[Smt-talk] rationalizing the octenary system

Richard Porterfield porterfr at hotmail.com
Tue Apr 21 16:14:17 PDT 2009

Eytan Agmon writes:

Isn’t it possible, however, that Hucbald is referring not to the entire melody, but rather to a phrase within it? Immediately following the discussion of upper-fifth endings (Babb, bottom of p. 39), Hucbald states that melodies in any mode (authentic and plagal are not distinguished) may begin up to a fifth above or below the final. Not only does Hucbald seem to refer to endings as well (in Babb’s translation: “… The endings and beginnings are confined within these series of eight—or sometimes nine—notes, be the mode authentic or plagal”)...
 I think it is important to keep Hucbald first statement on finals always in mind: “Thus every melody… is necessarily led back to one of these four [notes]. Therefore they are called “finals,” because anything that is sung finds its ending (finem) in [one of] them” (David Cohen’s translation). Surely he cannot state so emphatically that D-G are finals, and then immediately contradict himself saying that a-d are also finals. 
He's right on both counts. 
The Latin text is “fines vel initia” where Babb translates Hucbald to say that  “the endings and beginnings” fall within the space of a perfect fifth above and below the final (GS1:120, Babb 1978: 39). Just a few sentences earlier Hucbald has said that what are called “finales” are the notes “which among themselves take on the end of all things that are sung” (GS1:119, “quod finem in ipsis cuncta, quae canuntur, accipiant;” my translation is more literal than David Cohen’s). Thus “fines” are the generic category of final things (ends or endings),  and “finales” are specifically the modal finals, degrees of the tone-system “fitted to bring the modes or tropes to their perfection” (GS1:119: “modis vel tropis ... perficiendi aptantur”) . Babb’s translation distinguishes these as “endings” and “finals,” respectively, and http://www.chmtl.indiana.edu makes the Latin original readily available. 
So Eyton is absolutely right, I believe, to understand Hucbald to say that beginnings and ends of phrases fall within a fifth of the final. This is indeed generally true of the Gregorian repertoire – except for melodies of Mode 3 (deuterus authentic), whose phrases very often begin and end at the sixth above the final, as Guido notes (GS1:155; Babb 1978: 69). Hucbald’s silence regarding this suggests it may not have been so for the Mode-3 repertoire he knew; the Commemoratio brevis from the same period gives recitation tones for Mode 3 on [hard] b, the fifth above the regular final E, not the sixth on c we find in later sources. 
Nevertheless Hucbald’s language does not rule out the possibility that a chant might come to an end (finem) on a note other than the final (finalis) that perfects its mode or trope. Odd as this may seem, I know of at least one example: the Mode-1 Kyrie Cunctipotens genitor deus (LU 25). The opening Kyrie and Christe sections prolong the Mode-1 tenor a before cadencing on the Mode-1 regular final D. The last Kyrie continues similarly, ending however not on D but on a, the upper fifth. In this case I still hear D as the modal final, the goal toward which the melody progresses in spirit if not by letter. I would call D the “tonic” if that term didn’t bring up so many unwanted associations. You can see how this chant looks in a14c Florentine manuscript at the Metropolitan Museum of Art, and hear it sung by myself with the Mannes Schola here: http://www.youtube.com/watch?v=votvtpneqWk&feature=channel (notation projected at 3:20, singing begins at 5:00). 
This ending at a fifth hovering like a halo above the implied final – if that is indeed what’s happening here – is very unusual, however. Most Mode-1 chants notated to end on ‘a’ take that note as finalis as well as finis (writers later than Hucbald would call it an affinalis, final by affinity; Amerus in 1271 introduces the term confinalis). Such chants will include somewhere in their melody a semitone above the final, which Hucbald’s system cannot accommodate above D (there’s no E-flat in the system). This requires transposing the entire melody up by fifth so b-flat can take the semitone above a. Similar tricks allow for various similar inflections in all modes. 
Still, I find nothing in Hucbald’s treatise to suggest he had in mind this clever solution to a problem encountered in relatively few Gregorian melodies. Again Eyton is correct, I think, that Hucbald believed that one member or another of the set D-E-F-G is adequate to represent the goal (finem) of all that is sung. He observes that the tetrachord a-[sqare]b-c-d could in many cases do the same, and that melodies noted to end on them “remain entirely within the same mode or trope” as those on the regular finals (GS1:119, trans. Babb 1978: 39). This might have been intended to theorize the practice of organum at the fifth, which the Enchiriadis treatises of the same era describe. What it led to, when later theorists took on the task of setting down the repertoire according to the system Hucbald proposed, was transposition by affinity. 
Had they chosen to honor the system Hucbald wished for, where modal finals remain in place and mobile degrees move by semitone, they might have introduced E-flat or something like it, and other inflections as needed. Perhaps then no one would have confused mode with scale. Instead they honored the system he devised. Who, they might have thought, would not be able to recognize the modes by ear? 
Richard Porterfield 
Mannes, CUNY GC
porterfr at hotmail.com 

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