Musicologie Médiévale

Resources for medieval musicology and liturgy

Medieval Greek Chant Theoretical Streams as Scholia on the Harmonica of Claudios Ptolemaios: The Online Sources

In the present blog I’ll try to avoid terminologies and elements of Greek chant that, for one with no intimacy with the subject -a Gregorianist for example – can be perceived as foreign, difficult and laborious to deal with; mainly something exotic that should be left to those devoted to (Latin and / or Greek) music theory. I am aware that it could appear as more “neutral” and “unbiased” if I chose to simply list the online sources, but I prefer to go into more detail, adding some comments in the end about modern vocabularies. Addressing Latin chant specialists about online sources of Musica Enchiriadis is, after all, more straight-forward than informing them about Greek chant theory stuff. Last but not least, those who still believe that “it’s all Greek” to them can enjoy the diagrams and the schemes of the MSS; some of them are really beautiful.


A small introduction


The earliest Byzantine MSS of ancient Greek music theory (below I give the links of about 130 online MSS from 11th century onwards) appear to us –believe it or not- only after the 11th century. The D-Heu: Cod. Pal. gr. 281 (Mathiesen, 1988 No 14 [=Math. 14]) is written on 14 January of 1040 (or 6548 W.E.). The other MSS of 11th and 12th centuries are I-Vnm: Gr. app. cl. VI/3 (coll. 1347) (Math. 270, Vitrac 2019 [=Vitrac] p. 142, Acerbi-Gioffreda 2019, p. 655), I-Vnm: Gr. 307 (coll. 1027) (Math. 261, Vitrac p. 142) and later I-Rvat: Gr. 2338 (Math. 234, Acerbi-Gioffreda 2019 Va [13th century], p. 661) with I-Vnm: Gr. app. cl. VI/10 (coll. 1300) (Math. 273, Düring 79 M, additionally the 14th century hand of Grēgoras has been identified [Bianconi 2005, p. 413 No 12, Acerbi 2016, p. 186, No 10, e.g. he added the numbers and titles of chapters of book I of Ptolemaios’s Harmonica, see also Vitrac, p. 66 and p. 142]). But for us it is important to know the relation of them (and of the later ones) to medieval music.

Indeed, some of the, for example, 13th and 14th century Greek manuscripts that contain the treatises of ancient musicographers (who go back to 4th century B.C.), are full of medieval scholia and paratextual diagrams (mainly on Claudios Ptolemaios’s Harmonica [2nd century A.D.]) about Greek chant theory; a good deal of them (especially those connecting ēchoi to the names Dōrios, Phrygios etc.) never published. But first, let us begin with a useful note which shall underline the importance of these relatively late sources about the modern prospects of medieval chant in general.

A pattern? The earlier the sources the later the socio-cultural entity


We do not have in our disposal – in contrast to Latin chant- any text of chant theory in Greek (excluding few ekphonetic signs lists) from the 1st millennium. But in the neumes table of M. Lavra Γ 67, f. 159r (10th / beginning 11th century) there is the following - not rudimentary- chant theory sentence: the voices are seven, but the ēchoi four, three mesoi, two phthorai and four plagioi, voice 1st, voice 2nd, voice 3rd, voice 4th, voice 5th, voice 6th, voice 7th, that is the “fin(e)-al” (τελεία, more economically in French: “fin-al,” a medieval Latin speaking scholar would tended to translate it with the meaning of perfect, David Cohen, “‘The imperfect Seeks Its Perfection’: Harmonic Progression, Directed Motion, and Aristotelian Physics,’’ Music Theory Spectrum, Vol. 23, No. 2 [Autumn, 2001], p. 155 with n. 58 and 62). The, now conventionally named, Hagiopolitēs is a 14th century manuscript; we do not know how the 1st millennium appearance(s) of this treatise was. The first question is what happened and, given the cultural importance of medieval Jerusalem and New Rome, an earlier material didn’t reach us. As most people of M.M. know, the same question applies to the scarcity of indigenous sources from Old Rome before the Carolingian times [1*], not to mention theoretical treatises or even something like “primitive” considerations of – let us accept the linear phraseology for the moment – a not “full-fledged” Octoēchos. Rome was -and still continues frequently to be- thrown inferentially, together with any kind of material that “we” do not feel comfortable / understand, into the convenient box with the label “pre-theoretical period” (of exactly what and concerning whom?). The problematic on such speculations acquires even more importance if one thinks that we have MSS of Boethius’s De Institutione Musica already from 9th century – thanks to the preferences of the new Carolingian realm - and that the first Greek text of the Harmonica of Claudios Ptolemaios (who is quoted by Boethius) is appeared only in an above-mentioned 12th century MS (the MS Math. 273). Indeed, the sources that reached us [2*] didn’t appear in the past ex nihilo and / since, among others, they are the residues of many of historico-ideological sieves (like the issue of the existence of an Old Tropologion in Greek).


[1*] I am not referring here, of course, to the later notated sources of the so-called Old Roman chant.

[2*] Of disparate nature; as for the much better studied mathematical material see now, Vitrac, 2019, and for music already in Barbera’s edition of the Euclidean Division of the Canon (1991), especially pp. 104-111, see also p. 205 and n. 6 of my contribution to the 13th meeting of Cantus Planus (2006, here).


How music historiographies could be a projection to the past of modern conceptual frameworks


Let us now return to our subject. Surprisingly enough some of the above mentioned scholia / diagrams reflect, among others, Hagiopolitan music theory topics by quoting - and thus connecting them to - certain chapters of the Harmonica. One can assume that such an important material would attract the attention of the scholars of Byzantine chant of the 20th century, but this wasn’t the case and the aforesaid material remained a terra incognita. Why this happened is mainly the work of the ethnomusicologist of the future (here I give only some samples), but it is so amusing that Jorgen Raasted in his, “Quis Quid Ubi Quibus Auxilis… Notes on the transmission of the Hagiopolites,” Scriptorium 42-1 (1988), p.91 (Persée), passed just next to this Hagiopolitan material of Vat. gr. 192 since he referred to this MS but had not had the chance to consult it!

One can find such kind of information sporadically not in studies of Greek chant but in the book Ancient Greek Music Theory, by Thomas J. Mathiesen, RISM (BXI), 1988. In the bibliography (and mainly in the description of some MSS) Mathiesen gives information that there are interlineated and marginal scholia (extensively or not) mainly to the Harmonica of Ptolemaios and in some cases he understands that they have relation to Greek chant theory. Interestingly, he uses an atypical wording about the modern classification of Byzantine music theory in two classes (indeed, medieval reality appears to be more complex if one consults the MSS of ancient Greek music theory): “There are at least two major classes of Byzantine music theory, one dealing primarily with practical problems of musical notation and liturgical chant (the papadikai), and the other representing an archaicizing attempt to preserve ancient Greek music theory and philosophy and to apply it to Byzantine music theory” (emphasis mine). As a matter of fact the phrasing is not inaccurate if one recalls that even the earliest papadikai of the 14th century, report also a certain correlation of Dōrios Phrygios etc. with (i.e. apply them to) the numbering of the ēchoi in which, for example, the Lydios / Hypolydios is correlated to 2nd / pl.2nd ēchos respectively. Moreover, the papadikai system was also a product of intellectual (and “archaicizing”) effort (not only about the above mentioned correlation) [3*]. But for the above Mathiesen’s (1988) passage and his wider rationale and decisions see pp. xxx-xxxi (and about his hopes - some of them relative to our subject here - on p. xxxv-xxxvi). In my opinion, the high degree of isolation of these two frameworks in modern academia 1) on ancient Greek music and 2) on Greek (and other Eastern and Oriental) chant is the main reason that all this material remained unpublished, not catalogued and uncommented. A fitting analogy would be the scholia on Martianus Capella and Boethius having the same treatment. Adding to that is the seemingly established approach (based on our reconstructions) that Byzantine chant theory (whatever relation “had” this theory to actual practice) and ancient Greek music theory (whatever relation “had” this theory to actual practice) are treated as more separate entities in accordance to the degree of interaction they really had (especially after the documentation of the MSS of the 13th or 14th centuries we will see below). So this little presentation of online MSS is concerned with this “gray area” [4*] between the somewhat well-defined boarders of these two modern disciplines beginning the discussion with a primary selection of some online MSS just to realize the Byzantine chant status of affairs (or, the “accepted facts”) during the 20th century (and the first fifth of the 21st). The D. Touliatos-Banker, “Check List of Byzantine Musical Manuscripts in the Vatican Library,” Manuscripta. A Journal for Manuscript research 31 (1987) has to be seen under this paragraph’s prospect.


[3*] The exceptional use of a Hagiopolitan correlation in a papadikē would just demonstrate that a) in performance practice the results would be not of so much difference (at least, for us) and b) that all that theoretical effort and different streams was something important (for them), not only in terms of periphery-center.

[4*] As André Barbera, J.A.M.S., 43 2, 1990, p. 363 named it in his review of Mathiesen (1988) referring also to the importance of Vat. gr. 191 and connecting it, after A. Turyn of course, mainly to Maximos Planoudēs


N.B. A somehow exhaustive list of MSS, persons and scholia, given the problems of Düring’s edition of the Harmonica of Ptolemaios, could be possible only after a real critical edition of this text (Mathiesen, 1988, p. xxxiv and 2000, p. 432) and the inclusion of further paleographical studies (especially after the identification of the inks via spectral imaging) of the relative MSS. But the progress already made in the last few decades is of remarkable importance and any kind of skepticism based on the latest or future technologies (implying that the current state is not “convincing enough”) would be unfair, only alluding on supposed “neutrality” and an absence of “bias” and “ideology” of the wo/man who expresses such skepticism. The field is continuously being studied, with new additions being published; regarding earlier “codicological and palaeographic units” of the MSS we are dealing with, see now F. Acerbi-A. Gioffreda, “Harmonica membra disjecta,” Greek Roman and Byzantine Studies 59 4, Winter 2019 [=Acerbi-Gioffreda 2019] (here), accessed 24 November 2019. And one can also add the Mathiesen’s (1992) “Hermes or Clio…” (here), especially on p. 4 (on Why and How these treatises survived), p. 7 and pp. 14-15 with n. 22.

Below, slowly but surely, I have advanced my older work on the subject by giving a selection of eight MSS that include Greek chant information mainly on two - and occasionally on more - chant related topics i.e., α) on the I.16 of Ptolm. Harm. i.e., concerning the medieval use of equal diatonic genre and β) on the II.10 of Ptolm. Harm. i.e., concerning the correlation of Dōrios Phrygios etc. with the numbering of the ēchoi.

Eight online MSS with Greek chant information


I-Vat: Gr. 191 (Math. 214 [13th], Dür. 64 W [13th /14th], Acerbi 2016 p. 195, Vitrac [1296-1298] p. 145)

Content and Bibliographic References and at Pinakes (here)


According to Ingemar Düring, the editor of Harmonica (1930), it is stemming from the m-class and gives rise to the recension of its own subclass [W]. This is one of the most studied codices in relation to the included astronomical and mathematical material. Importantly, in some scholia the hand (the revisoris manus R of A. Turyn) of the intellectual and deacon Ioannēs Pothos Pediasimos recently has been identified (Pérez Martín, 2010) and he “assembled, and annotated at least between 1296 and 1302/3 the early Palaiologan mathematical encyclopaedia in Vat. gr. 191” (Acerbi 2016, p. 183 No. 3). His hand is also responsible for some crucial chant related scholia, within Harmonica, and a small theoretical text just after it. What, at first glance, we have here is:

α) As far as Ptol. Harm. I.16 (entitled, in Jon Solomon’s tr.: How Many and Which Genera Are More Familiar to the Hearing), on f. 331r, there is not any remarkable marginal or interlinear scholion in connection to equal diatonic.

β) Referencing to II.10 of Harmonica, on f. 340r, there is one extra correlation of the names Dōrios Phrygios etc. with the ordinals (and additionally, here, to the martyriai [modal signatures]) of the ēchoi. This correlation was the most proximate to the more widespread of the Latin chant and is different to the Hagiopolitan and the one of the Bryennios’s stream. I transliterate and provisionally translate in English:


Dōrios (is the name of) the 1st ēchos, Phrygios the 2nd, Lydios the 3rd, Mixolydios the 4th, Hypodōrios the plagios of the 1st, Hypophrygios the plagios of the 2nd, Hypolydios the plagios of the 3rd, that is the Varys, Hypomixolydios the plagios of the 4th. Ptolemaios, not properly (?!), says that the ēchoi of them are seven. And other people, speaking nonsense, name them otherwise. (emphasis mine, then follows the same nomenclature and the relative martyriai, I transliterate:)

Picture 1

The pneumata (spirits) are four, hypsilē, chamēlē, kentēma and elaphron, because we are in need of pneuma (both) for ascending and descending.


The tension in the wording is indicative of the tension among personalities of the time. Here most probably it is the monk Maximos Planoudēs (his friend Manuēl Bryennios and the historian and deacon George Pachymerēs represent the same ēchoi correlation stream [see them on f.101v of the autograph of Pachymerēs I-Ra: Gr. 38, not included in Math.]) that is implied to “speaking nonsense.” Remind also that –not only- in Hagiopolitēs the “schemes of diapason” are not numbered, as I wrote some years before, here in M.M., in the ancient way from 1 to 7 but from 2 to 8 (the online MSS that contain this form of Anōnymos III passage are: [Math. 87=] F-Pn: Gr. 2458 68r-v, [Math. 89=] F-Pn: Gr. 2460 27v, F-Pn: [Math. 95=] Gr. 2532  82r-v, [Math. 219=] I-Vat: Gr. 221 pp. 388, [Math. 230=] I-Vat: Gr. 1364 f. 134v, [Math. 238=] I-Vat: Barb. gr. 265 p. 458, [Math. 253=] I-Vat: Ross. gr. 977 pp. 178-179 and of course its ρ recension, the Hagiopolitēs MS F-Pn: Gr. 360 f. 229v together with the EG-MSsc: Gr. 1764, f. 94r-v [the very last MS, numbered 299, that Mathiesen decided to include in his Catalogue]). Vincent (p.224) already at 1847 realized that there is an interesting variation here and, reasonably, felt the need of an explanation.

Additionally, we have a totally unknown and unpublished small theoretical chant text on f. 359v, just after the Harmonica, with strong affinity, even in wording, to Pseudo-Damaskēnos [=Ps-D] text. Thus, we can legitimately label it as proto-pseudodamaskēnos and it is also important for the “pre-history” of Ps-D. The earliest testimony of the latter belongs to the 15th century. I provisionally translate the half of the whole text, in order to understand some of its content. It is also interesting regarding modern phraseologies about Latin chant in which we see terms like sign and neume. The relative concordances to Ps-D are given in parentheses as its editors did not use at all this early (as far as the Byzantine chant) text:


The principal (κύριοι) tonoi (are) ison, oligon and apostrophos (Ps-D 42-43): oxeia and petastē (are) so-called tonoi because they (are) dominated and diminished (συστέλλονται) (Ps-D 44) by the ison: as tonoi (are) called also the compound (σύνθετα) signs (contra [?] in Ps-D 49), but signs (σημάδια) (are) called when they are placed and written, and tonoi when they are sung (Ps-D 50-51):-

Ēchos and melos are different, because ēchos precedes melos (Ps-D 79-80), and there is not melos without ēchos, but ēchos exists without melos, and the ēchos always begins with the ison, but the melos begins with tonos and pneuma (spirit):

Psalm (is) melody with the use of a musical instrument, but Ōdē (is) the one with the use of mouth and without an instrument (Ps-D 85-88). The tonoi (are) fifteen since the (main) frets / bridges [5*] in Music are fifteen (Ps-D 152-153), and Ptolemaios said all these:-...


And then continues with another categorization of the 24 signs.

That means that the above text, one of the oldest best dated complete [6*] treatises of Greek chant, is not found in a papadikē and the like “church” MSS, as most people would expect, but just next to Ptolemaios, in a MS of ancient Greek music theory! This is an example of how “innocent” prospects predispose modern narrative as well as… findings.

Of the other online subclasses of Harmonica’s m-class we have 1) the E i.e., I-Vat: Gr. 186 (Math. 210, Vitrac p. 145, 13th c.), 2) the I-Vat: Pal. gr. 60 (Math. 242, Vitrac p. 165, where we see for α) the “softer of the intense diatonic” together with “equal diatonic” in the same scheme on f. 16r [like BNF gr. 2450, see below] and for β) ēchoi and enēchēmata (the intonation syllables of the ēchoi), on f. 26r in the order of Bryennios / Grēgoras) and 3) the 13th century I-Vat: Pal. gr. 95 (Math. 243, Dür. 73 13th/14th century, Pinakes [here]) of the M subclass.


[5*] Καβάλια / kavália (or καβάλλια / kavállia in Hagiopolitēs, as well as κάβαλα / kávala in other sources of Ps-D), in the edition of Ps-D a not good reading is adopted: kavála, see MS Dionysiou 570, 8r; best translation in French: chevalet (=almost a transliteration). In modern Greek something like καβαλάρηδες or better γέφυρες / περντέδες (from Ottoman-Turkish perde).

[6*] Complete, because there was plenty of space - in this initially blank page- for Pediasimos to continue to write if there was more text to add, but he didn’t. This text is not like 1) the (one) question-(one) answer material of the MS RUS-SPsc: Gr. 495, ff. 1v-4v, or 2) collections of en-ēchēmata (in-tonation formulas of the ēchoi) (here) without theoretical text, or 3) neumes material like F-Pn: Gr 260 ff. 253v or even 4) the dated 1289 F-Pn: Gr. 261 ff. 139v-140r that includes headings, and on f. 140v we have the oldest testimony - in the form of a “table”- of the widespread nomenclature of the papadikai. Here is not the place to discuss these –and more- cases (and their one by one labeling).


I-Vat: Gr. 192 (Math. 215 [13th], Dür. 65 V [13th /14th], Vitrac p. 145 [second half of 13th century])

Bibliographic References and at Pinakes (here)


This is a “mathematical miscellany” stemming from the m-class that gives rise to the recension of Düring’s subclass labeled V. It seems that this MS is the immediate (not entirely in chronological terms) predecessor of Vat. gr. 191 and unfortunately, it didn’t acquire so much –and not only - paleographical attention like that until now (consider e.g., the above Bibliographic References where some 11 works are sited in relation to the 116 for the Vat. gr. 191). As far as the content there are learned scholia written within and after the Harmonica linking it to the Hagiopolitan theoretical tradition of the Greek chant. But in this case we have one personality that published such an important material of scholia. He was the French polymath Théodore Reinach (1860-1928) in his - more than a century before – “Fragments Musicologiques Inédits,” Revue des Études Grecques, Tome X, No 39, July-September 1897, pp. 313-327 (Persée). Reinach transcribed and commented the theoretical texts / diagrams found - only after - the main texts of the MS Vat. gr. 192, leaving aside the scholia within the Harmonica. I will not elaborate, for the moment, on Reinach’s work. In relation to Greek chant and Ptolemaios we have the α) on f. 201v (and f. 223 [here there is only the name of “softer of the intense diatonic,” on that, see the next MS below] i.e., two times) and the β) on f. 225v (a scheme using whole tones and leimmata and in an name-order that Bryennios’s stream inverts in an absolute manner) respectively. Terms like mesos, phthora, enēchēmata, epēchēmata and apēchēmata and a trochos like scheme on f. 227r are found.

Other online MSS of this subclass [V] of Harmonica are F-Pn: Gr. 2451 (Math. 80) and F-Pn: Gr. 2453 (Math. 82).


F-Pn: Coislin gr. 173 (Math. 103 [15th], Dür. 51 [14th], see Acerbi 2016, p. 151, Vitrac p.154 [first half of 14th]) see also: Notice rédigée par Anne Lapasset, Fevrier 2015 (here) and at Pinakes (here)


On f.1 there is a possession note of the Megistē Lavra monastery at Mount Athos / Greece. Christos Terzēs in his edition of Dionysios (Athens, 2010, p. 115*) believes that the hands had not been identified (quoting Mathiesen, 1988) and that the MS is produced in Mount Athos. As far as the Harmonica the text belongs to Düring’s g-class that represents the recension of Nicēphoros Grēgoras (ca. summer 1293/June 1294 - 1358/1361 [after Divna Manolova’s Dissertation, Budapest, 2014,]). Indeed, “concerning the musical treatises, I-Vat.: Gr. 198 [Math. 218, Vitrac p. 146] is an apograph of Paris gr. 173” (Acerbi 2016, p.160). Note among Grēgoras’s autograph scholia (Bianconi, 2005, p. 415, No 25), the partly autograph one at the beginning of Harmonica on f. 32r (B. Mondrain, “Maxime Planoude, Nicéphore Grégoras et Ptolémée,” Palaeoslavica 10, 2002, p. 321 n.26).

α) On f.58r as scholion to I.16 of Harmonica. Here Ptolemaios begins accepting that the diatonic genera in general are more familiar to hearing than the enharmonic and the soft chromatic and continues extensively with the equal diatonic genus. Then he presents some other genera and their tunings / positions in musical instruments, and finally, he “can hardly fail to accept” the ditonal diatonic (roughly saying, the one using semitones and whole tones). But, since the “equal diatonic is a logical modification [and “more even / ὁμαλώτερον”] of the intense diatonic” (Mathiesen, 2000, pp. 450-451) the scheme here, together with “equal diatonic,” gives another title - referencing the position (numbers 24 to 18) – to it, this is the “softer of the intense diatonic”; thus uses the same ratios! The naming of the equal diatonic as (and its connection to) softer (μαλακώτερον, see also in Ptolm. Harm. I.12.28ff.) of the intense diatonic, has important consequences for the use of equal diatonic in the theory and the actual musical praxis in medieval times. A variation of this scheme exists also in the next F-Pn: Gr. 2540 (and I shall transliterate that form there).

β) On f. 74v, in relation to II.10, a scheme is given with the correlations of Dōrios Phrygios etc. with the ēchoi, their enēchēmata and the four phthorai. This correlation, at first glance, is the same as the tradition of Bryennios i.e, the prōtos ēchos is placed at the highest position (Hypermixolydios). For the moment, I have not any definitive opinion if it is exactly the same system as the one of Bryennios since we know that Grēgoras’s work consisted of, more or less, a new “adjustment” of the ancient material in order “to save the phenomena.” Here is a transliterated form of that diagram:

 Picture 2

See also the trochos like schemes on ff. 110v-111r.

Other online MSS of this Grēgoras’s recension of Harmonica are: GB-Ob: Bar. gr. 124 (Math. 134), F-Pn: Coislin gr. 336 (Math. 105), and F-Pn: Gr. 2456 (Math. 86) (from [?, Math. p. 226] I-Vat.: Gr. 2365 [Math. 235]), I-Rvat: Pal. gr. 389 (Math. 245), I-Rvat: Pal. gr. 390 (Math. 246).


F-Pn: Gr. 2450 (Math. 79 [14th], Dür. 42 [14th /15th], Acerbi 2016 p. 152, [about 1335], Vitrac p.157 [about 1335]) see also: Notice rédigée par Anne Lapasset, Fevrier 2015 (here) and at Pinakes (here).


According to Düring’s Harmonica edition the text of this MS belongs to the gp-subclass that stems from the main Grēgoras’s g-class. Is this a representation of a separate choice (to the degree Düring’s classes are reliable), in relation to the text / content, of (or someone close to) him? His hand is identified in some scholia of the ff. 57r, 59r, 71v, 72v, 73r. (Pérez Martín, 2008). As far as the schemes in relation to Greek chant the α) and the β) of F-Pn: Gr. 173 are found on 32r (in a different form but “better” as for our understanding) and 53r (again in Bryennios’s order) respectively. A transliterated form of that 32r diagram is the following:

Picture 3  

See also the trochos like scheme on 89v.

Other online MSS that belong to the gp recension of Harmonica are I-Vat: Gr. 221 (Math. 219, ēchoi, phthorai and enēchēmata on p. 106), I-Vat: Barb. gr. 265 (Math. 238, ēchoi, phthorai and enēchēmata on p. 138) that we’ve already met and note the transcription of Ismaël Boulliau (in 1656), in F-Pn: Sup. gr. 292 (Math. 111).


F-Pn : Coislin gr. 172 (Math. 102 [15th], Dür. 50 [14th /15th], Vitrac [14th /15th] p.154) see also: Notice rédigée par Anne Lapasset, Mars 2015 (here) and at Pinakes (here).


It is somewhat posterior to the aforementioned F-Pn: Coislin gr. 173, but this time its Harmonica, according to Düring, belongs to his f-class stemming from D-Mbs: Cod. gr. 361a (Math. 22 [13th-16th], Dur. 28 [13th-16th], see Vitrac p. 153, Acerbi-Gioffreda 2019 Mo, [2nd half of 13th century] p. 659). Again, is this a representation of one more separate choice, in relation to the text / content, of (or someone close to) Grēgoras? The relative scheme of α) is found on f. 13r (with no reference to “softer of the intense diatonic”). Note the diagrams on ff. 17r-18v on dynamis and thesis phenomena in relation to Ptolem. Harm. II.5-6.

There is another online MS that belongs to f-class the I-Vat: Barb. gr. 257 (Math. 237).


I-Vat: Gr. 187 (Math. 211 [14th], Dür, 61 [14th], Vitrac [14th] p. 145)

Bibliographic References and at Pinakes (here)


This is a MS that represents the circle of the monk Barlaam the Calabrian as the I-Vat: Gr. 196 (Math. 217 [14th], Dür, 66 [14th], Vitrac p. 146 [14th]) and F-Pn: Gr. 2452 [Math. 82]). Note the diagrams on ff. 32r, 34v and 35r on thesis and dynamis phenomena in relation to Ptolem. Harm. II.5-6.


I-Vat: Gr. 176 (Math. 208 [14th], Dür. 58 [14th], Vitrac [14th] p. 145)

Bibliographic References, and Pinakes (here).


Acerbi (2016, p. 173) notes: “A further recension of Harmonica was redacted by Isaac Argyros, whose fair copy is preserved (but recall that Argyros was used to correct in scribendo) in the autograph Vat. Gr. 176, ff. 101r-159v.” It is the A-subclass of Grēgoras’s g-class but this time “favoring the readings of the f-class” (Mathiesen 2000, p. 431).

The other online MS that belong to the same reduction of Harmonica is the F-Pn: Sup. gr. 449 (Math. 114).


F-Pn: Sup. gr. 1101 (not in Math., A. Gastoué 70 [14th]) See a description (here) and Pinakes (here)


The MS contains mainly the early translations of Maximos Planoudēs into Greek of Boethius’s, De Consolatione Philosophiae, Cicero’s, Somnium Scipionis and Macrobius’s Commentary on it and other material. But importantly enough for us, at the last folia, there are music related schemes on 162r, 163v, 164r and 165v. Also another small music related scholion on 137r. On 162r we see the correlation of ēchoi with the Dōrios Phrygios etc. in the order of Bryennios / Grēgoras (ie. prōtos ēchos placed in the position of Hypermixolydios) and a trochos like diagram; compare it with two small schemes in the later F-Pn: Gr. 2339 f.59v. On f. 163v there is a scheme of the 7- and 8-stringed lyres of Hermēs (or Orpheus in other MSS) and Pythagoras respectively. See them in F-Pn: Gr. 2339 f. 60v, and, together with Bryennios’s MSS, on f. 47r of Pachymerēs’s aforementioned autograph I-Ra: Gr. 38).


A note on modern classifications and vocabularies


Indeed, why 20th century people didn’t “see” all this set of sources of Ptolemaios with their relative to Byzantine chant material and why the studies for chant wasn’t so decisive as the other disciplines (especially for the medieval Greek MSS on mathematics, see Vitrac, 2019, 6.B, p. 48 and 7.B, p. 59)? A possible answer of mine is already known to the list of Μ.Μ.: “we” “see” only what we have pre-theorized to see or more simply, when two people look at the same direction (and set of things) they do not acknowledge (and taxonomize) the same phenomena, although ‘all of them’ are there. Think of the results if they look at different directions….

And some final notes on the grand narrative of the society, the time and our vocabulary remembering Christian Troelsgård’s, “Ancient Musical Theory in Byzantine Enviroments,” Cahiers de l’Institute du Moyen-Âge Grec et Latin 56 (1988), (here) in p. 229 where he writes: “On the other hand we find an increasing interest [7*] in copying, exerpting and commenting on the remains of ancient theory [are we sure that there wasn’t an – perhaps even more – “increasing interest” before?]. It is an accepted fact that these activities were centered around two different milieus in Byzantine society, the church [7*] on the one side and the scholarly circles of quadrivial study [7*] on the other. But I think there are some very important points or area of contact and interaction between these milieus.” And also, in the concluding p. 237, he speaks of “… the interaction between the two hemispheres [7*] of the musical culture of Byzantium. They imply that the Byzantines took a far more active and dynamic interest in the ancient musical theory than usually accepted.”

In my view, and after what we saw here, we can speak of an even far more active and dynamic interest in the ancient Greek theory and this, not only because we added the Harmonica, the main sholiated treatise in relation to chant.

But as it becomes obvious, the issue isn’t exactly the potential infinite discussions (past or future) on a degree of interaction of “two” domains. All these medieval theoretical constructions in this kind of sources are related to the everyday ecclesiastical music of the ordinary – differentiating, case by case, on degree of knowledge- faithful people (and psaltes). In contrast with other branches of knowledge, like Geometry or Arithmetic (with problems that sometimes still a modern wo/man, can’t understand), the ecclesiastical music circles or “parties” of people (recorded by the sources [remember the “many people” / πολλοì of Bryennios]), give us an idea about our narrative on the structure of that world. These intellectuals weren’t debating as isolated personalities because, among others, they had a vision about their society as a whole. I ask and explain: in our mind, where do we have to place an intellectual? Over, next to, in parallel or among ordinary people? Especially if we remember the other similar ecclesiastical case of theological debates among highly educated people (we met some of them already above) like Barlaam, Grēgoras, and others, not music related figures, like Grēgorios Palamas etc. who were also supported by their (larger or smaller) circles or “parties.”

Last but not least, referring to the current vocabulary (I will not criticize, for the moment, nation-centered vocabularies here in Greece) used on music related issues of the time: a generalized view of “church” and “scholarly circles of quadrivial study” would be misleading [8*] since a lot of the personalities (belonged to all the theoretical streams) we are dealing of were highly educated clerics, monks etc. And again, we have the same problematic with the “theoretical hemispheres.” In which MSS, who is theorizing, at what music(s) exactly? Are there more than two interacted “spheres” (including their “middle grounds,” a] and b], as I described them in my above given paper, pp. 217-218), thus not “hemispheres,” that we have to use in the narrative of the earlier or later medieval chant?


[7*] This is not a comment on what (and when) meant by “increasing interest,” “scholarly circles of quadrivial study,” “church” etc. as I have no intention to interfere in any kind of interpretation of “what the X scholar means,” but I make use of this quotation in order to express my skepticism – separately- on the use of certain terms.                 

[8*] Giving room even to potential polarization and not interaction, in other words, this could be a case of ‘glass half empty and glass half full’ within the same proposition.



Acerbi, Fabio. “Funzioni e modalità di transmissione delle notazioni numeriche nella trattatistica mathematica Greca: Due esempi paradigmatici.” Segno e Testo 11 (2013). (

----------------. “Byzantine recensions of Greek mathematical and astronomical texts: A survey.” Estudios Bizantinos 4 (1016). (

Bianconi, Daniele. “La biblioteca di Cora tra Massimo Planude e Niceforo Gregora. Una Questione di mani.” Segno e Testo 3 (2005).

----------------.“La controversia palamitica. Figure, libri e mani.” Segno e Testo 6 (2008). (

Düring, Ingemar (ed). Die Harmonielehre des Klaudios Ptolemaios. Göteborg, 1930.

Gastoué, Amédée. Catalogue des manuscrits de musique Byzantine de la Bibliothèque de Paris et des Bibliothèques publiques de France. Paris, 1907. (

Mathiesen, Thomas. Ancient Greek Music Theory. A catalogue raisonné of manuscripts (RISM, B XI). München, 1988.

---------------. Apollo's Lyre : Greek music and music theory in antiquity and the Middle Ages.Lincoln and London, 2000.

Mondrain, Brigitte. "Les écritures dans les manuscrits byzantins du XIVè siècle." Rivista di Studi Bizantini e Neoellenici (2008).

Pérez Martín, Inmaculada, “El estilo Hodegos y su proyección en las escrituras constantinopolitanas.” Segno e Testo 6 (2008). (

----------------. “L’ecriture de l’hypatos Jean Pothos Pédiasimos d’après ses scholies aux Elementa d’ Euclide.” Scriptorium 64 (2010). (Persée) and (

Ruelle, Charles-Émile. Études sur l’ancienne musique grecque. Paris, 1875. (BSBdigital)

Turyn, Alexandrer. Codices Graeci Vaticani saeculis XIII et XIV scripti annorumque notis instructi. Citta del Vaticano, 1964.

Vincent, Alexandre Joseph Hidulphe. Notice sur divers manuscrits Grecs relatifs à la musique. Paris, 1847. (Gallica)

Vitrac, Bernard. “Quand? Comment? Pourquoi les textes mathématiques grecs sont-ils parvenus en Occident?” (, April 2019, accessed 29 November 2019.

Wolfram, Gerda – Hannick, Christian (eds). Die Erotapokriseis des Pseudo-Johannes Damaskenos zum Kirchengesang. Vienna, 1997.


The links of the online MSS that has relation to the Harmonica of Claudios Ptolemaios are given above, together with a small description of some of them, since this is the treatise that medieval Greek speaking theorists scholiated the most in connection to chant theory. The other online MSS of ancient Greek musicographers I have located so far are the following (the MSS links that have already given in the above text are just referred to below with no link):



Wien, Österreichische Nationalbibliothek

A-Wn: Cod. Phil. gr. 64 (Math. 2), A-Wn: Cod. Phil. gr. 176 (Math. 5, Vitrac p.194).



Heidelberg, Universitätsbibliothek

D-Heu: Cod. Pal. gr. 281 (Math. 14), D-Heu: Cod. Pal. gr. 415 (Math. 15).

Leipzig, Universitätsbibliothek

D-Leu: Rep. I 2 (Math. 39).

München, Bayerische Staatsbibliothek

D-Mbs: Cod. gr. 104 (Math. 17, Vitrac p.179), D-Mbs: Cod. gr. 301 (Math. 21, Vitrac p.180), D-Mbs: Cod. gr. 385 (Math. 23, Vitrac p.180), D-Mbs: Cod. gr. 403 (Math. 24, Vitrac p. 180), D-Mbs: Cod. gr. 418 (Math. 25), D-Mbs: Cod. gr. 487 (Math. 26).

Wolfenbüttel, Herzog August Bibliothek

D-W: Cod. Guelf. 3 Gud. gr. (Math. 29, Vitrac p.195).



Madrid, Bibliotheca Nacional

E-Mn: Gr. 4621 (Math. 57, together with C. Laskarēs the codex has a relation to Sultan Cem), E-Mn: Gr. 4625 (Math. 58), E-Mn: Gr. 4678 (Math. 59), E-Mn: Gr. 4690 (Math. 60), E-Mn: Gr. 4692 (Math. 61).



Paris, Bibliothèque Nationale de France, Fonds Grec

F-Pn: Gr. 1671 (Math. 66), F-Pn: Gr. 1672 (Math. 67), F-Pn: Gr. 1806 (Math. 68, Vitrac p.185), F-Pn: Gr. 1819 (Math. 70, Vitrac p.185) F-Pn: Gr. 1820 (Math. 71, Vitrac p.185), F-Pn: Gr. 2013 (Math. 72), F-Pn: Gr. 2014 (Math. 73, Vitrac p.185), F-Pn: Gr. 2379 (Math. 74, Vitrac p.188), F-Pn: Gr. 2381 (Math. 75), F-Pn: Gr. 2397 (Math.-, Vitrac p.188) F-Pn: Gr. 2430 (Math. 77, Vitrac p.188), F-Pn: Gr. 2449 (Math. 78), F-Pn: Gr. 2450 (Math. 79), F-Pn: Gr 2451 (Math. 80, Vitrac p.188), F-Pn: Gr 2452 (Math. 81, Vitrac p.188), F-Pn: Gr 2453 (Math. 82, Vitrac p.188), F-Pn: Gr. 2454 (Math. 83, Vitrac p.188), F-Pn: Gr. 2455 (Math. 84), F-Pn: Gr 2456 (Math. 85, Vitrac p.188), F-Pn: Gr. 2458 (Math. 87), F-Pn: Gr. 2459 (Math. 88, Vitrac p.188), F-Pn: Gr. 2460 (Math. 89, Vitrac p.188), F-Pn: Gr. 2461 (Math. 90, Vitrac p.157), F-Pn: Gr. 2462 (Math. 91), F-Pn: Gr. 2463 (Math. 92), F-Pn: Gr. 2464 (Math. 93), F-Pn: Gr. 2531 (Math. 94, Vitrac p.189), F-Pn: Gr. 2532 (Math. 95), F-Pn: Gr. 2533 (Math. 96), F-Pn: Gr. 2534 (Math. 97), F-Pn: Gr. 2535 (Math. 98, Vitrac p.188), F-Pn: Gr. 2549 (Math. 99), F-Pn: Gr. 2622 (Math. 100), F-Pn: Gr. 3027 (Math. 101, Vitrac p.190).

Paris, Bibliothèque Nationale de France, Fonds Coislin

F-Pn: Coislin 172 (Math. 102), F-Pn: Coislin 173 (Math. 103), F-Pn: Coislin 174 (Math. 104, Vitrac p.154), F-Pn: Coislin 336 (Math. 105, Vitrac p.185).

Paris, Bibliothèque Nationale de France, Fonds Supplément Grec

F-Pn: Sup. gr. 20 (Math. 106), F-Pn: Sup. gr. 59 (Math. 107, Vitrac p.190), F-Pn: Sup. gr. 160 (Math. 108), F-Pn: Sup. gr. 195 (Math. 109, Vitrac p.190), F-Pn: Sup. gr. 213 (Math. 110, Vitrac p.190), F-Pn: Sup. gr. 292 (Math. 111, Vitrac p.190), F-Pn: Sup. gr. 335 (Math. 112, Vitrac p.190), F-Pn: Sup. gr. 336 (Math. 113, Vitrac p.190), F-Pn: Sup. gr. 449 (Math. 114, Vitrac p.190), F-Pn: Sup. gr. 450 (Math. 115, Vitrac p.190), F-Pn: Sup. gr. 1101 (Math. -).



London, British Library

GB-Lbm: Harley gr. 5691 (Math. 128), GB-Lbm: Additional 19353 (Math. 130, Vitrac p.175).

Oxford, Bodleian Library

GB-Ob: Barocci gr. 41 (Math. 133, Vitrac p.182), GB-Ob: Barocci gr. 124 (Math. 134, Vitrac p.182).

Oxford, Magdalen College Library

GB-Omc: Magdalen Col. gr. 12 (Math. 150), GB-Omc: Magdalen Col. gr. 13 (Math. 151, Vitrac p.184).



Bologna, Biblioteca Universitaria

I-Bu: Gr. 2048, v.1 (Math. 154, Vitrac p.162), I-Bu: Gr. 2048, v.2 (Math. 155, Vitrac p.162), I-Bu: Gr. 2048, v.5 (Math. 156, Vitrac p.162), I-Bu: Gr. 2280 (Math. 157, Vitrac p.162), I-Bu: Gr. 2432 (Math. 158, Vitrac p.162), I-Bu: Gr. 2700 (Math. 159).

Firenze, Biblioteca Medicea Laurenziana

I-Fl: Ms Plut.28.11 (Math. 160), I-Fl: Ms Plut.28.12 (Math. 161), I-Fl: Ms Plut.56.1 (Math. 162), I-Fl: Ms Plut.58.29 (Math. 163, Vitrac p. 151), I-Fl: Ms Plut.59.1 (Math. 164), I-Fl: Ms Plut.80.5 (Math. 165), I-Fl: Ms Plut.80.21 (Math. 166), I-Fl: Ms Plut.80.22 (Math. 167), I-Fl: Ms Plut.80.30 (Math. 168), I-Fl: Ms Plut.86.3 (Math. 169).

Napoli, Biblioteca Nazionale

I-Nn: Gr. 261 (f. 53r, Math. 202, Vitrac p. 153).

Roma, Biblioteca Angelica

I-Ra: Gr. 35 (Math. 205), I-Ra: Gr. 101 (Math. 206).

Citta del Vaticano, Biblioteca Apostolica Vaticana

I-Rvat: Gr. 139 (Math. 207), I-Rvat: Gr. 176 (Math. 208), I-Rvat: Gr. 186 (Math. 210, Vitrac p. 145), I-Rvat: Gr. 187 (Math. 211), I-Rvat: Gr. 191 (Math. 214), I-Rvat: Gr. 192 (Math. 215), I-Rvat: Gr. 196 (Math. 217), I-Rvat: Gr. 198 (Math. 218), I-Rvat: Gr. 221 (Math. 219, Vitrac p.166), I-Rvat: Gr. 1013 (Math. 221), I-Rvat: Gr. 1033 (Math. 222), I-Rvat: Gr. 1048 (Math. 225, Vitrac p.167), I-Rvat: Gr. 1060 (Math. 226), I-Rvat: Gr. 1364 (Math. 230, Vitrac p.167), I-Rvat: Gr. 1374 (Math. 231), I-Rvat: Gr. 2338 (Math. 234), I-Rvat: Gr. 2365 (Math. 235, Vitrac p.168), I-Rvat: Barb. gr. 257 (Math. 237), I-Rvat: Barb. gr. 265 (Math. 238, Vitrac p.164), I-Rvat: Barb. gr. 278 (not in Math.), I-Rvat: Ottob. gr. 372 (Math. 237), I-Rvat: Pal. gr. 53 (Math. 241), I-Rvat: Pal. gr. 60 (Math. 242, Vitrac p.165), I-Rvat: Pal. gr. 95 (Math. 243), I-Rvat: Pal. gr. 303 (Math. 244, Vitrac p.165), I-Rvat: Pal. gr. 389 (Math. 245, Vitrac p.165), I-Rvat: Pal. gr. 390 (Math. 246, Vitrac p.165), I-Rvat: Pal. gr. 392 (Math. 247), I-Rvat: Reg. gr. 80 (Math. 248), I-Vat: Ross. 977 (Math. 253, Vitrac p.165), I-Vat: Ross. 986 (Math. 254), I-Vat: Urb. gr. 78 (Math. 256, Vitrac p.166), I-Vat: Urb. gr. 99 (Math. 257).

Venezia, Biblioteca Nazionale Marciana

I-Vnm: Gr. app. cl. VI/3 (coll. 1347).



Uppsala, Universitetsbiblioteket

S-Uu: Gr. 45 (Math. 292, Vitrac p.193), S-Uu: Gr. 47 (Math. 293, Vitrac p.193), S-Uu: Gr. 52 (Math. 294, Vitrac p.193).



New Haven, Connecticut, Yale University, Beinecke Rare Book and Manuscript

US-NHub: MS 208 (f.30v, Math. 295)



Mount Sinai, St. Catherine’s Monastery

EG-MSsc: Gr. 1764 (Math. 299).

Additionally, a small collection of online MSS of BNF that include medieval music theory (some of them referred to in Vincent [1847]) is given below although I didn’t include, for example, all the Pachymerēs, Pediasimos etc. music related MSS. All these MSS need a fresh look together with the similar MSS of other libraries.


F-Pn: Gr. 2338, F-Pn: Gr. 2339, F-Pn: Gr. 2340, F-Pn: Gr. 2341, F-Pn: Gr 2448 see Notice rédigée par Anne Lapasset Mars 2015 (here) and (Pinakes), F-Pn: Gr. 2536, F-Pn: Gr. 2762 see: Notice rédigée par Morgane CARIOU (here) and (Pinakes).

And also: F-Pn: Gr. 1810 see: Notice rédigée par Jocelyn Groisard (novembre 2008) (here), F-Pn: Sup. gr. 51.

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Comment by pavlos erevnidis on December 28, 2019 at 19:05

I look forward, Oliver, to the moment you come back hoping you’ll have the time to read more carefully what I write, and not to continue with newer distortions of my stance like: “I was mainly interested in your specific focus on the Greater Perfect System [sic, not a reference of mine to GPS],” “But since you alluded [!] to the difference between iadgari and Greek tropologia.[!] […]” etc. etc. If you, Oliver, want to continue this way, so be it. To be more precise, I really look forward to the moment you will find time to return here, although not happy, if you continue elaborating on your own categorizations on who “is a scholar of” the X chant (or the Y+Z+Ω chants or the Y+Z chants but not of the Ω etc. etc.) or your interpretations on the decisions made by some people and your information on “the” reason that a certain scholar wrote on something, who are your dear colleagues, their presents to you and what you discussed with them, on the Balkan crisis etc. etc. As for your posts and your descriptions of MSS, thank you for your invitation (but I won’t join, except, perhaps, if a distortion of my writings occurs), but please allow me a general technical suggestion: When you give the dating of a MS do not inform people the dating of yours (or the one you prefer), exclusively, as “the” dating of a MS, but give your readers the chance to know the dating of other people. I am referring, for example, to the dating “1000” for the B32 of Lavra of your latest Nativity Surprise discussion.


I hope you won’t miss the deadline you have.

Comment by Oliver Gerlach on December 28, 2019 at 0:05

The period which was left unfinished:

Of course, one must consider that even in the case, where only one tone system is inherent in a certain notation, it can always be used in an odd way which allows also to transcribe melodies made according to another tone system. There are plenty examples of Dasia signs used in a way that the resulting tone system is in fact not organised in tetraphonia.

Comment by Oliver Gerlach on December 27, 2019 at 23:07

Reading it, it seems to me that you got bored yourself by your last ominous and melodramatic post, but I assure you it was not my fault... I am not Jesus. You should not get so annoyed, because almost 400 hits by other users here is an encouragment by itself to keep fresh in your mind (do not expect that everyone here has your personal problems, they do not, please do not worry, do not worry at all)!

You referred yourself to the Armenian and Georgian evidence through your quotation of Peter Jeffery, now you even mentioned my dear colleague Anna Arevshatyan who made me so many presents. Since you insisted so much in a certain pervert way which is unique for you, I will mention this evidence in this paragraph! Peter Jeffery by the way is a scholar of Latin chant (and quite capable to do so on his own behalf) and very engaged at Cantus planus (where I also met you). But since you alluded to the difference between iadgari and Greek tropologia, it is true that the Georgian sources are not as early as papyrus fragments of Greek tropologia, and certainly not as early as the Oxyrhynchus hymn. Nevertheless, the Georgian scribes passing at Mar Saba and then at Saint Caterine's where they brought all the Georgian chant books are important, because (and here I refer to the publications by Stig Frøyshov) they made a difference between three layers of Hagiopolitan hymnographers (while only the school of Andrew of Crete and the next generation, the latest layer, are present in the Greek redaction of the books, next to the earlier one of Constantinople like Germanus I, which is completely ignored in the current print editions published in Greece). It is a unique case, because the Georgian tradition changed between the 9th and the 10th century its own repertoire, and thus documented also the Sabaite tradition of the 7th century (in a way which was neither documented in Syriac nor Greek sources—of course those we do know today). This was the reason, why Peter Jeffery mentioned it, since this knowledge is not present in the earlier Greek fragments (which offer other evidence not given by Georgian scribes).

I just teach students in Byzantine chant and my experience is that it helps them very much, if you just stick with the chant manuscripts of the period in question and look at them as notated or unnotated as they are. It is quite natural that this study is also concerned about chant theory, even in case there is no theoretical source concerned about mousike (which was indeed not the same as harmonics as a subject). There is no other way to find out about the specific role which Greek terminology played for chant transmission, even if Ptolemaios, Alypios or Aristoxenos have thought about music theory before the earliest papyrus.

You liked to refer to Lorenzo Tardo and you should know about his context, if you don't just let me tell you. I am living there. But the medieval Italian reference is a completely different story, and Martani's interest for both heirmologia at Grottaferrata was, in as much Greek scribes in medieval Italy dealt with both transmissions (the one of Constantinopolitan and Athonite scribes present in Chartres notation, and the one of the Patriarchates at Jerusalem, Alexandria and Cyprus). Her finding was that both transmission were present, although Italian scribes preferred Coislin notation and ordered many books in Palestine and Cyprus (under the Normans, of course, for material reasons!).

This is just to summarise. Now, coming back to you, I was mainly interested in your specific focus on the Greater Perfect System (Ptolemaios and his Latin "interpreter” Boethius and, if you like, Pediasmos), because I am preparing a publication about it which involves other authors. My personal problem due to my limited knowledge is that I do understand very well that GPS is important for Western plainchant, but I have no idea whatsoever, whether it ever played any role in mousike (Byzantine chant). Maybe it did (you made many thoughts which dare to got beyond others and I do appreciate that), but I came never across about any evidence about it. Of course, one must consider the

I prefer to answer you immediately, because I have a deadline by the end of a year and to look after some students and I will not write you here again (at least within this year).

If you would like to describe other important manuscripts of Great Lavra collection, please feel free to make yourself useful in the Byzantine group, where you are already inscribed. As you know you are already welcome and it is up to you to comment my discussion or to add your own one!

Thank you anyway for all your pain! It was my pleasure!

Comment by pavlos erevnidis on December 27, 2019 at 18:21

I referred to Jeffery’s and Troelsgård’s tables saying that I will not make any comment on their decisions. What I wrote is that “the table of prof. Jeffery is not exhaustive and this is not because the ordering/naming of Pediasimos is not included.” To be more precise, this observation of mine, concerning mainly the Latin and Greek chants, by no means was any interpretation on why he decided not to include mode material of the Georgian and Armenian chant. This is said because of another Oliver’s information: In any case it relevant for the numbering 1-8 (which existed independently from the Byzantine tradition also in Armenia and Georgia).” It is not my intention to confuse the issue of numbering by mixing, in chronological terms, several streams of any chant; I prefer to give priority and stay focused on the earliest possible documentation (as well as I have not any ambition to give a full survey of Syriac, Slavonic, Armenian Georgian etc. chants). Here I’ll make use of two articles of Anna S. Arevšatyan in Revue des Études Arméniennes, Tome 26 1996-1997. The first on pp. 339-355 is the: Deux textes Arméniens attribués à Basile de Césarée sur l’interprétation des modes musicaux. The other is found on pp. 357-366 and its title is: Les traités Arméniens médiévaux sur l’interprétation des modes musicaux et leurs parallèles au Proche Orient.

I transcribe here the French translation, found in the first article, of some important excerpts (regarding the numbering(s) of modes, and other auxiliary phenomena [like the phthorai that we saw in the 8 MSS of ancient Greek music theory with Byzantine music information]). This passage comes from what Arevšatyan calls “la rédaction longue.” I, also, hope that this is an intriguing excerpt to attract more Latin chant people to have a careful look on the medieval Armenian evidence exposed usually in the last pages (dedicated to arts [and music]) of this journal. I copy:

 p. 346: Préface au Tropologion. Parole du Segneur Basile sur les modes des, chants, d’où et par qui ils furent trouvés; traduite par le philosophe Step‘anos, qui fut musicien et expert en cris de tous les animaux.[…] p.347: Pipien, fils de leur oncle maternel, inventa le demarton (τέταρτον [=tétarton]), à partir du bruit du ressac marin, et c’est le quatrième mode.

Les plagaux de ces modes

Ensuite Cynosthènes distingue le plaimin i pratoi, qui est le premier mode plagal. Puis vint le musicien Archelaos, qui inventa le płapłoroyn i pridu, auxiliaire du premier mode.

Et, distinquant le pridon i tewtewu [note 9.= C’est-à-dire «le premier du deuxième» (πρῶτον τοῦ δευτέρου)], iI créa le mode nommé kłewto, c’est-à-dire le deuxième mode plagal. Puis, conformément à cela, Aristarque et Pindare de Thèbes inventèrent le pap‘arown i deritu qui est l’auxiliaire du deuxième mode. Les memes inventèrent le mode bas, nommé tri(t)own, qui est aussi appelé lourd, c’est-à-dire le troisième mode plagal. Puis le musicien Eunome inventa le płais i (te)tartov, c’est-à-dire le quatrième mode plagal. Il inventa aussi un autre mode, nommé cinquième. […] [Double –bold- emphasis is mine]


Some preliminary observations: α) As Arevšatyan writes (p. 341): “Il n’est pas exclu que ce texte contienne des passages d’un traité grec perdu, rédigé à la limite de la basse antiquité et du haut Moyen-âge, qui, s’il n’appartient pas à Basile de Césarée, proviendrait peut-être d’un de ses contemporains hellénophones.” I will not elaborate now on the date of this material but one should see her essential notes on the Armenian terminology on p. 345 where “les modes plagaux” are “kołm jaynełankk‘,” “Tropologion” is “Kc ‘ordaran” or “[…] le mot ạpakanut ‘iwn, qui ne se recontre pas non plus dans les autres traits. Il faut sans doute le comprendre comme «écart, déviation» (litt. «altération, corruption») du mode principal.” α) Important for us here is that the Greek terms are “lost in the transliteration.” In some of them consonants or whole syllables are missing, e.g. płais i (te)tartov. Fortunately, as Arevšatyan did for tetarton etc., we can reconstruct the most of them i.e., plaimin i pratoi could not be something different than plagion/s tou prōtou. β) But most importantly, we see that the auxiliary modes have not name forms like mesos, moesi or medii toni. Their naming is more akin to the Latin term parapter (see Atkinson’s relative bibliography in his Critical Nexus). For the moment, we can’t exclude that the author(s) of this treatise used a term like pa[ra]p[t]‘arown i deritu i.e., parapteron/s tou deuterou. At least, we cannot suppose that, if they weren’t Greeks, they “Grecizing” in similar ways for similar phenomena with Latin speaking theorists. This is one reason that, we could think of the Armenian chant along with the Syriac one regarding the already proposed links of the latter to the early Latin chant. Meanwhile, I also think that those who believe that this term’s place is in the box with the label “Carolingian Grecizing movement of the 9th century,” they have to take this term out of that box and wait (all of us, together) if we will throw it back. γ) At first glance one, based on the personality-name transliterations of Arevšatyan (I could suggest alternatively Kinyras for Synerges but I will not make any comment on his connection to k‘nar, see p. 364), could think that these mythological inventors of ecclesiastical modes are from Greece; but my preliminary opinion is that the origin of this treatise (and of some of the referred personalities) is not Greece but Egypt. This is one reason, among others, that I suggest Egypt as a candidate “place of origin” of the Octoēchos (as an alternative or a parallel plan to the already important work). The case of a Heptaēchos is also important and not to be forgotten. Furthermore, I realize –roughly saying- that many people have an established foggy belief that the earliest Octoēchos is a “proto-system” that “created” in Jerusalem (or somewhere in Syropalestinian geography) by some Christians (“proto-theorists”?) “devoted” to the “creation” of a musical proto-tetraēchos, (if I discern some modern linear narrative trends well) or mainly, a “proto-octoēchos (=as something like a taxonomy of a collection of a melodic material). Egypt is also important about papyrus material as well as (secondarily in relation to our musical interests here) the most probable origin place of few of the oldest Greek liturgical MSS. These are some preparatory remarks on such late antiquity and medieval evidence(s) but as it is obvious I do not have any intention in this blog, to extent my exposition on any –modern- nation orientated origin issues. I, also, hope that no one will put –extra- words in my mouth on the subject.


After such an example, now is more apparent the urgent priority (and the importance) of the existence of a real multilingual Lexicum Musicum Medii Aevi.


And now, Oliver,

I proceed to less central issues of this blog but anyhow all this give me the opportunity to record here (as I had some free time these days) more precisely my views and work, albeit in a preliminary way (I have, also, to remind the one who decide to continue the reading that the following is, unfortunately, a long post not only because I include Oliver’s text [in “italics”] but because I chose to give the deserved accuracy to these topics.):


“Also here, there is a difference between Greek and Latin theory. You wrote [sic, is it me that I wrote the following? =] that the Greeks did not develop any [sic] kind of notation [sic] during the first millenium. But there is this hymn about Trinity in the Oxyrhynchus papyrus […] If I understand well this 2nd-century [sic] fragment uses Alypian notation (please correct me, if I got it wrong!), which means that Greek psaltes could have used musical notation since late Antiquity, if they did want to use it.”

Did you, Oliver, read what I wrote or you simply put words in my mouth? However, let us accept, for the moment, that I am not aware about 1st millennium’s Greek notations and of the existence of the Oxyrhynchus papyrus (there is also literature about papyri in relation to early chant’s modes): how could I correct you on something that I am not aware? For the Social Setting of this papyrus, the ethnic origins of the people of Oxyrhynchus and performance practice issues one should have a look to Cosgrove’s recent (2011) book especially after the p. 130. But, “2nd-century”? In DAGM (2001, No 59, pp. 190-194) we see in p. 192 that this papyrus is of the end of 3rd century and Cosgrove gives the same dating. Is this 2nd century one more dating of yours? BTW, “Bellermann fragment (11th century)”? “11th century”?


But let us be more precise. I did not write: “the Greeks did not develop any kind of notation during the first millenium.” How could be this done? What I wrote was about the scarcity of music theory writings, a part of which are the didactic (material which under certain circumstances can acquire theoretical status) tables or lists that expose the notational signs one by one, I give to the interested Latin chant people some examples: α) the oldest list of ekphonetic signs is included in the 10th cent. EG-MSsc: Gr. 213 (f. 116v) 10th century, note also similar lists as β) the most probably 11th/12th c. (or 14th for others) EG-MSsc: Gr. 217 (f. 2r) and the γ) 10th/11th c. EG-MSsc: Gr. 8 (f. 303r) with parallel notation in paleobyzantine signs (of a 11th/12th century hand). These tables are also “music theory,” in a way. The oldest sentence of Byzantine, “real,” music theory we have, until now, is found within another neumes list; this time not ekphonetic. So I wrote the following sentence: “But in the neumes table of M. Lavra Γ 67, f. 159r (10th / beginning 11th century) there is the following - not rudimentary- chant theory sentence: the voices are seven, but the ēchoi four, three mesoi, two phthorai and four plagioi, voice 1st, voice 2nd, voice 3rd, voice 4th, voice 5th, voice 6th, voice 7th, that is the “fin(e)-al” (τελεία,[…]).” In the same table there are also signs like 1) parēchon, 2) phthora, 3) semiphthora, 4) nana.

Indeed, pieces of evidence as α) the naming of the 7th voice as τελεία β) the existence of 3 mesoi and 2 phthorai and γ) the inclusion of, roughly speaking, several “modulation” signs, in my account, by no means represent the rudiments of that musical theory (and all the remaining neumes of this table, are also parts of a highly sophisticated system).

(This is, exclusively, an explanation to the abovementioned sentence of mine that belongs to the main text of this blog.)

Two more observations, in a more precise way: α) the “wheel of Koukouzelēs” is appeared in the sources several decades after the appearance, in F-Pn: Gr. 261 of AD 1289 (along with the term Papadikē), of the specific correlation (not the only one in Byzantium) of the names of ancient tropoi / tonoi with the ordinals of the ēchoi, e.g., Lydios/Hypolydios is associated to Deuteros/Plagios Deuteros respectively. There is no reason to continue, for the moment, on the subject. β) the issue is not if the ēchoi have two kind of names (διπλή παρονομασία is the modern Greek sometimes used, if I remember correctly) within an a posteriori musicological “unified [Byzantine] theory,” but the careful examination of the hierarchy of these “names/onómata” (as principal/κύρια etc.) in relation to the numberings of modes within the various Byzantine music theory streams through the ages. And all these not in a, wholesale linear narrative (e.g. that simpler structures are always prior to more complex structures). People, in this world, sometimes, make simplifications of older, more complex, phases/stages and there is no one who is characterized by a lack of ideology. In real history, and life, linear and economical solutions are not always the case, because people were (and are) human beings, not “unbiased” “statues or robots of positivism” with no ideology who always produce (what posteriorly could be -within differentiated ideologically environments- seen as) “consistent developments.”

Distortion of my stance (2):

“Why you are so eager to drop the Slavic evidence, since it was obviously about a whole reception just based on triphonia and on the Old Byzantine / adiastematic level of notation?”

To drop the Slavic evidence? Me? I believe just the opposite: all chants are central to the documentation of medieval times. And, Diphonia, Triphonia, tetraphonia…? So once again, what I wrote was: “Anyhow, the issue I am presenting is that the numbering 1 to 8 exists in Byzantine as well as in Slavonic and Syriac modes. Nothing more, nothing less.” Is this any “eagerness to drop” Slavic (or Syriac) evidence?!


“On the other hand, since you mentioned Cod. crypt. Ε.γ. ΙΙ (the first facsimile published within the main series of MMB) was written at a scriptorium of Constantinople and obviously ordered there (it fits perfectly for the needs of MMB who was interested in the 14th-century redaction of the heirmologion), a more local Italian redaction of Grottaferrata you will find in the earlier heirmologion Cod. crypt. Ε.γ. ΙΙI still with Old Byzantine notation written about mid 12th century, Sandra Martani has published about both heirmologia.”

It was Tardo’s reference not mine who referred to this to codex, Oliver. What I wrote in an elliptical way was the dating of Ε.γ.ΙΙ and that, in general, a Heirmologion is a book divided into mode-sections. This is the reason, and for the sake of brevity, I just alluded the “much earlier” 11th century Heirmologion Lavra Γ 9 (which also includes the poems [where, again, the pl.1 is “fifth in order” and the pl.2 is the “sixth ‘melodist’ ”). But you gave us, a piece of information about another Heirmologion (a MS not earlier than the 11th century Lavra Γ 9) in Grottaferrata… My issue wasn’t the Heirmologia of Italy (I hope that you will not consider this as an “eagerness to drop” the Italian evidence). My issue was the numbering of modes that is included in the small poems (epigrams, is another term) in some Heirmologia. Interesting is, though, what Troelsgård (MMB, IX, 2011, p. 13) writes about these small poems of these Heirmologia: “Some Heirmológia also include didactic material, such as Laura Γ 9 (11th cent.) and Grottaferrata E.γ. ΙΙ (AD 1281), in which a series of verses describes the particular ēthos and aesthetic qualities associated with each mode.”

A Lack? (4)

“Quoting from Wolfram / Hannick's edition of the dialogue treatises, they did also mention a reference to Alypian notation and its letters as a reference or marker for frets (you mentioned the Greek term kavallion).”

I extended the size of my excerpt from Gerda Wolfram-Christian Hannick’s Kommentar just for this reason, i.e., to exist the Alypios reference of them. BTW, the oldest phase’s best reading of this word, in my view, is kavália not only because is so recorded in the earliest best dated text (in I-Rvat: Gr. 191) but, additionally, because it is there so written, not simply by a copyist, but by the hand of a highly educated personality (i.e., consciously and reasonably), Ioannēs Pediasimos. Plousiadēnos is also such a (but much later) personality. Anyhow, what I wrote is found in the above posts and I have nothing more to write, for the moment, on Papadikai (it is important that also the term Psaltikē Technē exists in later expositions; we met it, in that previous post, in BNF Sup. gr. 1302), Pseudo-Ioannēs Damaskēnos text(s), and the problems of its 1997 edition and apparatus criticus. The same applies on kavália as frets and bridges.


Excursus. I hope, Oliver, that you will not write here more pieces of your general knowledge on earlier or later Armenian and Georgian chant, or possibly on the cris de tous les animaux and their relation to ancient music or to give more general information on OdO/CaO Heirmologia, the “Balkan crisis” etc. etc. (don’t take this as a discouragement to write here, you’re always welcome). There is not any need to add information that will confuse and discourage especially Latin chant people to continue reading. This is the reason that even though the Palatini Graeci have been available online for a few months, I included, in the main text of this blog, only the relative to ancient Greek music theory MSS of them and not the irrelevant here BAV, Pal. gr. 243. As for the Armenian chant, I’ll propose, something easy for you: to include in your Armenian and Georgian music and MSS posts the oldest Tałaran (Book of Odes), BNF Arménien 79, Consultation. As for Armenian Hymnals there are some more online like, the Utopia, armarium codicum bibliophilorum, Cod. 4, Hymnaire arménien, detailed description (here), the Chicago library (Goodspeed Col.) Ms 275 (Astuacatur Hymnal), the 2438 of the Jerusalem Armenian Patriarchate, the BNF Arménien 65, consultation and 75, consultation. And there are more … The online Georgian MSS e.g., of BNF (Nos 3, 5, 6, 7, 8, 30) are not notated but the 3 (consultation) and 30 (consultation) are frequently cited in the liturgical studies. I am sure Oliver, that you’ve met them many times in your readings. As for the Greek MSS of Megistē Lavra MSS and fragments (as far as the online LOC ones), in relation to your latest 25 December Discussion, Nativity Surprise: Old Byzantine chant books of the Great Lavra (Holy Mount Athos) there are also: Γ 12, Δ 68, and Ι 100. Finally, as you offered a myriad of presents to the readers of MM, you can also create a place for the online MSS with Greek ekphonetic notation (beginning e.g. from the BNF Grec 9 Codex Ephræmi Syri rescriptus, consultation); there are a lot of them…


But for me, a constant admirer of Armenian artists, their skills and esthetic capabilities, the Utopia, armarium codicum bibliophilorum, Cod. 3, detailed description (here) (in equally high resolution, even, with St. Gall 359 and Einsiedeln 121), is a superb example of a beautiful MS. It is one of the most fine and delicate musical codices I’ve ever seen. Moreover, for the days we run, for those who have had the patience (and passion) to read, up to this point this long post I would like to wish them, from this blog, to have strength or


Έρρωσθε τοις εντευξομένοις 

Comment by Oliver Gerlach on December 27, 2019 at 12:18

I do not understand, why certain colleagues believe that I am an advocate of an unchanging tradition of Orthodox, Jewish or Muslim chant, because if they did really read my publications more carefully, they would have understood that writing down every detail is something which I characterised as a strict or hard transmission. This is the case for most of the Latin scribes and history teaches us that written transmission can even be destructive, not just for oral transmission, but for musical transmission as a whole. Next to hard transmission there are different forms based on a more “dynamic transmission” as it was called by Iannis Zannos.

My point was another one, if I do not agree with certain commonplaces which were published about music theory, it is simply that I have no confidence that Western musicology has the right point of view and methodological approach to understand Ancient Greek harmonics or even its own history which is not the point of view of any modal tradition, because they still preserved unsimplified forms of monody. It is not an individual aspect (even if you do insist so much to treat others like an individual which is dedinitely nice and polite to do so), there is a collective aspect as well, since it is part of European history that they have moved so far away from Oriental Europeans (an ignorance which has also political dimensions, just think of the Balkan crisis), but also moved far away from a profound understanding of European music and its history (whatever some might regard as their own or as Occidental is only concerned about a small part of Europe and it is not even true that such a geographic way of dividing Europe does work). Between a so-called “Western” European and an “Eastern” European there are so many cultural differences, that they do even attract each other by being so different. I personally think it is more important to understand these differences than to be polite for the price that one stops to question these commonplaces.

The more dynamic form of transmission is not less changing, it causes even more changes, even local differences, since oral transmission has been always local and dynamic transmission also does not interfere so much with these local differences and cultural diversity. But just because one needs to know very much to perceive and to understand these differences, it does not mean that these changes and differences do not exist. Together with this understanding, there is also a certain responsibility! But ignorance is never responsible, it is always fatal and the real cause of cruelty and intolerance.

Comment by Oliver Gerlach on December 24, 2019 at 12:30

I wrote:

Greek transmission of chant did change less or more (very likely less, if it is true that the notation was less concerned about the concrete level melos and its thesis—to put it into Aristotelian terms)

It basically means it is always different, depending on the very moment of performance or celebration, but chant transmission did not care about all these superficial details, the art according to Aristotle was potent (δύναμις), transmission was not about the frozen moment. It came later!

Comment by Oliver Gerlach on December 21, 2019 at 11:34

Quoting from Wolfram / Hannick's edition of the dialogue treatises, they did also mention a reference to Alypian notation and its letters as a reference or marker for frets (you mentioned the Greek term kavallion).

Also here, there is a difference between Greek and Latin theory. You wrote that the Greeks did not develop any kind of notation during the first millenium. But there is this hymn about Trinity in the Oxyrhynchus papyrus (unfortunately, only available at wikimedia, since the official link was obviously removed):

If I understand well this 2nd-century fragment uses Alypian notation (please correct me, if I got it wrong!), which means that Greek psaltes could have used musical notation since late Antiquity, if they did want to use it. Also Latin theorists had the Boethian letters and Nancy Phillips studied the way it had been used during the centuries.

The discussion is in fact not, whether the Greek transmission of chant did change less or more (very likely less, if it is true that the notation was less concerned about the concrete level melos and its thesis—to put it into Aristotelian terms), but what was the precise role of different tone systems within chant transmission.

In part your argumentation touched the discussion, whether the Hagiopolites was already used since the 9th century as an introduction to the unnotated book tropologion (although the few tropologia known to us reveal that it did not exist simply as one tropologion, since their organisation is so different among each other) or was it not so much older than the Bellermann fragment (11th century) and with its focus on music rather intended as an introduction to a notated chant book (sticherarion or heirmologion) which was definitely not very concrete in its early phase between theta / diple and the elaboration of just one sign in Coislin or Chartres notation.

Concerning Latin theory, we do know that the scribes had no access to Alypius, but they knew the Lesser Perfect System (or triphonia) through Martianus Capella and Cassiodorus who was quoted unchanged by Aurelian of Réôme. I asked here at Musicologie médiévale, whether anything is known about a use of LPS in Western plainchant, and there was no answer. But at least, there was a Carolingian notion of this tone system, even if it is hard to say, whether it had made sense to them...

Why you are so eager to drop the Slavic evidence, since it was obviously about a whole reception just based on triphonia and on the Old Byzantine / adiastematic level of notation? It is definitely relevant to the whole discussion and it has been already the outcome, when we discussed your earlier essay (where I also discussed Claire Maître’s pre-theory in absence of theoretical evidence preceding the tonary). It is always relative, for a Hebrew scholar such a lament about a lack of sources seems rather like the reaction of a spoiled child...

Comment by Oliver Gerlach on December 15, 2019 at 23:24

Dear Pavlos

Thank you for your very extensive answer which is most appreciated.

I understand now better your reference to Lorenzo Tardo. There is indeed a discussion going on between experts doing fieldwork within the Arbëresh communities, where I am actively involved. One must bear in mind that an interest in this field was originally (by the turn to the 20th century) also motivated by the ideolological approach to find an “uncorrupted Byzantine tradition” in Italy. My opinion on the subject is that the Italo-Byzantine synthesis is not so much different from the one of Constantinople, also because Italian contributors like the Sicilian Joseph the Hymnographer who had to leave Sicily during the Arab conquest of the island and who got his education in a monastery of Thessalonica, were well acquainted to the Stoudites travelling between the Polis and the Patriarchate of Jerusalem and Alexandria. On the other hand, since you mentioned Cod. crypt. Ε.γ. ΙΙ (the first facsimile published within the main series of MMB) was written at a scriptorium of Constantinople and obviously ordered there (it fits perfectly for the needs of MMB who was interested in the 14th-century redaction of the heirmologion), a more local Italian redaction of Grottaferrata you will find in the earlier heirmologion Cod. crypt. Ε.γ. ΙΙI still with Old Byzantine notation written about mid 12th century. Sandra Martani has published about both heirmologia.

“Teoretici” in Italian does not mean anything specific (just “theorists”, not harmonikoi nor Aristoxenoi), but one should bare in mind that Lorenzo Tardo coming from the Arbëresh background did not only identify with Latin sources such as Boethius and Aurelius Cassiodorus (who translated the local Italo-Greek heritage of the Pythagorean mathemata at Vivarium in Calabria), but also Greek authors from Southern Italy such as Euclid and Archytas. At that time Pythagorism was still based at the Poleis along the coast, while the medieval period of the Catepanate of Italy (with residence in Bari) rather developed a very excentric and rural form of hidden anachoretism (also due to persecutions of Slave-trading berbers who brought Greek knowledge to John of Damascus).

Fact is that the current oral tradition of liturgical chant (which cannot be dated earlier than to the 18th century, in the best case) intonates the Dorian octave almost like a minor scale, but I think even if the local heritage is partly independent from the Constantinopolitan, it was not so completely (and the Italian sources of Papadikai which Tardo treated in his book, are somehow proof for that) and the explanation for that is rather conventional: it developed out of a temporary use of phthora nana (my opinion which is opposed to my colleague Giuseppe Sanfratello). Her is my publication of our panel we had together in Licosia:

Concerning the Slavic evidence, I do not think you can so simply exclude the subject as “my information”. It is part of Byzantine history, even if Panonia and Tsar Boris (First Bulgarian Empire) dealt with both options, in the first case they decided for the Roman administration, in the second for the one of Constantinople, the Adriatic East coast is definitely something inbetween which is best understood as something of its own (which caused many misunderstandings and persecutions during the centuries). In any case it relevant for the numbering 1-8 (which existed independently from the Byzantine tradition also in Armenia and Georgia).

Please accept this as a first answer I will refer to your quotations more into detail in a later answer. 

Comment by pavlos erevnidis on December 15, 2019 at 18:21

I want to be more precise about a reference of mine related to the edition of Pseudo-Damaskēnos. My critique in note [5*] of the main text of this blog was about the reading of the editors of Ps-D of an important terminus technicus, Kavál(i)a (in plur., Fr. Chevalet, which is written also by the hand of Pediasimos on f. 359v of I-Rvat: Gr. 191). Here I make an exception to my original statement that I will avoid talking about specialized Greek terms a) because of the proximity of this medieval Greek word to the French Chevalet and mainly b) because of a proposal of mine in the end of this section. The editors of these text(s) dedicate to this term in their Kommentar (pp. 118-119) about half a page, but without any reference to the other readings of the MSS of the text they edit (I took the pain, Oliver, to transcribe almost all of their relative text [retaining the orthography] because you don’t have the book easily available, since you are in Italia):

 118 […] Die Frage nach den καβάλα der τελεία μουσική entstammt dem HAGIOPOLITES § 11 (RAASTED 18). p. 119 Hier werden die Zeichen für die Tonstufen des lydischen diatonischen Tropos des ALYPIOS 1 3-4 (JAN 368 f.) aufgezeichnet. Alypios benützt die Buchstaben des griechischen Alphabets, jeweils paarweise, in verschiedenen Positionen für jede Tonstufe. Mit diesem System entstehen wesentlich mehr als fünfzehn Zeichenkombinationen für die Tonstufen aller Tropoi. Die 15 καβάλα dürften sich daher auf die 15 Tonstufen des δὶς διὰ πασῶν beziehen. In seiner Edition des HAGIOPOLITES gibt RAASTED 90, Anmerkung 4 folgenden Text wieder: … [a Greek text follows that there is reference not of kavála = plural but of kavália = plural and kaválion = singular, I’ll give the relative link below] Wenn auch der Terminus καβάλα weder in der antiken noch in der byzantinischen Musiktheorie zu belegen ist, so gibt es doch noch heute in der griechischen Musikinstrumentenkunde die Bezeichnung καβαλάρης für den Steg einer Lyra, dokumentiert in: Μουσεῖο λληνικῶν Λαϊκῶν Οργάνων, Athen: siehe auch A.P. BRELLES, Λεξικὸ λληνικῶν λαϊκῶν μουσικῶν ρων ΙΙ. Ioannina 1992, 126 f.


Α) There are not only Lyras/Kemençe that have bridges/καβαλάρηδες or γέφυρες, but also Βιολιά/Violin/Keman, and psalterium like instruments as Κανόνια/Kanun, Σαντούρια/Santur etc.. Frets and bridges, because of their positions and names/onómata, can perfectly be music theory terms as well as musical instrument terms. These cases are not mutual exclusive.  

Β) Now it is time for all of us to see this term in the online MSS beginning by its reference, in a more precise way, in MS Dionysiou 570: This word it is found on f. 8r line 10 of this MS. Let us then look at this Byzantine music theory word also in the Hagiopolitēs theoretical treatise in F-Pn: Gr. 360; it is found two times on f. 217v and on 218r = tōn kavallíōn (gen., in Raasted [ed.] p. 18 and p. 20 [In his Index in p. 96 he uses the singular form kavállion and on p. 96 as onómata tōn kavallíōn). The other MS with reference to Raasted p. 90 is the EG-MSsc: Gr. 1764 (Math. 299) and is appeared two times on 34v = kavália (plur.) [this is the same form and orthography in relation to its oldest best dated evidence written by the hand of the intellectual Ioannēs Pediasimos] and kaválion (sing.) Now the appearance of this word in the other online MSS of Pseudo-Damaskēnos: Panagios Taphos gr. 332 f. 6r = kávala, G-An: Gr. 965 (“Schlechte Orthographie”) 63v = kávala, F-Pn: Sup. gr. 815 7v = kavállia. Of course, we need for a complete critical apparatus the other MSS. As it becomes apparent this is one of the reasons that I should write the beginning of that old Invitatorium, Ecce iam venit plenitudo temporis and

Γ) More importantly, I think that the time has come to start the construction of a real Lexicum Musicum Medii Aevi continuing the initiative of Thrasývoulos Georgiádis and Walter Bulst with the Latin case and, let us hope that, eventually, we will be able to incorporate in the same, with Latin, site the medieval musical terms in Greek, Syriac, Armenian, Hebrew, Georgian, Slavonic etc.    

But as I said Syriac and Slavonic,

You write Oliver (1): […] and why you think that Slavic apostles and the reception of the cathedral rite in Novgorod and elsewhere in the Kievan Rus’ are not part of the Byzantine history... Since Byzantine notators and cantors made visits to instruct them, by the way: […]

Are you, Oliver, adding “your information” (=“Slavic apostles […] Kievan Rus’ ” and “Since…them”) to what you believe (once more) that I think (“why you think […] history…”) or you just put words in my mouth (all these within a question) and we are derailing the issue? Anyhow, the issue I am presenting is that the numbering 1 to 8 exists in Byzantine as well as in Slavonic and Syriac modes. Nothing more, nothing less.


(2):Глась а'–и' is the common numbering of Slavic chant books since the Tipografsky Ustav (about 1100) or earlier manuscripts with signatures dating to the 11th century, but I never came across a Greek manuscript which used this system.”

Yes, I strongly support the idea that in Byzantium there were two numberings of MODES, 1 to 8 and of course 1,2,3,4, pl.1, pl.2, pl.3, pl.4. What I want to add is that in my rationale there is no place for “lost MSS.” One aspect of the issue is on when and to what degree liturgical book ordering reflects modal ordering, as terminologies has been used like (here I use Aelred Cody’s categories) “musical or modal octoechos,” “litugical or hymnographic octoechos,” and “a book containing texts so arranged, the Oktoechos.” In more recent literature we see also studies of other –specific- sections of the liturgical material and their relation to musical issues which in the older days would be categorized in the then “pre-theoretical period.” But, it is better to leave to the ethnomusicologist of the future the issue of the shifts (in time and geography) of the “pre-theoretical period” (and the size of the box with the label “Grecizing movement of the 9th century”) during 20th-21st centuries and for the moment, let us remain on Bryennios’s information, Father Lorenzo (Tardo) and the medieval poems he published.


(3):“I could now ask you, why do you think that Lorenzo Tardo told you not to support double numbering in order to become his authentic interpreter,…”


On p. 363 n. 1 of his L’antica melurgia bizantina (Grottaferrata 1938) he writes: (1) Questa e l seguenti strofe, già note, sono tratte dall’ Εἱρμολόγιον Ε. γ. ΙΙ. In alcuni codici vengono attribuite a Teodoro di Cizico, […]. This notated Ε. γ. ΙΙ. published by him (Roma 1951, in fcsm., at those days there wasn’t internet) is of AD 1281 (Bryennios was in life at that time). But these poems (with slight differences in the text) are found much earlier and are placed in the beginning of every ēchos, since Heirmologion books taxonomize and collect “the pieces” in mode sections (this is somewhat elliptical but there is not any reason here to describe this book in a more detailed way). The epistolographer and bishop Theodore of Kyzikos (8 km from Erdek/Türkiye) lived in mid-10th century.

Now, if we see Tardo’s exposition of the four plagioi ēchoi in this book we read (again I am transcribing an extensive reference):


  1. 375: 56. - Ἦχος πλάγιος πρώτου – PLAGALE DEL TONO PRIMO.

Then the relative poem in Greek is given where there is a verse that this ēchos is fifth in order; and the first sentence of Tardo reads:

Il plagale del tono primo dai teoretici viene chiamato ipodorio. […]

  1. p. 377: - Ἦχος πλάγιος δεύτερος – TONO SECONDO PLAGALE.

Then the relative poem in Greek starts with something like: “you are the sixth ‘melodist’ ”; and the first sentence of Tardo reads:

Il plagale del modo secondo dai theoretici viene chiamato ipolydio. […]

  1. 379 as we already saw: 60. - Ἦχος βαρύς – TONO GRAVE [SETTIMO].

Then the relative poem in Greek with no reference to seven (but calls pl.3rd as “secondothird” [δευτερότριτε]); and the first sentence of Tardo reads:

l modo settimo dai teoretici è chiamato ipofrigio. […]

  1. p. 382: - Ἦχος πλάγιος τοῦ τετάρτου – TONO QUARTO PLAGALE.

Then the relative poem in Greek with no reference to it as eighth; and the first sentence of Tardo reads:

Il modo ottavo dai teoretici viene chiamato ipomissolidio. […]


Some observations: α) the ancient names of the ēchoi are not those of Hagiopolitēs but of the usual exposition of the papadikai. This nomenclature is first recorded (I gave the link above) in F-Pn: Gr. 261 of AD 1289 on f. 140v. β) what exactly is this teoretici? Is it possible for someone to give me a translation of this word? γ) in his text there is not any hint that 1) this is not the only nomenclature (of the ancient names of the ēchoi) 2) that this specific nomenclature is not representative of the whole “Byzantine Music” and 3) that it represents just a later stream which prevailed also in Ottoman times.

Now, for why I said that I do not claim any authenticity on the interpretation of Tardo: If we examine closer, the word settimo for pl.3rd is included in square brackets. Additionally in the first sentences of pl. 1st and pl. 2nd exposition Tardo gives them as plagals of the 1st and 2nd, but in the exposition of pl. 3rd and pl. 4th gives them as settimo and ottavo. Possibly, one can state that this numbering belongs to Tardo himself in order to describe the modes and that in reality he didn’t believe that this is a, second, historical Byzantine numbering. In favor of the reading that Tardo supports also the 1 to 8 as a historical numbering are the published by him small poems that give this 1 to 8 numbering (I don’t even know if all this is an intentionally ambiguous exposition of him, i.e., if he wasn’t sure on the subject). Additionally, in his later L’Ottoeco nei MSS. Melurgici (Grottaferrata 1955) in pp. LVIII-LIX he explains the modes as eco I, eco II, eco III, eco IV, eco V, eco VI, eco VII and eco VIII.

So, once more, when I think that in a wording or an exposition (or even an information) there is -even a hint of- ambiguity I prefer not to give my explanation on what someone “means” because I prefer to concentrate on central issues and not losing time on who is right on the interpretation of a scholar. The same stance I keep even on overall narratives when I have not all the data available. But, more importantly, if we remember how Wellesz messed up in a specific case of his narrative on modes (in his A History of Byzantine music and hymnography, I criticized that case in that old paper of mine of 2001 [my exposition about what he wrote, on the same case, on modes is more analytical in the 14 Oct. 2019 presentation of that paper]), perhaps then one could have a better idea on how the modern views on “musical” Octōēchos has been formed. The whole idea, in my - not definite- opinion, is that some people tried to create a musicological “unified [Byzantine] theory” selecting (perhaps unintentionally at those times) a little bit from the one stream, a little bit from the other and then made their reconstructions. As for Father Lorenzo (Tardo), here I did my best (in the time framework I have), although it is not central to me to know what he believed (in all of his writings, but I would be happy if we are in agreement with him) on the subject; the ethnomusicologists of the future, I am sure, will examine all these issues more fully.

For the moment, what I know (the following does not constitute any interpretation to anything already written in the relevant literature) is that medieval theorists did not write “nonsense,” and that to explain Hagiopolitan theory with the later papadikai is like explaining Alia Musica via Hermannus Contractus! To say it in my old way (as in that paper of mine in CP 2006): Byzantine chant is not a “less changed” chant that the Latin ones.

To conclude, I wrote the above in order to clarify that my opinion on the two numberings of the Byzantine modes is not depend on whether Tardo believes (or not) that in Byzantium there were two numberings of the modes.


(4): “You will anyway argue that most people will hardly give a toss and I should not touch such a silly question. Who can exclude the possibility that you might be right?”

Some of the issues you referred are interesting. What I wrote is that I am sure that the people, especially of M.M., are not interested on discussions among persons on who is offended when, why etc. although we all have to be extremely cautious because, additionally, in an international discussion, something that is offensive to a South American is not to a North European.


(5):“[…] that could be also a convenient […] of cheironomia and its unknown use of triphonia!”


“From a modern point of view it […] our oktoechos discussion […] with a secondary role of heptaphonia inherent with the melos (and present in Chrysanthos’ monosyllabic parallage).”


Triphonia, tetraphonia, heptaphonia, parallage … What I did at that old discussion of ours I continue to do here: I will not make any comment on your (and my) exposition of the Hagiopolitan theory. Moreover, in the beginning of this blog I wrote that I’ll try to avoid terminologies and elements of Greek chant that, for one with no intimacy with the subject -a Gregorianist for example – can be perceived as foreign, difficult and laborious to deal with; mainly something exotic that should be left to those devoted to (Latin and / or Greek) music theory.



Comment by Oliver Gerlach on December 11, 2019 at 12:00

No need to sorry. You just take your time, we are not in a hurry.

I am used to Bulgarian and Greek chant editions. Thus, I am familiar with both numberings.

Глась а'–и' is the common numbering of Slavic chant books since the Tipografsky Ustav (about 1100) or earlier manuscripts with signatures dating to the 11th century, but I never came across a Greek manuscript which used this system.

From a modern point of view it seems like a scratch on the surface, while znamennaya notation always stuck to the adiastematic level of Old Byzantine notation. The step to diastematic notation came quite late with hook or kryuki notation, where melodic steps were defined within trichords (which is triphonia organised in four trichords of two whole tones, but always divided by a half tone). This theory dates back not earlier than to the late 15th century. If there was a Greek treatise preceding the Asmatikon (since the Kondakarian notation is basically an Asmatikon notation from a Byzantine point of view), one would have a proof that the Slavic reception (even for the sematic notation used in the office miney, the combination of stichirar, irmolog together with the unnotated kondaks) was based on triphonia. That was precisely the point, where Galina Alekse'eva joined our oktoechos discussion which was dedicated to your contribution for Lillafüred.

If one summarises the difference between the Carolingian synthesis (given by the book tonary) and the Hagiopolitan synthesis also present in the notated chant books of the Stoudites’ reform (sticherarion and heirmologion), you have only a need for seven octave species in the Carolingian theory (where the authentic and plagal tone uses one and the same finales and thus, only one tetrachord of finales or terminales which are everywhere due to the practice of parallage).

Within the oktoechos the “Hypomixolydian”, in harmonics still called “Hypermixolydian” (it makes sense, because it the last trope after Mixolydian in the ancient and proper order), regenerates according to modal synthesis the Dorian species, the only difference is that the tetrachord lies under the pentachord.

On the other hand, within the Hagiopolitan oktoechos there were only four octaves based on the plagioi and the Mixolydian octave (C–c) must have had a major seventh due to the dominant role of tetraphonia.

Thus, an adaptation was needed for the tritos octave which was called «emmelis» (also mentioned in a paragraph of alia musica which summarised the “echoi used among the Greeks“), otherwise the result was an augmented octave. This is the point where a difference between the tetraphonic tone system and the melos was needed, and it was obviously connected with a secondary role of heptaphonia inherent with the melos (and present in Chrysanthos’ monosyllabic parallage).

For these reasons I think that Galina Alekse'eva’s intervention was very useful, because she offered a different perspective coming from the study of the Slavic evidence.


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