[Smt-talk] rationalizing the octenary system

Eytan Agmon agmonz at 012.net.il
Fri Apr 17 23:57:35 PDT 2009

Hello All,


I guess that Nicolas, David, and I will have to agree to disagree on our readings of Hucbald. I read him as saying “look, the note a fifth above the final is so closely related to the final, that one can even end a melody on that note as if it were the final!” Quoting Hucbald in David Cohen’s translation from his CHWMT article (p. 322): “many melodies are found to end in them [the notes a fifth above the final, EA] as if by rule… and to run their course perfectly according to the same mode or trope [as that of the true final, DC].” This statement should be read in the context of an earlier one (also quoted in Cohen’s translation): “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.” I don’t believe Hucbald uses any finem-related word in describing upper-fifth endings.


On the other hand, as David observes, the three of us do seem to be getting closer to the spirit of my original query. David essentially acknowledges that the octenary system can only be rationalized as a subset of the dodecachordal, and Nicolas states that “Glarean cannot be considered the "inventor" of the modes on A or C: they existed from the start.”


Perhaps, then, we can close this very fruitful discussion with two points for further thought. 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?






-----Original Message-----
From: David Clampitt [mailto:david.clampitt51 at gmail.com] 
Sent: Saturday, April 18, 2009 2:05 AM
To: Nicolas Meeשs
Cc: Eytan Agmon; smt-talk at societymusictheory.org
Subject: Re: [Smt-talk] rationalizing the octenary system


Hello Eytan, hello Nicholas,

 Yes, Hucbald is clear that there are alternative finals for each tone, alternatively lichanos hypaton [D] or mese [a], hypate meson [E] or paramese [hard-b], parhypate meson [F] or trite diezeugmenon [c], and lichanos meson [G] to paranete diezeugmenon [d]. 

Then, in the passage I cited earlier, Hucbald insists that the lower notes are suitable for placing the beginnings, not endings, of chants:

Hucbald’s text (p. 202 of Chartier’s edition):

Cum inferioribus quoque quartis et in quibusdam quintis, parem quodamodo obtinent [hae quattuor finales] habitudinem, quamuis non fini sed initiis deputentur: usque ad has enim metam inchoandi declinant. Hae sunt. Proslambanomenos: ad lichanos hypaton…

What follows is what I cited earlier: A is associated with D, B with E (rarely), C with F, D with G.

The crucial phrase is qamuis non fini sed initiis depetuentur: these [lower notes] should be assigned not to the end but to beginnings.

So, I think that literally B (the lower element) cannot be a finalis, but the higher hard-b, can so serve. I agree with Nicolas that our 21st-century notions blind us to some of these distinctions, above all octave equivalence.

Nicolas, I see your latest post has arrived before I have finished this one. I will say that yes, the four maneriae suffice to include the higher notes in the system, a and c, and hard-b, via socialitas, so in medieval terms there was no need for six, agreed. As to the meaning of the Hermannus Contractus phrase, I’ll have to digest your article. I notice you discuss Crocker, which is where I derive my understanding of that treatise, and that may be outmoded, so to speak. But, since Eytan asked about post-Hucbald developments, I note that you begin with this from Guido (which I don’t take exception to): “Puisqu’il n’y a que sept notes, car les autres, comme nous l’avons dit, sont les mêmes, il suffit d’en expliquer sept, qui diffère par le mode et par le qualité.” Your article goes deeply into issues of mode and quality. But already there is more recognition of seven note names of a diatonic system (Guido also quotes Vergil: septem discrimina vocum). This would seem to be getting closer to Eytan’s query. 


David Clampitt

School of Music

The Ohio State University

<david.clampitt51 at gmail.com>  

2009/4/17 Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr>

Dear Eytan,

I really do believe that your interpretation is not in line with what Hucbald means. You understand that a melody may end a fifth above its own final or, in other words, that the final is not necessarily the last note of the melody but rather some abstract reference note. Such a view rests, in my opinion, on presuppositions about modality/tonality, or about the link between the melodies and the underlying diatonic system, that cannot fit the situation in the late 9th century.

My own view is largely inspired by a paper by R. Weakland, "Hucbald as Musician and Theorist", MQ 42/1 (1956), to which you might refer. 
    Hucbald's readers were familiar with the chant repertory, but they had no idea of the diatonic system, nor of ways of comparing the melodies between themselves from an intervallic point of view; they did not even have note names, nor any clear notion of the modal final. Hucbald's purpose, therefore, cannot have been to discuss which degrees of the system could serve as finals, as none of these notions was available. What he tried to show is that, if the melodies were considered in terms of their inner intervals (to the description of which he devotes a lot of space), it is possible to align them all along one single general scale (the diatonic system) – the alignment, as we today can realize, really is a matter of adjusting the pitches to a single standard; but they had no notion of that.
    Hucbald further says that if the alignment is done correctly, one discovers that all the melodies in the repertory can be adjusted so as to have their final note on D, E, F or G. Why he chooses that particular tetrachord is unclear, but may result from the fact that the modes already were numbered and that these finals fitted their numerical order. He immediately adds that the same melodies could also be adjusted to end on other degrees of the underlying system: so doing, he is trying to describe aspects of the structure of the diatonic scale, but he is not discussing differences in the structure of the melodies. When he states that many (plera) melodies may end a fifth above D E F G, he does not mean that these cannot end on D E F G, but well that they can also end on A B C D.
    The reason to think so is that this remains a constant doctrine for centuries after Hucbald. The theory of the affinitas (or socialitas) is a theory of the structure of the diatonic scale, which states that notes a fifth (or a fourth) apart are surrounded by the same intervals. Guido's hexachordal theory is a theory of the extent to which affinitas is true. In solmization terminology, the four modal finals are re, mi, fa and sol. Until late in the middle ages, some theorists state that the melodies of the protus end on re – that is, any re, be it D, G or A –, those of the deuterus on (any) mi, of the tritus on fa, of the tetrardus on sol.
    I wrote a paper on Jacques of Liège and the practice of partial transposition (Revue belge de musicologie, 1995), in which I discuss Jacques's statement that, in some churches of Liège, when the melody lingered too long in the high, singers mistakenly end it a fifth too high: it is not that they end on the "fifth above the final" in the way you seem to imply, but rather that they end, say, on the wrong re, on Are instead of Dre – not realizing, in other words, that they had shifted their pitch standard.

The number of melodies notated with A or C as final was higher in the middle ages than today: it is because the 19th-century normalization of the chant reduced all these melodies to their theoretical final whenever possible. The very fact that this was possible shows that the question of the affinals in many cases merely is a matter of notational convenience, not of a structural difference in the melodies. Note also that changing from the regular finals to the affinals a fifth above merely involves replacing the F-clef by the C-clef on the same line.

A and C were not rejected as possible finals, they merely were not deemed necessary in Hucbald's highly pedagogical description because modes on D and F respectively could be written with a B flat. As a matter of fact, melodies ending on F almost always have a B flat, so that strictly speaking it are the modes on F that do not exist, not those on C. It would theoretically have been possible to write melodies on E with B flat (corresponding to modes on B), but these merely do not exist. As to melodies on G with B flat, they can as easily be written on D without.

Glarean cannot be considered the "inventor" of the modes on A or C: they existed from the start. What he did is normalize the notation, considering that modes written with a B flat were transpositions. This, by the way, happened not so long after another, more important invention, that of pitch standards (Arnolt Schlick, 1511).





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