Munich, Bayerische Staatsbibliothek
Tonary of the alia musica compilation (manuscript M) with neumed intonations, psalmody, and glossed tonaries, music theoretical collection of the Abbey St Emmeram, Regensburg (1006-1028).
When I published my article about this particular intonation:
Hartvic's tonary was not yet online, so that I could reconstruct the original echema as it was notated in this manuscript. It is one of those with a melisma on the last syllable:
The text (Chailley 1965, 141):
Hoc quoque senties canendo A[punctum]I[virga cum episema]A[virga cum episema]-NE[climacus/pressus?]O[punctum]E[pes]A[pes]NE[clinis, salicus & torculus].
Siquidem a paramese [♮], peracta quarta specie diapente, ad lichanos hypaton [D] descendit, et ad lichanos meson [G] per singulas chordas ascendendo diapente intendit, rursusque ad trite diezeugmenon [c] gravando remittit; ad extremum in sua finali hoc est hypate meson [E♭] definitum.
I think we could do this reconstruction work together, based on this source.
Any suggestions, how this echema AIANEOEANE should sound like according to the neumes and the verbal description?
You might download this graphic to insert letter notation:
Replies
What are the proportions, if you sing G+? I understood that the fourth species of the fifth is between G and d...
And how would you understand the melos presented by the echema, if you try to read the neumes that they fit to this description?
Sorry, I missed the word 'descend'. Good question. For the ascending interval G - A (fourth to the fifth), I sing sometimes G as the pure fourth of D (it depends also on the vowel); but if descending down to D, I certainly sing a high G+, this gives the descending scale A G+ F+ E D. The interval E - F+ or F+ - E, is characteristic of the E mode. A good and simple example: antiphon Nigra sum sed formosa.
You did not answer my question which intervals you would choose for the descending direction as described by the author of the tonary compiled wihtin alia musica...
Would you choose the pure fourth between C—F, if you descend from G?
I certainly would choose the high fourth, given, if starting from C, by the interval C - F+ (11/8) or starting from D, D - G+ (99/64). But it doesn't make a tritone, it is, starting from C, between F and F#. To return to the (pure) E mode, E - F is high (11/10), E - G is high also (approx. G+), the fourth E - A may be pure i.e. 4/3 or high (depending on the vowel and the word); the fifth is pure, and then the interval H - C (si - do, above the fifth) is the same semi-tone as E - F. All this can be sung easily. These are the intervals I recommand for singing e.g. the extraordinary verse Beati immaculati in via, of Offertory Benedictus es ... in labiis, which sounds very much as a Spanish cante jondo (or flamenco): a similar treatment of the E mode, that prooves that the cante jondo comes from the ancient Iberico-Gallo-Roman tradition and not from some Arabic influence.
I see!
You would like to use a meantone intonation 9:8 x 10:9 x 11:10, but the result is almost a tritone, if you use 11:10 instead of 16:15. Hence, there is an attraction towards the kyrios tetartos, because the difference of the pure minor third (6:5) is 12:11 for the step between F+ and G.
But which intervals would you choose to descend from G to D?
When speaking of ancient intervals, based on the sequence of harmonics (overtones), the fundamental tone is supposed, theoretically, to be C (the pitch is irrelevant). Then, the fifth G, is the third harmonic and 3/2 of the height of C; E, the natural third is given (in the third octave) by the fifth harmonic, ratio 5/4; the pure fourth F is never a harmonic but is the complementary to the fifth in the octave (4/3); the second D is given by the nineth harmonic (in the fourth octave) i.e. the fifth of the fifth (9/8); then we have again the third E as the tenth harmonic, and now F+, the eleventh harmonic which ratio to the preceding E is 11/10. This is already sufficient to manage with quite a lot of traditional intervals. Particularly in the fourth octave, the Pythagorian third is given as the second of a second (81/64); the small second as the interval natural third - pure fourth; the high minor fourth by the interval D - F+ (11/9); the high fourth by C - F+ (11/8), etc.
The advantage is that all these intervals can be heard (by a little trained ear; it was certainly the case in ancient times and nowadays with children!). Moreover as harmonics of the voice, they have a meaning, a modal meaning, corresponding to the subbtle expressions of the voice.
I'm not forgetting to send you the CD Le Chant du Mont St-Michel.
Light and Joy in the New Year!
Talking of Karas, me neither...
Did I understand you well that the interval between between E and F (according “Pythagorean” tuning semitonium) should have the proportion 11:10, so that the eleventh partial tone of E comes together with the tenth one of F?
If C—D should be a tonus the resulting interval (between D—E) is: 4:3 x 8:9 x 10:11 = 320:297. I think 12:11 (D—E) instead is rather manageable... even if the resulting smallest interval (E—F) is 88:81.
I personally do not expect that E—a is a pure fourth (it does not need to be as a mesos tetartos, but the tetartos pentachord should have the proportion 3:2), but of course 11:10 has the result that E becomes considerably lower...
The decision of Latin cantors to define this mode as deuterus, just because it is an E mode, corresponds to the Greek interpretation of the 17th century, that echos legetos is supposed to be the old diatonic plagios devteros, but both are not correct, because the fifth E—b natural is usually augmented, which is not possible in devteros due to tetraphonia. But if you tune both tetrachords (D—G, a—d) 12:11 x 88:81 x 9:8, there is tetraphonia and the devteros pentachord has 3:2!
In the great Western repertory which - because of the high mastering of modal intervals, melodic formulae, words, vowels, etc. - belongs to the Gallo-Roman antiquity (IV-VI c.), I understand the modes more in the Indo-European harmonic way. Namely for the E mode, the interval e-f is high(11/10; interval - taking c as fondamental tone - between the tenth harmonic e and the eleventh f+). It is typical of oral traditions, and of Indian (North or South) music, Spanish cante jondo and e.g. in the antiphon Nigra sum or the extraordinary verse Beati immaculati in via of the Offertory Benedictus es ... in labiis. Because f = f+ (large half-tone) in a descending melodic movement e appears (very) low. Shortly for other intervals, e-g is high; the fourth a is high or pure; the fifth h pure; the sixth c high (h-c is the same interval as e-f: c is high). The Boethian theory, as we know, is concerned only by the theory of main intervals, and of course is far from the oral tradition.
I'm not always in accordance with S. Karas; note that 11/10 > 27/25. We all have interval 11/10 in our ears, because the f+, the high harmonic fourth is easily heard and necessary to form some vowels. When you heard it once and practiced a little, it is quite managable, while 27/25 is not.
Interesting is certainly Hartvic's addition "hoc est hypate meson definitum" which does not exist in Chailley's edition (note that Hartvic's copy does also start on page 99 of Chailley's edition, the beginning of his source is missing in the collection of St Emmeram). He pointed right at the odd circumstance that a low intonation of E was beyond the systema teleion, since the first and last element (phthongos) of the meson tetrachord was immobile (estōtes) and therefore did not exist within the Boethian diagramme.
This problem confronts us right with the synthesis between the Ancient Greek Great Perfect System (GPS) and the oktōēchoi in church music. The Byzantine theory defines "D" as the first element or "prōtos", Hucbald followed this kind of synthesis, so that the synnemenon tetrachord started on "G" instead of "a" (see my comment in a recent discussion, where I inserted a diagramme from a publication by Christian Meyer), while the anonymous author of the enchiriadis treatises rather relied on the Byzantine synthesis which used the tetraphonic tone system, and not the GPS.
First, I have to read carefully your paper. I don't have the book and don't plan to buy it; is it possible to ask you to send me the paper?
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