Le manuscrit Mas 138 de la Bibliothèque de l'École nationale supérieure des beaux-arts de Paris est un manuscrit de la fin du XIème début XIIème siècle originaire de l'Est de la France, provenant de l'Abbaye Saint-Pierre d’Hautmont, contenant principalement des vies de saints et des versus.
Trois versus ont reçu une notation contemporaine au texte.
85r Item versus cuiusdam doctoris : Ut belli sonuere tubae violenta peremit...
85v Versus Prisciani de XII signis : Ad Boree partes Arcti vertuntur.... ; Eiusdem de XII ventis : Quattuor a quadro consurgunt limite venti. His quoque octo gemini...
D'autres additions musicales, en notation neumatique lorraine, ont été faites au cours du XIIème siècle. 66r In dedicatione ecclesiae Sequetia. Clara chorus dulce pangat (AH 54:94) ; 75v S. Marcialis apostolus officiium [In.] Iustus ut palma* ; R/ Isutus ut palma* ; All. Ipse peibit ante illum* ; Of. In virtute tua domine ; Co. Psuisti domine*. 86r R/ Evigilans Noe ex vino... V/ Benedictus dominus deus...
L'addition la plus important de ce manuscrit est certainement celle concernant la théorie musicale aux folio 130v et 131r.
Au folio 130v, nous voyons une main guidonienne avec une particularité unique, jamais vu jusqu'à ce jour. Il s'agit de la correspondance des notes en notation dasianne.
Au folio suivant (131r), nous trouvons un traité, inédit jusqu'à ce jour, qui est une clef de lecture de la main guidonienne.
Je vous propose l'édition du texte ci-dessous :
De notis musicae artis quibus per cuncta tetracorda cantus quos volveris calculare valeas animadverte. Intimabo paucis. Incipiens a G prima monocordi litera quae ponitur, in principio pollicis et ibi pones vt, In secundo articulo Re In tertio mi. In quarto quarte primus in indice pones fa et in eodem vt ut cum cantus ascenderit pronuntietetur vt. Cum uno descenderit ad inferior quae sunt in pollice dicatur fa in secundo eius articulo. Inde in medio digito ut bene nosti ponitur Re. In anulari mi. In auriculari uno fa. In secundo eius loco sol et in eodem vt scilicet propter ascendentem cantum. Inde progrediens ad tertium articulum per dicti auricularis ponito ibi La quae vox etiam dici poterit Re. In summo uno digiti eiusdem ponito mi In sequentis uno summo fa quae vox erit etiam vt sicut priori factum est tetracordo propter ascendentem cantum. Inde precedens in summo medii digiti ponitur Re. In indicis uno summo mi. In primo eiusdem articulo fa. In sequenti Sol. Sic omnis cantus per manuale monocordum cantare poteris si sollerticura ad aequae predicta sunt diligentiam adhibebis.
Replies
Nice diagram! Is it from the article by Christian Meyer that you cite beneath it? Or . . .?
See also the tone systems according to Boethius (GPS), Hucbald and Musica enchiriadis:
It happens to us all that we add comments and the discussion has alreay 4 pages and one might not have read everything. You can always delete your own or add a corrected version of a former one.
The Dasian system with protus, deuterus, tritus and tetrardus could be represented by the Guidonian syllables re, mi, a sol, so that you have Γ re, A mi, B fa and C sol in the graves, but e re, f mi (f sharp), g fa and aa sol in the excellentes tetrachord. But this would require a lower hexachord which starts on the F as the phthongos below to γ (φ?) so you start not with Γ ut, but Γ re ut, A mi re, B fa and C sol fa etc. and you drop F ut, because b fa does not exist as phthongos within the tetraphonia of the Daseian system, so that d la sol re becomes actually d sol re ut. As I said Guido was against it, because he excluded the other tone systems. Nevertheless, the Dasian system worked somehow within the ambitus C—e and f sharp was anyway the last element. If you use the old solfeggio (parallage) with the echemata you must start on a very low pitch with protos, devteros, tritos, tetartos, protos etc. in order to pass the disjunct (separated) tetrachords four times!
I do not think this scribe did misunderstand anything, he was more experimental than Guido himself who used just three mutations in order to exclude the Dasian system. But nevertheless the author of the Vatican organum treatise had not Guido's problems and used the fourth mutation anyway! Somehow the later practice of florid organum met the first one...
A similar sort of misunderstanding of the relation between distinct scalar systems affects the very interesting table from Metz BM 494 that M. Gatte' posted on 6 September. There, proslambanomenos of the Boethian 2-octave system is equated with the protus gravium of the daseian tetrachordal system. Inevitably, all the subsequent correlations are incorrect. E.g;, the lowest of the finals, protus finalium, is equated, not with lichanos hypaton, as it should be, but with the note a step higher, hypate meson. The attempt may have been misled by the fact that the same series of intervals, T-S-T, lies, of course, at the bottom of both systems.
I wish to explain that I wrote my response (below) after having read only the first of the four "pages" of discussion of this topic. My mistake! That is why it ignores much of what has been said here, also why I did not credit Prof. Meeus with observing that the hand under discussion seems to regard B-mi as the same as the daseian tritus gravium. My apologies for that!
David E. Cohen said:
While the hand, as noted, includes indications belonging to several conflicting systems, I suggest that the crucial point is the fact that it comprises just fifteen notes, from Gamma-ut to a g-sol two octaves higher: in other words, a 2-octave system (like the Greater Perfect System and Hucbald's system) but bounded by G's at bottom and top. Note that the hand is incomplete from the point of view of Guidonian hexachordal solmization (there are empty spaces on the middle two fingers!), since that system comprises 19 or (later) 20 notes, from Gamma-ut up to dd-la-sol or (later) e-la, which this hand omits, as it also omits (as has already been noticed) the "soft" hexachords. Similarly it fails to represent properly the daseian system: its third note is B-mi where the latter would have a "B-fa" (B flat), though it nonetheless applies to that note the daseian sign for Tritus, which in the daseian system always lies a semitone above the note below it. And of course, as Prof. Meeus has pointed out, the hand conflates the all-disjunct tetrachordal structure of the perfect-fifth-based daseian system with the octave-based system of someone like Hucbald. It seems to me, then, that this is essentially a deviant 2-octave system (Gamma to gg), which someone has rather clumsily tried to integrate with the other available systems, viz., the daseian and the hexachordal.
The logic of absonia
I hope that you do understand that all these incoherences are too many that you might simply rely on a so-called "logic of absonia".
The term was left and loaded with everything which was left aside by Carolingian theorists. But since our heritage is Ancient Greek harmonics, we are obliged to be precise!
I tried to demonstrate this in my discussion of Rebecca Maloy who dared to open the gates of absonia.
I would not say these theories did prepare Guido's theory, the enchiriadis treatises did in fact so less that Guido decided to abandon the tetraphonic tone system, commonly called the Dasian system, as a whole! He was clearly against it, because he saw no relevance for chant (despite the fact that it was the most present tone system in Byzantine chant which employed at least three tone systems). Unfortunately this decision also influenced your choice of treatises in your material.
The weakness of Carolingian theory, or better: the conscious decision of certain music theorists during the second and third Carolingian renaissance to ban the change of tone system (μεταβολή κατὰ σύστημα) from chant theory, was a clear decision to base chant transmission on a simplification. Latin theory is mostly very much concerned about the practice of chant (although very few musicologists do understand that it is!), while early Greek chant manuals like the Hagiopolites do not even treat all the necessary terms. But if you do not know them, you are completely unfit even to read Greek chant manuscripts!
It is necessary to teach both theories, Davide Daolmi did at least try to teach the Byzantine oktoechos, but he got it all wrong, because he described the Western synthesis instead without knowing the difference. On the other hand, I made the test in the Melos groupe, and quoted the passage of Aurelianus Reomensis about the Lesser Perfect System in the Melos groupe which is a quotation of Cassiodorus and probably the reason, how the author got his name "Aurelianus". No one here was able to make a connection with chant theory, but within the Papadikai the triphonic system was connected with the phthora nana.
This is the problem, we have all three tone systems:
- LPS (Martianus Capella, Cassiodorus/Aurelianus)
- GPS (Boethius and every theorist who referred to him)
- Dasiane system (in Greek theory called the "trochos system", since it referred to the wheel-shaped diagramme of parallage, a solfeggio based on the echemata of protos, devteros, tritos, and tetartos in ascending direction and to their plagioi in descending direction)
You see the decision is not so coherent as some might think, also because there is only a very limited coherence between Guido and the earlier theory, he just cemented an earlier simplification!
May I remind that the discussion, from the start, was about the Guidonian hand? It did turn to earlier periods (Hucbald and Musica enchiriadis), but only insofar as these prepared Guidonian theories. I do believe therefore that including it in here was a very coherent decision.
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