Musicologie Médiévale

Resources for medieval musicology and liturgy

Erevnidis, P., 2006. “'In the Name of the Mode': Intervallic Content, Nomenclature and Numbering of the Modes.” In L. Dobszay, ed. Papers read at the 12th Meeting of the IMS Study Group “Cantus Planus” Lillafüred/Hungary, 2004. Aug. 23–28. Budapest: Institute for Musicology of the Hungarian Academy of Sciences, pp. 93–114. CP 2004.


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.



Alekseeva, G. & Gordeev, D., 2012. Механизмы адаптации византийской культуры в России: пение, церковна.... Българско музикознание, 2012(3-4), pp.170–179.
Bernhard, M., 2003. „Die Rezeption der ‚Institutione musica‘ des Boethius im frühen Mittelalter“. In Boèce ou la chaîne des savoirs: Actes du colloque international de la Fondation Singer-Polignac, présidée par Edouard Bonnefous, Paris, 8-12 Juin 1999, ed. Alain Galonnier, 601–12. Leuven: Peeters Publishers. Google.
Berthelot, P.E.M. & Ruelle, Ch.-É. eds., 1887-1888. Collection des anciens alchimistes grecs. 4 vol (vol. 1, 1887; vol. 2, 1888; vol. 3, 1888; vol. 4, 1888). Paris: G. Steinheil (reprinted London: Holland 1963; Osnabrück: Zeller 1967).
Chailley, J., 1956. Le mythe des modes grecs. Acta Musicologica, 28(4), pp.137–163. doi:10.2307/932142.
Chrysanthos, 1832. Θεωρητικὸν μεγὰ τῆς Μουσικῆς. P. G. Pelopidēs, ed. Triest: Michele Weis.
Romanou, K.G., 2010. Great Theory of Music by Chrysanthos of Madytos translated by Katy Romanou. New Rochelle, New York: Axion Estin Foundation.
Gombosi, O., 1938. Studien zur Tonartenlehre des frühen Mittelalters. I. Acta Musicologica, 10(4), pp.149–174. JSTOR.
Gombosi, O., 1939a. Studien zur Tonartenlehre des frühen Mittelalters II. Acta Musicologica, 11(1/2), pp.28–39. JSTOR.
Gombosi, O., 1939b. Studien zur Tonartenlehre des frühen Mittelalters II. (Fortsetzung). Acta Musicologica, 11(4), pp.128–135. JSTOR.
Gombosi, O., 1940a. Studien zur Tonartenlehre des frühen Mittelalters. II. (Schluss). Acta Musicologica, 12(1/4), pp.21–29. JSTOR.
Gombosi, O., 1940b. Studien zur Tonartenlehre des frühen Mittelalters. III. Acta Musicologica, 12(1/4), pp.29–52. JSTOR.
Kujumdzieva, S., 2012. The Тropologion: Sources and Identifications of a Hymnographic Book. Българско музикознание, 2012(3-4), pp.9–22.
Lagercrantz, O., 1911. Elementum: eine lexikologische Studie, I., Uppsala: Akademiska Bokhandeln. Leipzig: Otto Harassowitz. Archive.
Lagercrantz, O., 1913. Papyrus graecus holmiensis (P. holm.); Recepte für Silber, Steine und Purpur, bearb. von Otto Lagercrantz. Hrsg. mit Unterstützung des Vilh. Ekman’schen Universitätsfonds, Uppsala: Akademiska bokhandeln. Archive.
Lawergreen, B. 2009. Music History i (Pre-Islamic Iran). Encyclopædia Iranica.
Lewis, F., 2002. Hafez ix. Hafez and Music. Encyclopædia Iranica 11 (5), pp.491-498.
Lingas, A., 1999. Performance Practice and the Politics of Transcribing Byzantine Chant. Acta Musicae Byzantinae: Revista Centrului De Studii Bizantine Iaşi, 6, pp.56–76.
Maguire, H. ed., 1995. Byzantine Magic, Washington, D.C.: Dumbarton Oaks Research Library and Collection.
Neubauer, E., 1990. Arabische Anleitungen zur Musiktherapie. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften, 6, pp.227–272.
Neubauer, E., 1994. Die acht “Wege” der arabischen Musiklehre und der Oktoechos – Ibn Misğah, al-Kindī und der syrisch-byzantinische oktōēchos. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften, 9, pp.373–414.
Neubauer, E., 2009. Music History ii (ca. 650 to 1370 CE). Encyclopædia Iranica.
Nuvoloni, L., 2007. Medieval Medical and Alchemy Manuscripts in the Harleian Collection. London: British Library.
Raasted, J., 1966. Intonation formulas and modal signatures in Byzantine musical manuscripts, MMB, Subsidia, 7. Copenhagen: E. Munksgaard.
Raasted, J. ed., 1983. The Hagiopolites —A Byzantine Treatise on Musical Theory, Cahiers de l'Institut du Moyen-âge Grec et Latin, 45, pp. 1-99.
Sahas, D.J., 1972. John of Damascus on Islam: The “Heresy of the Ishmaelites”. Leiden etc.: Brill. Google.
Školnik, I. & Školnik, M., 1994. Echos in the Byzantine-Russian Heirmologion. An Experience of Compa.... Cahiers de l’Institut du Moyen-Âge grec et latin, 64, pp.3–17.
Strunk, W.O., 1942. The Tonal System of Byzantine Music. The Musical Quarterly, 28, pp.190–204.
Terzioğlu, A., 1990. Über die Architektur der seldschukischen Krankenhäuser in Iran, im Irak, in Syrien und in der Türkei und ihre weltweite Bedeutung. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften, 6, pp.195–226.
Wright, O., 2004. The Sight of Sound. Muqarnas, 21 (Essays in Honor of J. M. Rogers), pp.359–371.
Wright, O., 2006. Al-Kindi’s braid. Bulletin of the School of Oriental and African Studies, 69, pp.1–32.

Tags: Arab Music, Boethius, Greek alchemy compilation, Hagiopolites, Ioannes Damaskenos, Jerome of Moravia, Oktoechos, Ptolemy, Syria, Tropologion, More…al-Farabi, al-Kindi, al-Mawsili

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Replies to This Discussion

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






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


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.


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. 


Гексаих — древнерусская ладовая система

Cт. Смоленский. О древнерусских певческих нотациях. Памятники древней письменности и  искусства. т. 145, 1901,


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.

May be, You are wright. I must think about this question. large - this is CDEF, small - DEFG, ukosnenny tetrachord - EFGA

The "Byzantine tonal system" was certainly not just the systema teleion (as some might understand by reading the summary written by the sisters Školnik), but this was probably also my contribution to the subject since I recommended to reconsider the role of the three tone systems (after Chrysanthos it became even four due to his concept of diphonia ruling the current melos of echos devteros). Such a view would also prove that a Al-Kindi's reception of the Byzantine tradition was sufficient, even if he could not have access to the later translations of Ancient Greek treatises of science as did Al-Farabi.

Plousiadenos' triphonic parallage worked surprisingly well for its integration of all genos combinations used in psaltic art:

Now considering the theory of hexaechos, you might be also interested in Jean Claire's theory of an archaic system based on DO, RE, and MI, preceding the Carolingian reception of the Hagiopolitan Oktoechos. I quoted in the group "Meloi" the Lesser perfect system (according to Aurelianus' Cassiodorus quotation), but nobody was ready to draw any parallels to this theory. I like that in case of the Russian reception, it is rather creative than archaic. I leave you here Thomas Kelly's translation of Jean Claire's crucial essay:

Claire, J., 2008. Modality in Western Chant: An Overview. Plainsong and Medieval Music, 17, pp.101-127, doi:10.1017/S0961137108000831.

It might be possible that these modes were not that "primitive" as Jean Claire was tempted to believe...

Dear Oliver! Thank You for Your information. It is very important. I am sorry, I can not open this article by Claire, I read only abstract about the author. I hope, in Russian chant adaptation of Byzantine system of singing was realy. I am sorry, I dont know about  Al-Kindi and Al-Farabi theories. Write me please several works about these scientists. I will be read. I think about the adaptation problems all time, but I have not full information about these questions. And I have not enough time, because I am teacher for my students and aspirants, who study different problems, not only palaeography.

Dear Oliver! In Greece (October 2015) I listened report of Achilles about connection between tones of arabic instruments and Byzantine Echoses. I send you the program of thus conference. This report may be important for understanding the Al-Kindi theory. I see many similar ideas.

Achilles not only spoke about this, but invited the orchestra of arabic musik.


Ἀχιλλεὺς Χαλδαιάκης, νεομεθοδικὲς συνθετικὲς πρακτικές: ἰδέα, διαμόρφωση καὶ ἐπέκεινα προ- οπτικές  - this is report.

My Greek colleagues told me about it last year, when we met before in Sofia. Despite of his traditionalist approach, they are some musicians like Kyriakos Kalaitzides in Thessaloniki and Evgenios Voulgares in Patras who both teach the instruments of "the Polis" to young musicians since 2005, see for instance the concert of November 2008 with a rather radical approach (simply understanding makam segah as ἦχος λἐγετος). Now, they become more relaxed about the Ottoman history which is important. On the other hand, I appreciate that Greeks have such a profound understanding of history, since Plovdiv became "European capital of world heritage" many just call the Ottoman architecture of the historical centre "Old Bulgarian," the ony exception is the beautiful mosque which is 100 years older than all the mosques of Istanbul!

But the exchange is much older than the history of the Ottoman Empire and Al-Kindi is one of the earlier sources we have...

Please do not worry about Jean Claire, it is probably not so relevant for you. I just would like to tell you that there is also Western theory of primitive modes based on DO, RE and MI. Only the formalist consequence (à la Todorov or Shklovskiy) is missing that its tone system could be organised in triphonia. But as a Russian reception of Byzantine music this is very interesting!



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