 2) an extended (compound) triphonia
  • Acoustic parameters in to the Byzantine music system: 1) the hypothesis; 2) the idea of the "unequal fourths"; 3) the "unequal fourths" in to the context of the Byzantine echoi
  • Nana, nenano, legetos
  • The Triphonia in to the didactic aids: 1) "Η σοφοτάτη παραλλαγή" of John Plousiadenos; 2) the method of John Laskaris
  • The Triphonia in to the manuscripts
  • The Byzantine music system by the example of the sticheron "Θεαρχίω νεύματι".

Unfortunately, Klara Mechkova's books are only available in Bulgarian for the time being.

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Comment by Nikola Antonov on June 11, 2020 at 7:45

The Oktaechon System of the Byzantine Music in the Theoretical Text Sources. The Tetraphonia (2009).

Main Topics:

  • The theological background related to the specifics, contents and time of appearance of the Byzantine theoretical texts
  • The idea of phone in the Byzantine music system and medieval treatises
  • Phone and the accompanying terms in the texts sources
  • Phone - the definition
  • The quality of the note and phone
  • Phone and Tetraphonia
  • The melos of the note
  • The melos of the note and the polysyllabic naming of the notes
  • The melos of the note and the interval matter of phone
  • Tetraphonia and genus
  • Metrophonia and parallage
  • The functionality of tetraphonia. The Oktaechia.
  • The tetraphonia features: 1) the tetraphonia as a hypostatic union; 2) the principle of the corresponding pair phone-tetraphonia; 3) the principle of the circular motion-tetraphonia; 4) the common operations ot the both principles
  • The tetraphonia and mastering of the acoustic space
  • The Oktaechia: 1) the principle of the corresponding pairs; 2) the tetraphonia and the filling of scales of the echoi
  • The principle of the circular motion in the Oktaechia
  • The Wheel of the St. John Koukouzelis: 1) the meaning of the small circles; 2) the meaning of the Tree; 3) the optimal variant of the circular motion in the Wheel and the small circles of the Wheel; 4) the second element of the Wheel; 5) the maximal variant of the circular motion in the Tree and the Wheel; 6) the spiral motion in the Tree; 7) the central body of the Wheel; 8) about the Wheel as a musical incarnation of the theological idea about the "saved space"
  • The Ancient naming of the scales and Byzantine echoi in the treatise of Agiopolitis. The principle of the circular motion. The treatise Vaticanus Graecus 871. The principle of the corresponding pairs echoi in to the Koukouzeli's Wheel.
  • A functional theory of the echoi: the historical and theological background; the meaning of the term ήχος; the theological aspect of the terms κύριος and πλάγιος.
  • The main ideas in to the treatise of the Monk Gabriel (Codex Lavra 610): γνωριστική and δηλωτική idea; mesos, diplasmos, naos.

The Triphonia in the Tetraphonic Musical System and in the Life of the Byzantine Oktaechon (2018)

Main Topics:

  • The Triphonia in to the contemporary science and the medieval text sources
  • The basics of Triphonia: 1) definition; 2) the functionality of the triphonia and tetraphonia; 3) a functional relationships between the triphonia and tetraphonia; 4) the melodic "holdingness" and "unholdingness" as a prerequisite for a functional "holdingness" and "unholdingness"
  • The Triphonia as a phtora: 1) different kind of modulations in the echoi; 2) the double parallage
  • The "turnover" of the Triphonia: 1) the monophonia; 2) an extended (compound) triphonia
  • Acoustic parameters in to the Byzantine music system: 1) the hypothesis; 2) the idea of the "unequal fourths"; 3) the "unequal fourths" in to the context of the Byzantine echoi
  • Nana, nenano, legetos
  • The Triphonia in to the didactic aids: 1) "Η σοφοτάτη παραλλαγή" of John Plousiadenos; 2) the method of John Laskaris
  • The Triphonia in to the manuscripts
  • The Byzantine music system by the example of the sticheron "Θεαρχίω νεύματι".
Comment by Oliver Gerlach on June 2, 2020 at 9:59

But the last example was not chosen to convince you that notators of the kontakarion-psaltikon did not use the xeron klasma in general, I just wanted to prove that they use it in a different way. Just my first example (with the second ode) had a xeron klasma which was written over a neume before a step down where the minore tone is reduced to an enharmonic interval called “diesis”. Here I have another example where the xeron klasma is used within a prokeimenon (which corresponds to responsorium preceding a scriptural lesson), but on the protos phthongos which means that in certain protos mele, there must be an enharmonic tetrachord between plagios protos and (following tetraphonic parallage down about three steps) plagios devteros (πλα᾽—πλβ᾽). I do not know, if it can also mean phthora nenano or just nana?

If you have a look at the prophetologion, you see an Old Testament reading for Orthros on Good Friday which is concluded by a second prokeimenon Σοῦ, κύριε, φύλαξον with the double vers (stichos Ps. 11:2) Σῶσον με, κύριε in echos plagios protos:

Prophetologion with OT readings on Good Friday (Cod. Sin. gr. 8, f. 223r)

If you look for a kontakarion-asmatikon of the same collection (like Cod. Sin. gr. 1280, for instance, which can be find in the same collection at Saint Catherine’s on Mount Sinai, ET-MSsc), you find the prokeimena right at the beginning of the first cycle. The prokeimena have to be sung on feasts of Holy Megalomartyres. Both prokeimena open with ison on the base phthongos of plagios protos and you find the xeron klasma at the very beginning:

ET-MSsc Sin. gr. 1280, f.2r

Here the second stichos with a xeron klasma at the beginning. I am curious, if you find a good suggestion how to read it by consulting Ioannes Plousiadenos parallage.

But you see triphonia was obviously quite early and had an important role within the Byzantine tonal system in the narrow sense.

I am finished here, dear Nikola, and do not worry about my "inappropriate way" to comment here. I am confident that Klara will not mind, if the announcement of her book get some more hits. Among scholars we are very few and we usually try to support each other. I also think that these subjects I dared to treat here are of a common interest and it is worth to do these discussions in public. I do not know what is your actual knowledge of Byzantine music and I have no business here to judge it. I certainly did not welcome you here as an ignorant, but there can be no doubt that we can profit from each other, even it might take some time to find out... and that could be one reason to be here.

Comment by Oliver Gerlach on May 31, 2020 at 10:47

Last October I taught at the Comenius University of Bratislava a very specific subject “kontakia”. Thus, I had to sing out of different kontakaria and my students realised that each kontakion is elaborated according to the individual skills of a local protopsaltis and notator who had written down and documented his own way. If you have a look at Constantin Floros’ edition (his habilitation of 1961, published only recently in 2015), you find a general distinction of two versions or redactions which are both located in Italy: the first is basically represented by the Florentine kontakarion-psaltikon (I-Fl Cod. Ashburn 64, published as volume 4 of the facsimilia or principal series at MMB) which was written at the Abbey Grottaferrata, while the second redaction is usually one of those four kontakaria-asmatika, a particular book which organised the asmatikon and the psaltikon together in a local way that pointed at its origin: the scriptorium of the Archimandritate SS. Salvatore which had also its own cathedral.

To study the difference between the tetraphonic medium of Middle Byzantine notation and the triphonic way the tonal system of the cathedral rite had been organised, one might choose a very famous kontakion by Romanos the Melode which also played a central role in his vita: the Nativity kontakion for 25 December composed in echos tritos where the kyrios (Glas’ 3) is only represented by its mesos form on protos phthongos. It is also famous, because the prooimion of this particular kontakion idiomelon became the model of so many prooimia proshomoia in other kontakia of the some echos, that also the tritos proshomoion of the weekly cycle of kontakia anastasima was composed over it. Here you can compare the Middle Byzantine notation of the Greek kontakaria with the Kondakarian notation of the Rus’ (where this model was also chosen for the composition of a kondak in honour of the local martyre princes Boris and Gleb):

Various kontakia made over the prooimion of Romanos’ Nativity kontakion
(RUS-SPsc Ms. Q.п.I.32, ff.52 & 76; ET-MSsc Ms. Gr. 1280, ff.131r-132v & 117v-119r; Ms. Gr. 1314, f.212)

Also here you might replace the Guidonian letters by symbols for the echemata used for the metrophonia. Thus, you might discover that the first kolon until the first apoderma starts and ends on the protos phthongos on a. Now the mesos form of the tritos enechema already fix the tritos pentachord between γ᾽ (c) and υαρ (F) on the mesos of the protos phthongos (a), and if you look at the whole kontakion and its melos, you will find out that the ambitus of its melos (δ᾽—α᾽—πλβ᾽) is organised on two conjunct tetrachords organised around the mesos. The protos phthongos is a cadential tone, but the concluding cadence at the end of the ephymnion (the tritos refrain) is on the varys phthongos (F), the finalis of plagios tritos.

This is exactly what I meant when I wrote “my recent discovery was that we have to make a difference between tone systems which are really part of the music (and were already in the mind of the composers), and tone systems which are part of the notational system.”

I already pointed at the different realisations of this kontakion within local schools, and this is even more astonishing, since we can find them at the very end of the prooimion at the conclusion of the ephymnion παιδίον νέον, ὁ πρὸ αἰώνων Θεός should always follow one and the same melody, because it is the same for all kontakia composed in echos tritos.

You will be surprised, if you compare the version of Cod. Vat. gr. 345 (a kontakarion close to the school of Grottaferrata) with the one of the kontakarion-asmatikon Cod. Mess. gr. 129 which shows a realisation of a protopsaltis celebrated at the cathedral of the Archimandritate SS. Salvatore close to the sea entrance of the prot of Messina:

Conclusions of the prooimion (I-Rvat Vat. gr. 345, ff.72v-73r, I-ME Mess. gr. 129, ff. 43r-44r) 

In the kontakarion-asmatikon of Messina there is no use of xeron klasma during the cadence which precedes the first medial signature. The change to the triphonia is just indicated by the medial signature which does not relate to the preceding, but only to the following. We have here a cadence on the phthongos of plagios tetartos, but the nana phthora is on the devteros phthongos (see the ison in red ink about). Thus, it causes that the devteros phthongos turns into the one of tritos and triphonia is organised from the varys phthongos (F—♭—e♭). These two conjunct tetrachords are now organised with the parallage of phthora nana which you might also find on the bottom left (the third x) of the parallage diagramme by Ioannes Plousiadenos.

Both solutions are quite different, while the protopsaltis of Messina arranged a transposition (μεταβολή κατὰ τόνον), so that certain formulas (which appear a third, two steps, too high!) are integrated within the melos, the protopsaltes and notator of the kontakarion-psaltikon close to the school of Grottaferrata prefers a change to the chromatic genus of phthora nenano (μεταβολή κατὰ γένος of the upper tetrachord between the phthongoi of protos and tetartos: α᾽—δ᾽). See the first x on the top left of the diagramme by Plousiadenos!

Comment by Oliver Gerlach on May 30, 2020 at 7:01

The comparison of the echemata revealed the particular mesoi and phthorai of the Byzantine oktoechos, and also the fact that many kyrioi echoi are simply represented by a mesos (medial) or eso (based on the plagios) shaped echos! As far as the repertoire of kontakia is concerned, one finds 2 or 3 protos echemata, 4 devteros echemata (mesos for kyrios, and a nana phthora for each kyrios and plagios), 3 tritos echemata (with a mesos substitute for kyrios tritos), 5 tetartos echemata. This comparison is already based on an important synthesis which preceded the Koukouzelian reform about 1230s.

Of course, one has to do the same comparison for the prokeimena and allelouiaria (tritos echemata ar completely missing concering the latter), and the chant of the Asma which includes the troparia (refrains) of the prokeimena and allelouiaria, but also the cycle of koinonika.

Concerning Chrysanthos and the psaltic art during the Ottoman period, he mentioned in the second book of the Theoretikon mega an archon protopsaltis who said he was ready to go as far as to another continent, if this would help to find someone who could teach him the cheironomiai. Hence, the cheironomiai is not simply leading a choir by gestures (as it is often misunderstood nowadays!), but using a sophisticated system of signs which also developed an own notation system which had a second line translating each gesture in a sequence of signs of the Old Byzantine notation.

The Slavic evidence of kondakar’ is the earliest testimony of this practice, and experts do make a difference between the second line notation and znamennaya notation which was only used for sticheraria and heirmologia. Nevertheless, both systems have many signs in common. From this point of view the Middle Byzantine asmatika and kontakaria-psaltika are missing a line above, where the cheironomiai are expected which did segregate the second line (by sequences of signs analysing one cheironomia).

Thus, switching back to the system gestures and the cheironomiai, it seems that the echema (at least sometimes) depended on the initial cheironomia. In the Blagovĕščensky kondakar‘ (RUS-SPsc Q.п.I.32) the Easter koinonikon asmatikon σῶμα χριστοῦ in plagios protos is a well known tune which was introduced by the standard echema of plagios protos. Here you might compare it with the cheironomiai of a Greek hand of the 14th century who had transcribed the gestures in a second line by the use Middle Byzantine notation:

Easter koinonikon тҍло христово / σῶμα χριστοῦ (RUS-SPsc Ms. Q.п.I.32, f.97v; GR-KA Ms. 8, f.36v)

Only the Slavic source (probably written for the Sofiysky Sobor of Novgorod) has also a main intonation which transcribed this echema in the analytical notation of the second row. But note that the main signature itself (Glas’ 4 instead of Glas’ 5) is wrong!

Another hint, the modal classification (between kyrios and plagios) was not always identical in comparison with Greek notatores. The Laurentian codex with the "tale of bygone years" reported that the Grand Prince Vladimir sent a legacy to a mosque in Bulgaria, to a cathedral in Germany and to the Hagia Sophia of Constantinople. They adviced Vladimir to accept the Orthodox faith as a state religion and thus, cantors from Constantinople had been sent over the Black Sea to instruct notators and chanters in the spiritual centers of the Rus’.

Comment by Oliver Gerlach on May 29, 2020 at 14:01

Concerning the tonal system, already the author of the Hagiopolites remarked considerable differences between the chant of the Asma (which obviously referred to the use of cheironomiai to coordinate the choir and the notation of the asmatikon which derived from them) and the oktoechos needed for Hagiopolitan hymnography (which needed the two additional phthorai nana and nenano to include the contribution of the late school of Mar Saba—the school of Andrew the Crete with Kosmas, Ioannes and his nephew Stephanos the Sabaite to mention three generations of it):

https://en.wikipedia.org/wiki/Hagiopolitan_Octoechos#Phthorai_and_m...

According to this paragraph, the asmatikon was based on a system of sixteen echoi, symmetrically organised as kyrios, plagios, mesos and phthora for protos, devteros, tritos and tetartos. This needs to be verified (you might be surprised, but nothing of that kind has been done so far, not even by Christian Thodberg!), but I warmly recommend the study of my Italian colleague Annalisa Doneda, the only expert of asmatikon notation:

Doneda, Annalisa. «I Koinonikà dell’Anno Liturgico nel Ms Kastoria 8.» PhD, University of Pavia, 1994.

I personally verified it for the repertoire of kontakia, since the synthesis within Middle Byzantine notation allows a comparison for the echemata and I found fourteen (not sixteen!) echemata but without such a symmetrical disposition. There is the number sixteen as well, since we have sixteen prooimia (the introductory stanza of a kontakion) among the idiomela which had been used as model for other prooimia (proshomoia), among them six for devteros and six for tetartos, while the remaining four are composed in the other echoi:

Gerlach, Oliver. “The Sources of the Kontakion as Evidence of a Contradictory History of Reception.” In Theorie und Geschichte der Monodie – Bericht der Internationalen Tagung Wien 2018, ed. Maria Pischlöger. Theorie und Geschichte der Monodie, 10. Brno: Tribun EU, 2020. academia.

Here is the list of fourteen echemata with all its mesoi and phthorai (the column phthongos means, where the echema ends, and the melos usually begins, the final cadences are supposed to be according to the finalis of a certain echos, either its kyrios or plagios which can be also the finalis for many kyrioi echoi):

Already a first look at it reveals, that the role of the phthorai is completely different from the Hagiopolitan oktoechos (phthora nana is widely used, especially in devteros echoi! phthora nenano only rarely). Thus, we have to forget about everything, what Manuel Chrysaphes wrote about the use of phthorai, because his main concern was the repertoire of idiomela within the sticherarion.

And Christian Thodberg also mentioned the crucial meaning of triphonia, which already explains the frequent use of xeron klasma, but here we might look for the different use of it among the notatores of kontakaria-psaltika and kontakaria-asmatika with respect to their customs concerning the sticherarion.

Comment by Oliver Gerlach on May 28, 2020 at 11:25

So far everything I write here was about nothing else than about something I would call the mainstream of Byzantine musicology, including my contribution to it.

Why mainstream?

Because Middle Byzantine notation is the only one which can be read, even if it is not always as simple as it seems on the first sight. For more information I recommend Christian Hannick’s and Gerda Wolfram’s contributions to the entry “Notation” and “Alstslawische Musik” concerning Byzantine and Old Slavic notation in the MGG who tried to explain, how difficult it is sometimes to understand Old Byzantine notation out of a comparison with later Middle Byzantine versions of the same chant. 

I would like to focus here on a discussion about the real role that Ioannes Koukouzeles (and the preceding generation of Ioannes Glykys, Michael Aneotes and Nikolaos Kampanes etc.) was with respect to the ealier past, and this is Christian Troelsgård’s discussion, whether a distinction between Middle Byzantine notation (before Koukouzeles) and a Late Byzantine notation (established by Koukouzeles) does make sense?

His argument is based on his current critical edition of the whole corpus of Papadikai during the centuries together with Maria Alexandru (the article I posted before was just an short insight into this edition project), and is about the circumstance that all the signs listed in the Papadikai were the result of earlier syntheses of different chant books within the sticherarion and heirmologion notation which had developed out theta notation and which even included other chant repertoires like the one of the cathedral rite at the Constantinopolitan Hagia Sophia (the Byzantine tonal system in the narrow sense) whose books were the asmatikon (choir book) and the kontakarion-psaltikon (book of the monophonaris singing from the ambo).

You might know Troelsgård’s article about “What kind of chant books were the Byzantine Sticheraria?”—a paper he held at the Cantus planus conference at Esztergom and Visegrád in 1998. He emphasised that the book was an overregional collection of hymns whose most local part was not even written down in the earlier books, because it belonged to a local oral tradition. How was this possible? It is first of all part of the history of the tropologion which started at the Patriarchate of Antioch (closely associated to the Armenian tradition, its books Šaraknoc’ and later the Manrusum) and spread over the Patriarchate of Jerusalem which was also the point of reference for the Georgian tradition and the Iadgari. During the time of the Stoudites (after the local school of Germanos concerning canon poetry, but note that his school was also motivated by a dogmatic background against iconoclastic Constantinople), there is not only the orientation to Jerusalem, but also to Sinai (and innovations in hymnography also lead to new re-translation within the Georgian tradition).

Concerning the cathedral rite, there was another paradox, while Middle Byzantine notation developed, it was no longer present in Constantinople due to the third crusade which forced the Byzantine court and the patriarchate into an exile in Nicæa (Nikaia). Thus, Athos, Italy, Patmos and Sinai became monastic scriptoria whose scribes became very active (also in an innovative way to save this tradition), while it was simply continued at the Hagia Sophia of Thessalonika. This collection had without any doubt a local focus, but was written outside Constaninople in “another notation”.

Thus, talking about the great signs (also called great hypostases) we must make a difference between two evolutions of notation, the one of sticherarion which developed out of differentiation of thematismoi and the one of the asmatikon which developed out of the “Roman” practice of cheironomiai (the hand signs which coordinated the singers of the choir, a congregation of specialised singers who served at the Hagia Sophia).

The crucial condition for the synthesis of the Papadike was actually the work of those external scriptoria who transcribed asmatika and kontakaria-psaltika in Old and Middle Byzantine notation, while no notated chant book of the cathedral rite has survived which had been written in the Constantinople before 1201. Of course, it does not mean that those books had not existed and the open question is what has been their authentic local notation.

In my next contribution, I will return once more to the question of the tonal system!

Comment by Oliver Gerlach on May 27, 2020 at 11:12

When I teach Byzantine music at universities, the most difficult thing is to teach about the different roles that different tone systems had.

Why did Chrysanthos introduce heptaphonia with the monosyllabic solfeggio like νη, πα, βου, γα, δι etc.?

Because he decided to fix the melos in notation for the first time in history! The answer is short, but not easy to explain, because it raises the question what was the level of Middle Byzantine notation and metrophonia, and if there was tetraphonia, which tone system ruled the melos.

To answer this question, we need one paragraph of a Latin treatise compilation of the 11th century known as «Alia musica» which did not care about the Carolingian oktoechos, but “about the Greeks” and their way to use the oktoechos. You find the quotation and its English translation here, and it is about an important term which can be found in Greek chant manuals as well called ἐμμελής:

https://en.wikipedia.org/wiki/Hagiopolitan_Octoechos#8_diatonic_ech...

And by the way, it is not “my private opinion”, dear Nikola, it is hard work to verify analytical observations and careful participating fieldwork (learning from traditional singers) by consulting historical sources.

Because there is one conflict between tetraphonia which might either appear within the octave species of tritos (F-f) or of devteros (E—e), and the result is also that the one of tetartos is in fact C—c (if you imagine the white keys with a particular low intonation for E and b natural for the diatonic genus). The Koukouzelian wheel does indeed a better job, as I already said, because one tetrachord and tetraphonia is enough to understand that Byzantine music and the living tradition is very well one tradition. But it means that mixolydian octave species is NOT G—g as Oliver Strunk and many other scholars of the “occidental school” believed! Thus, we have also an elegant explanation for Manuel Chrysaphes’ concept of phthora nana which clearly belongs to the Hagiopolitan oktoechos, and means "phthora nana is an elegant way to change from the tritos to the tetartos octave”.

It was a finding by Maria Alexandru and Christian Troelsgård who published the great wheel of Ioannes Koukouzeles in her contribution for the conference at Hernen Castle 2008 (fig. 4):

Alexandru, Maria, e Christian Troelsgård. «Development of a Didactic Tradition—The Elements of the Papadike.» In Tradition and Innovation in Late Byzantine and Postbyzantine Liturgical Chant II: Proceedings of the Congress Held at Hernen Castle, the Netherlands, 30 October - 3 November 2008, a cura di Gerda Wolfram e Christian Troelsgård, 17:1–57. Eastern Christian Studies. Leuven, Paris, Walpole: Peeters, 2013.

Papadike of the Great Lavra written in 1436 (GR-AOml ε.173, f.7v)

It is the earliest source with a great Koukouzelian wheel which has been preserved at Koukouzeles’ monastery and each peripheral circle has two parallagai, the usual for the pentachord (as represented by each little wheel itself) which has been written outside [!], while there is a second one inside which goes down from the kyrios phthongos seven steps (phonai), as you can see here at the devteros wheel (which is by the way called “lydios” and not “phrygios”):

The interesting detail is, if the singer goes down seven steps in (tetraphonic) polysyllabic parallage, the result is an augmented octave between the devteros and the varys phthongos!

One might think, in that case within the devteros melos there is an “emmelis” at order, and I have no doubt that it is correct, but within the context of the kalophonic method we should also consider the other possibility in case the singer is interested to leave the echos.

This exactly does happen in a kalophonic composition by Petros Bereketis about the first ode of the first canon ἐν βυθῷ κατέστρωσε ποτὲ of the devteros section in the heirmologion. Here is the old heirmologion:

Transcription according I-GR Cod. crypt. Ε.γ. II, f.29r

You find a comparison of Gregorios the Protopsaltes’ exegesis and Bereketis’ own notation here (both based on manuscripts of the music department of the Berliner Staatsbibliothek) here (click at the centred "Eirmos kalophōnikos Ἐν βυθῷ von Petros Bereketīs"):

http://ensembleison.de/publications/oktoichos/III/2/kalophonia.htm

Now, if you exactly apply metrophonia to the Middle Byzantine version of Petros Bereketis (Gregorios Stathes would rather call it “exegetic notation” and this might provide an argument for emmelis, but note the polysyllabic parallage was still tetraphonic in Bereketis’ time!), you will find at least a key to Thrasyvoulos Stanitsas’ intonation which is according to the “trochos”! Nevertheless, the medial signature leaves no doubt that exactly this was meant by the composer, because this is not a notation of the New Method:

Transcription according to an 18th-century Anthology (D-Bsb Mus. ms. 25053, f.24r)

How that sounds you can listen there!

There is also something which is not so trochos-like. Right at the beginning of the kolon πανστρατίαν you can hear that Stanitsas intonation of both tetrachords is not analogue, the legetos intonation of the plagios devteros is slightly deeper and results in an augmented fifth. The only explanation is a very particular medial signature for echos legetos used by Bereketis!

Comment by Oliver Gerlach on May 26, 2020 at 11:56

Last September, when I was at a conference in Bucharest (you might remember my announcement here among the events), something happened which I could not believe that it is possible! Maria Alexandru and her students at the Aristotle University of Thessaloniki dedicated a whole hour to the Mega Ison, the method of Ioannes Koukouzeles!

Together with her students and with the help of Adrian Sirbu (who made the protopsaltes and sang the echema, whenever the group of singers got lost!) it was not just them, but everyone in the room who had attended in great number the presentation to sing the whole Mega Ison. Not once, but twice! First the version written in Middle Byzantine notation, later the long version of Petros Peloponnesios which has been published as an exegesis (transcription according to the New Method) by Chourmouzios the Archivist.

The difference between both versions is that only one of them finds its way out of the maze of Oktoechos!

Especially tricky are the sections in echos varys and the following one dedicated to the plagios tetartos, because here there is a permanent change, between the enharmonic form of echos varys (which dominates the current melopœia of the oktoechos) and the heptaphonic form (which corresponded roughly the octave species F—f). These switches between tetraphonia, triphonia and heptaphonia made this section to the most difficult and most feared section of the mathema Mega Ison!

You also find an analysis here in the article Papadic Oktoechos:

https://en.wikipedia.org/wiki/Papadic_Octoechos#Mega_Ison

This article is entirely by me, because during my revision of the article Oktoechos, I was forced by administrators to divide it into three parts. A certain user found it worth to translate all three parts as three new articles in the Greek wikipedia.

If you expect something like this as a conclusion of the first section of the sticheron idiomelon τῷ τριττῷ τῆς ἐρωτήσεως (since the Koukouzelian method was chosen to beautify it and since the revised edition of the sticherarion also begins the next section on the heptaphonon and not on the triphonon like in ealier sticheraria), you might be dissapointed, because the nenanismata at the end simply recapitulate the modal structure of the first section given by its medial signatures.

In fact, this mathema does recapitulate the given structure twice. First in a prolonged echema which uses the first syllable of the text as a kind of introducing kalopismos:

Beginning with echema for the sticheron kalophonikon over SAV 628 (D-Bsb Mus. ms. 25059, f.757v-758r)

I used three frames in different colours, because we have the diatonic melos of the tetartos echoi (the kyrios in red and the plagios in blue, later we also have the diatonic mesos or diphonon in white!) and the yellow frame for the enharmonic melos of phthora nana as second mesos on the triphonon. You can study the same within nenanismata at the end, and the tension between the phthongos tritos and devteros are exactly what the organum about the responsorium «Petre amas me» is about.

Concerning this recapitulation one might quote again Manuel Chrysaphes, who said (you find the quotation in my doctoral thesis in the introduction to the very same section):

ἔνθεντοι κἄν τοῖς καλοφωνικοῖς στιχηροῖς οἱ τούτων ποιηταὶ τῶν κατὰ τὰ ἰδιόμελα μελῶν οὐκ ἀπολείπονται, ἀλλὰ κατ’ ἴχνος ἀκριϐῶς ἀκολουθοῦσιν αὐτοῖς καὶ αὐτοῖς μέμνηνται. ὡς γοῦν ἐν μέλεσι διὰ μαρτυρίας καὶ τῶν ἐκεῖσε καιμένων μελῶν ἔνια παραλαμϐάνουσον ἀπαραλλάκτως, καθάπερ δὴ καὶ ἐν τῷ στιχηραρίῳ ἔκκειντο, καὶ τὸν ἐκεῖσε πάντες δρόμον παρ’ ὅλον τὸ ποίημα τρέχουσιν ἀμετατρέπτει, καὶ τῷ πρωτέρῳ τε τῶν τοιητῶν  εὶ ὁ δεύτερος ἕπεται καὶ τοῦτο ὁ μετ’ αὐτόν, καὶ πάντες ἁπλῶς ἔχονται τῆς τέχνης ὁδοῦ. ὄτι δὲ ταῦθ’ οὕτως ἐχει, καθάπερ ἐγώ φημι νῦν δῆλον ἐντεῦθεν.

Thus even in the kalophonic stichera the composers of these do depart from their original melodies but follow them accurately, step by step, and retain them. Therefore, they take over some melodies unchanged from tradition and from the music thus preserved (as it is recorded in the old Sticherarion), and they all follow the path unaltered throughout the entire composition. The second composer always follows his predecessor and his successor follows him and, to put it simply, everyone retains the technique of the art. That things are as I now say can be seen from that follows.

On the other hand, we have to face a challenge within the musical architecture, because the main echos of the sticheron is echos tetartos and the use of phthora nana forces a resolution into plagios tetartos, at least according to the Hagiopolitan oktoechos!

Here Ioannes Plousiadenos introduced a category which he called “echos kratema” which is in fact a paraphrase of a paragraph taken from the Hagiopolites:

Εἰσὶ δὲ καὶ φθοραὶ δύο, αἵτινες ψάλλονται σὺν αὐτοῖς, τὸ νανὰ καὶ τὸ νενανὼ. Εἰσί δὲ καὶ ἄλλαι φθοραὶ τῶν ἄλλων ἤχων ἀλλοὐκ εἰσὶ τέλειαι ὡς αὗται. Εκεῖναι γὰρ δεικνύουσιν ἐναλλαγὴν μερικὴν ἀπὸ ἤχου εἰς ἕτερονἶ αὐταὶ δὲ τέλειαι οὖσαι ἔχουσι καὶ κρατήματα ποινθέντα παρὰ τῶν κατὰ καιροὺς ποιητῶν ὡς εἰς κυρίους ἤχους, καὶ εἰκότως ἄν [τις] καλέσειεν αὐτὰς τελείους ἤχους καὶ οὐ φθορὰς.

There are two phthorai which can be sung with these [eight echoi]: the ‘nana’ and the ‘nenanô’. There are also phthorai for the other [diatonic] echoi, but they are not as perfect as these. Because those show a temporary change going from one to another echos. But these had been used by other composers as echoi kratemata, because they are perfect. Thus they might be called ‘perfect echoi’ and not just ‘destroyers’ (phthorai).

It means that within the tropologion, there was a need to integrate two additional echoi within the system of eight diatonic echoi, but due to their perfection, it is also correct to compose the concluding section of nenanismata in an own echos which is called “echos kratema”. In short: in this particular case a composition which opens in echos tetartos and concludes in the echos nana is correct, because the latter is an echos kratema!

Its perfection also means that the kratema or nenanismata can stand for itself. Note that the kratemata section of the printed heirmologion kalophonikon has three kratemata composed by Petros Peloponnesios which he did not compose as conclusions for heirmoi kalophonikoi, but as conclusions for stichera kalophonika!

Comment by Oliver Gerlach on May 25, 2020 at 17:56

Now what is the role of triphonia within a notation system which is so obviously based on the trochos system?

There is always a simple way to integrate triphonia within the trochos, you can always do a transposition (ἡ μεταβολή κατὰ τόνον) to change between the rings, in ascending direction you can always change the ring, whenever you arrived in a yellow room of tritos (the end of a nana tetrachord) by looking for the violett room... Thus, echos tritos becomes plagios tetartos and the beginning of another tetrachord (a transposition up about a fourth). In that case we have to do very frequently transpositions which requires the use of a particular phthora for the phthongos of plagios tetartos! By the way, this is a quite common practice for editors today who have to deal with Chrysanthos’ New Method, but not so common for notators using Middle Byzantine notation since the 14th century!

Why?

The xeron klasma is a much more elegant solution, because it indicates a change of parallage (also because there is not simply a transposition, but also a change from the diatonic to the enharmonic genus)! I would like to remind you that this concept already existed in the Hagiopolites (you can check it in the wikipedia article about phthora nana which was improved by myself, where you find a chronology of theoretical definitions of one and the same phthora)!

We shall see, what it really means by a look at the Old Byzantine and the Middle Byzantine version!

As you can see, the first section of the sticheron SAV 628 ends clearly on the phthongos πλδ῾ which lies on C (a fifth under the beginning on G which was indicated by a tetartos echema as phthongos δ᾽!).

But what follows in the 12th-century version is a fourth (tritos as triphonon with respect to plagios tetartos), while Athanasios transposes the triphonon defined as tritos nana (the enharmonic mesos) a fifth higher which results in heptaphonia: the nana echema on the heptaphonon which is the octave!

Now, I would like that you have a look at a manuscript at the Staatsbibliothek of Berlin which you can find, if you click at the centred line "Stichīron kalophōnikon τῷ τριττῷ τῆς ἐρωτήσεως" and a window opens which allows a comparison of the Milanese sticherarion with this sticherarion kalophonikon:

http://ensembleison.de/publications/oktoichos/III/3/analysis.htm

This manuscript (Mus. ms. 25059 at the collection of the music department) is a systematic menaion notated as a sticherarion kalophonikon which has more than 1900 pages. It was written by Gabriel of Yeniköy, where also Petros Peloponnesios follower and protégé Petros Vyzantios came from. I do not know, when exactly. But it seems that this menaion could be a systematic effort which followed Petros Peloponnesios’ own occupation with the Byzantine heritage of sticheron kalophonikon and anagrammatismos which basically means the kalophonic method to do the thesis of melos as they had been defined by composers of the Late Byzantine period.

In case of this particular sticheron kalophonikon made over the first section of SAV 628, it is a realisation by Nikolaos Kampanes, but with nenanismata made according to the Koukouzelian method by Mega Ison. It is also useful to compare this sticherarion kalophonikon which was obviously meant as an exercise book (mathematarion) for the students of Petros Peloponnesios with the less systematic collection of an earlier sticherarion kalophonikon of the British Library (MS 28821, see my description here). This manuscript has been continued over a span of more than 100 years, but only treated major feasts where such a kalophonic realisation might be expected!

I would like you to take a look at this particular realisation written down in the analytical way of the 18th century, before I will continue this evening with more details about a kalophonic realisation of this particular section.

Comment by Oliver Gerlach on May 24, 2020 at 17:33

To say finally something about the tone system which is inherent Middle Byzantine notation: it is tetraphonia.

For that very reason I would like to apologise that the last example taken from the sticherarion of the Ambrosian Library at Milan was annotated with Guidonian letters, although the implicated intonation is quite different.

We need an appropriate medium for it, and its basis is parallage (ἡ παραλλαγή)! It means first of all the basic exercise to go through the phthongoi step by step with the echemata, either in ascending (δ᾽, α᾽, β᾽, γ᾽, δ᾽, α᾽ etc.) or in descending direction (β᾽, πλα᾽, πλδ᾽, υαρ, πλβ᾽, πλα᾽ etc.). But if we use this technique of solfeggio for what was written down with phonic neumes, it was called metrophonia.

This all is not too much interesting for Nikola, because he knows this very well. But from a first impression one might get from the last example one might even understand August Wilhelm Ambrose who just looked at it without any proper understanding for the music: he said the Byzantine music is a Chinese translation of Ancient Greek harmonics.

In fact, also medieval Greek authors remarked a difference, thus, they called the contemporary music "music" (ἡ μουσική) and this has also been an inspiration for the Arabic perception of Byzantine music (even before Ancient Greek treatises of science had been translated: it happend during the 10th century in Baghdad). But already during the 8th century there was someone in Baghdad who had a very high appreciation for Greek musicians and their system of parallage. It was Abū Yaʿqūb ibn Ishāq al-Kindī and he wrote:

"Every style of any tribe takes part of the Byzantine eight tones (hiya min al-alhān at-tamāniya ar-rūmīya) which I mentioned here. Everything which can be heard, be it the human or be it the animal voice – like the neighing of a horse, the braying of a donkey, or the carking of a cock, can be classified according to one of the eight modes, and it is impossible to find anything outside of the eight mode system."

This quotation does not prove, of there existed transposition in al-Kindi’s time, but it definitely does prove that each phthongos (whatever it was) could be classified as an echos which he translated with "al-lahn" (this term is still in use among Coptic Christians). It means that contemporary musicians were deeply inspired by the Greek technique of parallage and the inherent use of tetraphonia. Even so much, that they characterised the Arabic-Islamic music (today known as "maqam music") as a synthesis of the best of Persian music and the Byzantine tradition of Damascus. And, since Persian and Greek were the main points of reference for the cultural renaissance of the Eastern caliphates, they even adopted the Greek term "mousike" (transcribed al-muziqī) to describe the difference between Ancient Greek harmonics and their autochthonous contemporary music theory.

Thus, it would be much more appropriate to replace for the beginning G—CG—Gab—aG with the numerals of the echemata such as δ᾽—πλδ᾽δ—᾽δ᾽α᾽β᾽—πλα᾽πλδ᾽ etc. Or: if you prefer a spatial imagination:

The numbers stand for the sequence of medial signatures as they are used in the first section of the sticheron. As you can see, it worked very well. One can say the simple form of the wheel is enough to stay in the melos within one echos, but with a medial signature I have to change to the room of another echos!

But there is one very important thing to understand (something which was not understood by Ambros, but very well understood by Chrysanthos who still learnt psaltic art with Papadic teaching), is that just reading notation as we have done so far, is not yet doing the thesis of the melos. The melos comes after the memorisation of the base structure by metrophonia, and there are different methods to do the thesis (like palaion or kalophonia).

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