[Smt-talk] rationalizing the octenary system

Richard Porterfield porterfr at hotmail.com
Sun Apr 19 20:39:25 PDT 2009

Dear Eytan Agmon, Nicolas Meèus, and List,  
Eytan articulates precisely what prompted Glarean to propose a 12-mode system in place of the established 8-mode system: 
"First, if the modes on A or C indeed existed from the start, then the recognition of six finals by Glarean is probably the most extreme case in the history of music theory of theory lagging behind practice. Second (and here I guess that Nicolas and others would strongly disagree), if the modes on A or C indeed existed from the start, then are we really doing service to medieval music and musicians by being (trying to be!) “emic” rather than “etic”? I am stressing “music” rather than “culture” in some broad sense. Of course the doctrine of the eight modes is part of “medieval culture” in some broad sense. Indeed, it was probably very difficult, from a medieval point of view, to openly contradict a doctrine so closely associated with the authority of the Church. But rather than succumbing to the intellectual pressures of medieval culture ourselves, shouldn’t we be voicing what Hucbald, Guido, and other great medieval musicians, seem to have understood perfectly well, but were prevented from stating explicitly?"
This also reflects a fundamental error of Glarean, still very much with us, as to what the eight modes are. Clarifying this will help to answer, among other things, Eytan’s earlier questions to this forum: why the segment A-C of the medieval gamut was “passed over” in the search for modal finals, and what made the segment D-G particularly apt for their location. 
The eight-mode concept was established in the Latin West by 800 AD. This was several generations before Hucbald’s treatise introduced a vocabulary for locating individual notes in a tone-system, and roughly a century before the Alia musica’s attempt to identify the modes with the ancient Greek tonoi. The noanoeane formulas that appear in the early tonaries, like the Primum quaerite antiphons that Guido later recommended for learning the eight modes, are not scales but melodic prototypes to be compared to melodies encountered in the repertoire. “We learn the mode of the chant,” says Guido, “from the way it fits these [type-melodies], just as we often discover from the way it fits the body which tunic is whose” (Guido, Micrologus Ch. 13; translation Babb 1978: 68). Many of these type-melodies, like much of the chant repertoire, operate within the range of a fifth or sixth (see Babb 1978: 120-21). Thus even after Hucbald’s successful adaptation from the ancient Greek diatonic of a tone-system for Western chant, the modes were still primarily conceived as melodic types, not scales. Note the use of type-melodies by Hucbald as well (Babb 1978: 31-32, 35-37). Neither Hucbald nor Guido discusses octave-spanning scales. 
That’s because the modes of the octenary system are melodic types, not scales. This statement is both “emic” and “etic.” 
Hucbald was compelled to combine two separate Greek diatonic systems, one with b-natural and one with b-flat, because Gregorian song makes use of a mobile degree. Each and every mode includes some chants with melodic motions that require for their notation the b-flat, others the b-natural; many chants alternate between the two. Mode 8 (tetrardus plagal), for example, which usually has b-natural over the final G, also includes the antiphon Omnis sapientia (LU 990), which employs b-flat and not b-natural. That’s because Mode 8 is not a scale, it’s the kind of melody that sounds like “Noeagis” (G/c/a/G) or “Noeagi” (C/F-E/D/C), or “Octo sunt beatitudines” (F/F-G/G/a-c/c/c-b/a/G/G); examples from  Terence Bailey, The Intonation Formulas of Western Chant (Toronto: Pontifical Institute of Mediaeval Studies, 1974: 57, 90). 
David Cohen calls the approach to mode based on the octenary system and practical experience of the chant repertoire ‘the cantus tradition,’ as opposed to ‘the harmonics tradition’ that seeks to define mode as species of the octave; see his “Notes, scales, and modes in the earlier Middle Ages” for The Cambridge History of Western Music Theory (2002: 308). These rival traditions, despite attempts at synthesis, continued to operate side by side through the 17th century, with practical musicians favoring the cantus approach; see Frans Wiering, The Language of the Modes (Routledge, 2001). An important exception was Marchetto of Padua, a choirmaster whose theory that the eight modes were species of octave divided into species of fourth and species of fifth exerted enormous influence in the later Middle Ages. 
Problem was, as the academic humanist Glarean pointed out, Marchetto’s species theory 1) was not logically consistent, and 2) could not be reconciled to the reality of the chant repertoire. Glarean’s solution – alas! – was to seek in Greek diatony the scales of Gregorian chant, mistaking these for the modes. Chants with b-flat consistently over the final D, he argued, were not of the same mode as chants with b-natural over that final, but the transposition of another mode entirely, whose natural final was A. Chants with b-flat over F as final represented a C mode in transposition. The B modes he rejected as unsuitable for lack of a perfect fifth over the final; in an earlier message I listed several chants to the contrary. 
So, to answer Eyton’s original query: Hucbald didn’t take as finals the first three steps of his tone-system because plagal melodies often dip a fourth or more below the final. If you pitch the final on your lowest string, there’s no place to go down any further. The Mode-2 Introit Salve sancta parens, for example, is written to end on D (LU 1263). The setting of its first word “Salve” (A-C-D-E/D) exemplifies what Hucbald meant when he said these low notes are useful for beginnings, not endings. Hucbald was making a tone-system to accomodate the melodic repertoire, not for the speculative generation of scales through the division of the octave. 
As to why the D-E-F-G tetrachord is more apt to serve for the finals than, say E-F-G-a, they  correspond in order to the tonal qualities protus, deuterus, tritus, and tetrardus, respectively – tonal qualities that everyone knew from their cantus-tradition pedagogy meant first, second, third, and fourth, respectively. (This certainly suggests that the tetrachord of finals was already established and understood in TTS relation even before there was a larger tone-system to place them in.) E-a would give them in order 2nd, 3rd, 4th, 1st. D-G are also high enough in the system to allow for almost every plagal melody (later, for melodies ranging a fifth below D the Γ would later be added), and still low enough to allow for melodic development in the upper ranges. Furthermore this places the finals most conveniently in relation to the mobile b-flat/b-natural: very many protus melodies have the mobile note on the sixth degree above the final, some deuterus melodies have it on the fifth degree, very many tritus melodies have it on the fourth degree, and a fair number of tetrardus melodies have a mobile third above the final. For the more rare but not uncommon instances where the mobile degree is the second above the protus or deuterus, “a” may serve as final, and so on. Bravo Hucbald! 
Harold S. Powers, among others, has argued the octenary system as church doctrine, and the whole question of mode as “emic.” Well, just because it’s church doctrine doesn’t mean it ain’t so. If the octenary system were nothing more than a vast Carolingian conspiracy I believe it would not have long outlasted Carolingian culture. The eight modes would have gone the way of the Noanoeane formulas, Byzantine exercises replaced with Latin-texted antiphons soon after the waning of Byzantine influence in the west. Don’t for a minute think that Guido wanted to say there were more modes, or that the modes were of a different nature, than his training had taught him: he knew the repertoire, and we know he wasn’t afraid to introduce new ideas. It is by learning the repertoire, he said, that we learn mode: “most helpful for this are the verses of the responsories of nocturns, the psalms of the offices, and all the chants that are prescribed in the formulas of the modes [here by modorum formulis I believe he refers to the tonaries]. It is a wonder if someone who does not know these understands any part of what is being said here (Micrologus Ch. 13, Babb 1978: 68).” 
Richard Porterfield
Instructor, Mannes College
Ph.D. Candidate in Music Theory, CUNY GC
porterfr at hotmail.com   
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