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 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 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 text 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 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 into 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 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).

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 into 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 into 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 Oliver Gerlach on May 24, 2020 at 11:21

So far about simple echos-melodies which are not that simple within an heirmos, because the ode meter is a very sophisticated one and it can be used to compose new canons as well as akrosticha which multiply each ode with the composition of new stanzas for a certain feast.

This is one genre of the tropologion, another one are the so-called idiomela (unique melodies which have to be rather understood from the complex nature of the musical form which might change the echos within its melos and these changes—αἱ μεταβολαὶ κατὰ ἤχον—are indicated by medial signatures). Although there are called idiomela, there are exceptional cases which had been used as models for newly composed stichera (at least by Iosiph, the brother of Theodore Stoudites). We also find the term used in a similar way for kontakia. Those kontakia which are not made as prosomoia  about another prooimion or oikos, are also called idiomela, some of them had been used as model (either the prooimion or the oikos), most of them are truly unique.

In my doctoral thesis I tried to show that whole stichera idiomela of the menaion or of the moveable cycle could have been sung as whole pieces by the choir (with temporary changes to a soloist) acording to the conventional method (called "palaion" which could be translated as "old school") or according to a new method which was called "kalophonic" ("embellished" or "beautified") and so elaborated that the stichera idiomela had to be divided in parts, because the performance of the whole sticheron in this way would take too much time!

Within section three of my third chapter of my doctoral thesis, I analysed this kalophonic method about the first section of the sticheron idiomelon τῷ τριττῷ τῆς ἐρωτήσεως composed in echos tetartos (SAV 628).

Here is the sticheron in well developed Coislin notation (12th century):

A-Wn Cod. theol. gr. 360, f.143v  (MMB Facsimilia 10)

The red frame is again around the main signature and the xeron klasma which indicates the change to phthora nana (its enharmonic genus and its triphonic tone system). Note that also this scribe did not even use medial signasignatures, but the notator Athanasios Hieromonachos did who added the notation in this sticherarion written during the 14th century in Constantinople:

I-Ma Cod. ambros. A 139 sup., f.141v (MMB Facsimilia 11)

This particular use of xeron klasma (as we can see at the following medial signature) causes the enharmonic tritos signature: the echema nana!

This sticheron idiomelon (SAV 628) corresponds roughly (in its liturgical function) to the reponsorium prolixum "Petre amas me" composed in the Phrygian E mode, but its text is a homiletic poem more remote of the Gospel text (John 21:17) which dominates in the Latin responsorium. Its feast is St Peter and Paul (29 June).

Comment by Oliver Gerlach on May 23, 2020 at 7:09

So far, this was just mainstream Byzantine musicology. Here it  seems the phthora nana indicated by a xeron klasma marks the top of a tetrachord (mesos or diphonon within the protos pentachord), the open question is if it causes another connected tetrachord which tunes the b to the proportion 4:3 (b flat), but it is not clear for how long, because the protos cadence requires b natural. In any case this seems to be a case, where phthora nana was only used temporarily in an accidental way.

In an Old Byzantine heirmologion written with Coislin notation (because we are still watching out for the xeron klasma), we might consult the fonds Coislin 220, where the 17th canon of echos protos has an alternative version for the second ode which uses the same text (a rubric says that it is sung during the third week of Lent).

F-Pn fonds Coislin ms. 220, f.21r

In fact there is no xeron klasma!

Here the same kolon obviously begins a fifth higher (protos phthongos) and descends at the end of the kolon to the mesos which simply has a klasma and followed by chamile which indicated that the following kolon begins a fifth lower (not a fourth). Thus, the cadence on the tritos phthongos has its plagios called "varys" under it and the whole flavour of phthora nana was obviously a redaction of this ode which belongs to the 14th century and Ioannes Koukouzeles period, but it was different during the 12th century.

Comment by Oliver Gerlach on May 22, 2020 at 10:54

Now, what was something which I only discovered in my last publications, let us say since 2016, was that tone systems are already inherent in notational systems. Thus, they form the musical mind and structure the musical memory. I learnt it already during my doctoral thesis while I developed a three-dimensional form of the wheel, but 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. Doing such a difference, one discovers notation as a cognitive tool to understand music, but it is not neutral, it is a kind of medium!

The comparison between Slavic and Greek notation proves that. Znamennaya notation was obviously ruled by triphonia, Middle Byzantine notation by tetraphonia, the repertoire of the tropologion is basically the same (and we have since the late 14th century manuscripts whose scribes tried hard to reconnect to the redaction of the standard abridged sticherarion and heirmologion of the Koukouzelian reform, see my list for these anthologies at the Russian State Library). The open question is, what was the inherent tone system of Kondakarian notation and its Greek counterpart Asmatikon notation (this notation was taught by Byzantine chanters in the eclesiastic centres of the Rus’, not the other way round!).

My first example is just, how the Coislin sign xeron klasma worked within Middle Byzantine notation of the heirmologion:

Copied after I-GR Cod. crypt. 88 (E.γ. II), fol. 6 (MMB Facsimilia, 1)

If you click at the picture you can listen to my proposal to sing out of this notation (it is a Bonum est episode at Concertzender Amsterdam dedicated to the work of my Ensemble: listen at 3'20"). I did it as a sound track of a film, a recording which was done at the studios of Cinecittà at Rome in summer 2003. I do not think that the melos was much different from the basic structure fixed here in Byzantine round.

In the forelast line, we have a first medial signature for phthora nana which is preceded by xeron klasma. It causes a temporary change to phthora nenano, but the canon belongs to the first (echos protos) section of this Constantinopolitan heirmologion! Please note that the original scribe did not use medial signatures, just a main signature and kola within the text.

In a way, Nikola was right to call this "teaching", because what I am doing here is re-inventing a lost tradition of Byzantine chant. It is not on the same level, what Nikola does who is part of the Bulgarian tradition. Within the tradition of Bulgarian chant, we have an Anthology for Orthros (Utrenna) whose middle section is mainly based on the katavasies taken from the Slow Heirmologion by Petros Peloponnesios (there is also a fast one created by his student and follower Petros Vyzantios). As Manolis Giannopoulos has proved, Petros Peloponnesios relied in great parts on the abridged heirmologion by Balasios the Priest, he merely corrected Balasios accentuation of the text. Chrysanthos’ is indeed a rich source for the school of the two Petroi, and documents a change in the prosody of the Greek in canon poetry, or at least a change in the way how chant and its text has to be combined with respect to accentuation (especially Chrysanthos’ polemics against Petros Peloponnesios’ rival Iakovos are interesting).

What Nikola does is the current tradition, what I tried here is an experiment which claims no authority that he might claim for his contribution. I am quite aware of it, but one should note that the old models were still present during Ottoman times in the kalophonic melos of the heirmologion (the heirmologion kalophonikon was published by Gregorios the Protopsaltes in print in 1835). Apart from Petros Peloponnesios and Gregorios the main contributor were Petros Bereketes and Balasios, who learnt their art on Mount Athos.

I used some passages from the model and tried also kalophonic way (2'24"), because thus, it was easy to arrange with the cuts in the film.

To summarise the written version, it begins one step higher from a as phthongos of echos protos, if you follow the steps in tetraphonia, the so-called metroponia (kyrioi echoi for ascending steps, plagios for descending ones), it starts: β᾽γ᾽—πλα᾽ etc. the cadence in phthora nana is on F.

Comment by Oliver Gerlach on May 21, 2020 at 17:09

Now, after all these preliminary remarks I come to the subject tone systems which is one of the basic categories of harmonics (sg. τὸ σύστημα, pl. τὰ συστήματα). The change between them is called ἡ μεταβολή κατὰ σύστημα.

The change to triphonia was indicated by a sign which indicated the phthora nana (φθορά νανὰ). The interesting circumstance is that it is called phthora ("destroyer"), but in fact according to Papadic teaching such a change to the system of triphonia was not indicated by a phthora, but by a great hypostasis called "xeron klasma" (τὸ ξηρὸν κλάσμα):

You can check the section phthorai in the Papadikai, but you will not find any phthora which indicates the change of genos (to the enharmonic genos) and the change to the triphonic tone system, but it is this sign which has a very particular history.

The history of notation within the sticherarion and the heirmologion can be described between theta notation and Middle Byzantine notation. The theta or Slavic fita notation means the letter θ (τὸ θέμα) which had various meanings (see Liddel & Scott). It could be as well an oxeia (ἡ ὀξεῖα) / or a diple (ἡ διπλή) // which just marked syllables with a melisma. Two different Old Byzantine notations developed out of an explanation of these signs by adding other signs, one was Coislin notation used at the scriptoria of Jerusalem and Egypt and the other Chartres notation used at the scriptoria of Constantinople and of the Holy Mount Athos. The sign ξηρὸν κλάσμα can be used to make a difference between both notations, because it does only exist in Coislin notation!

Now if we compare roughly Slavic znamennaya and Greek round (uncial) notation, there is one odd thing:

The first basically always remained on the diastematic imprecision of Old Byzantine notation, while round notation was the next step to Middle Byzantine notation which was already done roughly about 1220. The kryuki notation (late 15th century) used additional signs which indicated the exact position within trichords (which meant triphonia defined as two whole tones separated by a half tone), while round notation was based on tetraphonia.

The first and most important thing, a singer familiar with Neobyzantine or Chrysanthine notation has to learn when she or he reads Middle Byzantine notation is tetraphonia (the polysyllabic parallage and metrophonia). This is even true for musicologist, if they stopped to underlay Middle Byzantine notation heptaphonia by the use of the modern or monosyllabic parallage (solfeggio based on seven syllables according to Chrysanthos), they would be able to correct manifold errors they made in their editions.

But the switch from tetraphonia to triphonia within Middle Byzantine notation was done by the use of xeron klasma, the great sign which originally derived from Coislin notation.

I think this is pretty enough to learn for today! But it will enable us to study the different use of Middle Byzantine notation between the books of the cathedral rite and the sticherarion and heirmologion...

Comment by Oliver Gerlach on May 20, 2020 at 11:40

But if you like to go more into detail with this, we have this early papyrus (here the reconstuction with Lykourgos Angelopoulos):

Here the fragment itself:

The fragment, although from the end of the 3rd century, already delivers a whole melody be the use of Alypius notation. As you can hear from Angelopoulos’ choir it is a kind of phthora nana, not by chance, but because the Alypius notation represents in itself the system of triphonia, also known in Ancient Greek theory as the Lesser Perfect system.

Carolingian knowledge is simple to describe, because we have a limited corpus of manuscripts even with contemporary glosses and comments. Thus, we know about Boethius, not based in sources of Boethius’ time, but by late copies made during the Carolingian renaissance.

Concerning the Lesser Perfect system, they did know Martianus Capella, they did know Aurelius Cassiodorus (whose paragraph about LPS was copied by Aurelianus Reomensis, but he did not add anithing further that allows us to understand, what was the use of it), but they did not any treatise by Alypius nor his notation system.

Notation (even in the West) developed later by the end of the 9th century. Musicians in Byzantium could have used it. The fact is, they did not, simply because it was not useful! And Western notation was not very useful to notate temporary transposition, while we have very early evidence that it was crucial for Byzantine music (although it was rare even there).

Musica and Scolica enchiriadis have amazing descriptions of tetraphonia, which proves it was known in that period, but they also clearly reveal by the use of terminology that it was something Byzantine. They were important findings by Charles Atlinson who looked for conicidences between Papadic teaching especially in this early Carolingian theory explicitly dedicated to the oktoechos (a theoretical "tonary" as it was called). See my comment where I quoted from the handout which was made for Charles’ presentation during the conference in Bucharest last September.

I hope this picture corrected a little bit the wrong impression, one might get from a lecture of Chrysanthos, although his Theoretikon mega is definitely an important source for Ottoman music (and the Byzantine heritage and its notation was a crucial part of it).

Comment by Oliver Gerlach on May 20, 2020 at 0:50

First of all, you should first forget about certain ideas mentioned by Chysanthos that the Western reception is closer to Ancient Greeks harmonics than the Byzantine reception of it. This was also some decades later an idea by the Viennese composer and music journalist August Wilhelm Ambros, but unless Chrysanthos he had a very poor understanding of what has been written down in Byzantine chant books.

It is not very useful to occupy yourself with such a fog, it might be interesting for someone who studies the history of research in Byzantine studies and similar arguments among classical philologists like the ethnikoi in Greece...

Comment by Oliver Gerlach on May 19, 2020 at 18:50

Dear Nikola

No need to sorry, I am not here to be agreed. I will just send you, what is on my plate for just 20 minutes.

I answered the invitation with this title and abstract:


The generation around John Koukouzeles and the re-definition of the
Constantinopolitan tradition by the "Koukouzelian" reform


After the return of the Court and the Patriarchate from the exile of
Nikaia, the local tradition of the cathedral rite was not continued. The
Byzantine tonal system according to a common understanding taught by the
Papadike was defined according to the Koukouzelian wheel which was based
on fifth aequivalence (the trochos system and the practice of parallage)
and deeply rooted in the Middle Byzantine notation and the
chant books sticherarion and the heirmologion.

Since John Koukouzeles' Mega Ison as a method to teach all notational
signs did not change the notation system, but rather exploited a former
synthesis to transcribe the chant books of the cathedral rite (asmatikon
and kontakarion-psaltikon) with the notation of the sticherarion, the
synthesis of all chant books within one universal notation system was
well prepared and this preparation motivated Christian Troelsgård to
abandon the distinction of Middle from Late Byzantine notation. It was
also the basis of the integrative role of Papadic teaching which was
continued until the 19th century and the integration of the practice of
cheironomia in Koukouzeles' theory of the great signs. According to the
new theory of Papadike, the Hagiopolitan oktoechos was the universal
tonal system which had to integrate also the Constantinopolitan
tradition of the cathedral rite.

This synthesis is also the basic understanding of the Byzantine tonal
system since its description by Oliver Strunk in 1942. The current
understanding of the heritage of Byzantine chant is so deeply rooted on
the Papadic synthesis of the 14th century that it lacks a proper
understanding of the preceding tradition which was unified by the synthesis.

My paper is focussed on the kalophonic melos concerned with the
repertoire of the kontakia and its modal transformation."

I fear your imagination that we can go through it one by one is not realistic, even if I try (like I succeeded to organise as much time as possible my last time in Sofia). There are many details in my current publication which I will offer here as a case, but it will not be possible in Sofia, because I have also to present the maze of oktoechos, since the conference is dedicated to Ioannes Koukouzeles.

Nevertheless, the discussion has some public relevance and you might use it to prepare our exchange!

Comment by Nikola Antonov on May 19, 2020 at 10:39

Dear Oliver,

I'm sorry, but I couldn't agree with most of your statements. Each of them should be considered one by one. There are also some very serious and general misunderstandings regarding the Byzantine music theory, some basic definitions etc.  We will have to discuss it in detail at an opportunity to do it later face to face. Hope to meet you in Sofia.

Best regards,


Comment by Oliver Gerlach on May 19, 2020 at 7:22

I would rather avoid to say too much about Klara Mečkova’s first book, since I have not read it, but I can tell you about my own approach within my doctoral thesis (although I did trace it back to the Carolingian period, like Nina-Maria Wanek did it recently) that Byzantine history basically started with the 14th century and a new orientation towards Jerusalem during the period of the Stoudites.

This approach is not wrong, but with respect to Byzantine history one must be aware that we are looking back at it from the end of Byzantine history, some years after the fall of Constantinople and through the glasses of Manuel Chrysaphes. The tonal system described by Oliver Strunk was focussed on sticherarion and the Hagiopolitan oktoechos (it is obvious that the treatise itself was already written in Constantinople within a circle associated with the Stoudites). From this point of view, one can say it included many tone systems, but the question is what kind of evolution was necessary to integrate them. It seems tetraphonia was the earlier system, but this approach to the oktoechos is obviously focussed on the hymnography of Jerusalem (and with respect to Constantinople on Germanos’ school as far as canon poetry is concerned) and its book tropologion (also present in the Georgian Iadgari and the Armenian Šaraknoc'). It is not focussed on the oktoechos present at the Hagia Sophia and the repertoire of the cathedral rite (psalmody like in prokeimena, allelouiaria and koinonika, and other hymn genres like kontakia and hypakoai).

One should also bare in mind that those kontakaria-psaltika and asmatika had been written outside Constantinople and that Middle Byzantine notation developed during the last two thirds of the 13th century, when this famous tradition did no longer exist in the Polis. And then comes the question, what were the tone systems of the Byzantine tonal system in the narrow sense, something which was mainly discussed by Christian Thodberg, by Russian and Ukrainian scholars, and by Heinrich Husmann (who also supervised Constantin Floros’ habilitation)?

Comment by Oliver Gerlach on May 18, 2020 at 9:52

I did not only mention it, because experts of Eastern chant are rather a minority in this social network, and others might like to know more about the connection between Latin and Greek theory which was in fact a transfer from Greek to Latin.

But I agree with you, in that respect they have to care more about Greek and not Byzantine musicologists about Latin sources. I did this citicism already during another discussion (it was meant as as constructive criticism to articles published about Latin terms, see LmL) and result of this exchange was that I was asked to comment on concepts to teach Western music theory (see this discussion).

But here, I had to do it anyway, because it was my preparation to mention another group of sources which are more about Byzantine music (I already mentioned Oliver Strunk’s view on it) in the narrow sense which is the cathedral rite how it was celebrated at the Hagia Sophia (the Slavic kondakar’, the kontakarion-psaltikon and the asmatikon and a local book form created at the scriptorium of the Archimandritate SS. Salbatore of Messina: the kontakarion-asmatikon).

All these manuscripts were obviously not introduced by a chant manual unlike the tropologion and the notated chant books which followed the unnotated tropologion, at least not before the new book of the 14th century Akolouthiai. The latter was meant to replace three former books: the liturgical typikon, the kontakarion-psaltikon and the asmatikon and whose introduction was the Papadike, because the Middle Byzantine notation had become the integration of all these different chant repertoires which had once their own notation systems.


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