Manuscrits (1)


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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