[Smt-talk] rationalizing the octenary system

Eytan Agmon agmonz at 012.net.il
Fri Apr 17 06:18:33 PDT 2009



Thanks for your thoughtful message. I look forward to reading your paper (hopefully my French is up to it!). In the meantime, here is a comment and a question.


Hucbald most certainly does not say A, B, and C can serve as finals. Even though a melody may end on the upper fifth, there is a clear distinction between the upper fifth and the final. On the other hand, Hucbald refers to “the four finals” D, E, F, and G so many times, that the exclusion of A, B, and C (for whatever reason), can hardly be missed.


In terms of your “emic” theory, why does Hucbald choose D-G as finals, rather than (say) E to a? The lower fourth that he supposedly needs will exist, and he will even be using a true tetrachord of the Greater Perfect System, rather than an arbitrary one.


Glarean, by the way, rejects a B-mode, due to the diminished fifth above the final.






-----Original Message-----
From: Nicolas Mee?s [mailto:nicolas.meeus at paris-sorbonne.fr] 
Sent: Friday, April 17, 2009 11:27 AM
To: Eytan Agmon
Cc: smt-talk at societymusictheory.org
Subject: Re: [Smt-talk] rationalizing the octenary system



I wrote years ago a paper that touches upon this question. The publication of it has repeatedly been promised for "next month", but next month does not seem to come... In order to make it available for the present discussion, I deposited it at the URL http://www.plm.paris-sorbonne.fr/Modi_vocum.pdf, where it can be downloaded. (It is in French.)

I do not have Babb's translation, but I feel that "passing over the first three notes" somehow overstresses what Hucbald writes. The latin text reads: Quatuor a primis tribus..., which means "the four [notes] after the first three"; Hucbald continues saying that these four notes "are adapted to the perfection of the modes in such a way that each of these four notes rules the pair of modes subjected to it, both the principal, called authentic, and the lateral, called plagal" (Quatuor a primis tribus [...] quatuor modis vel tropis [...] perficiendis aptantur, ita ut singulae earum quatuor chordarum geminos sibi tropos regant subiectos, principalem, qui autentus, et lateralem, qui plagius appellatur). The reason why he passes the first three notes merely is that he needs them below the finals for the plagal modes. But he does not say that A, B or C cannot serve as finals, and nobody I can think of ever said so in the centuries between Hucbald and Glarean. (Even B seems a possible final!)

The important difference between the medieval conception and ours (or Glarean's) is that we view the system, the diatonic scale, as a concatenation of sets of seven pitch classes, while the middle ages (and many other musical cultures) saw it as a complex concatenation of four classes only, forming alternating conjunct and disjunct tetrachords. I am convinced that it is because the system is formed of tetrachords that there are only four (pairs of) modes – in very much the same way as we (or Glarean) would expect seven modes.

If I follow you correctly, you seem to understand socialitas as indicating that a final must have a perfect fifth above (and that that excludes B as a possible final). This is not what Hucbald says: he writes that any note a fifth above D E F G can also serve as final: "It should not surprise that, neglecting the synemmenon tetrachord, the degrees a fifth above these said four [notes] link to them in a bond of connection such that one finds many melodies ending on these so to say regularly, without any contradiction of reason or sense, and unfolding in the same mode or trope" (Illud nihil attendendum, quod synemmenon tetrachordo summoto, quinta semper loca his quatuor superiora quadam sibi connexionis unione iunguntur, adeo, ut pleraque etiam in eis quasi regulariter mela inveniantur desinere, nec rationi ob hoc vel sensui quid contraire, et sub eodem modo vel  tropo recte decurrere.) It goes without saying that if the synemmenon tetrachord is taken into account, finals can also be found a fourth above D E F G, etc.

As I explain in my paper refered to above, Hucbald provides the earliest mention not only of the socialitas, but also of the concept of final itself. And what he means by "the perfection of the modes", or by "ruling" the modes as "subjects", etc., is far from simple. "Perfection" is a heavily loaded term in these times. Guido, a century later, explains that the final is the note by which we understand the melody as a whole – i.e. as perfected. And the author of the Dialogus (the pseudo Odo of Cluny) states that "mode" is "a rule allowing to judge the melody as a whole by its final" (what has been misunderstood, from the middle ages until now, as meaning that mode allows to judge "any melody").

My claim is that according to what seems to have been a recurrent doctrine in the 10th and 11th centuries (and possibly later), each of the four notes in each tetrachord has a "mode" (called modus vocum by Guido of Arezzo). "Mode", in other words, is first of all a quality of the four degrees of the tetrachord (any tetrachord); and the melodies ending (attaining perfection) on any of these degrees acquire the quality (the mode) of their final. I claim also that this has been misunderstood in recent times (e.g. by Powers in the NG); it also was misunderstood by Glarean.

[The question whether A and C are unfit to serve as finals can and must be asked from an etic point of view, of course, and there remains a lot to discuss here; but from an emic, medieval point of view, they are not.]


 <mailto:nicolas.meeus at paris-sorbonne.fr> nicolas.meeus at paris-sorbonne.fr

Eytan Agmon a écrit : 

Dear Collective Wisdom,


Hucbald’s classic definition of the octenary modal system (Babb’s translation, pp. 38-39) begins with the clause “passing over the first three notes,…” meaning A, B, and C. One could be somewhat audacious and argue that it took music theory some six-and-a-half centuries to discover that this “passing over,” except in the case of B, is totally arbitrary. Indeed, Hucbald’s important notion of “a bond of similarity” (socialitas) that holds between the final and the note a perfect fifth above (or perfect fourth below), is suggestive of why B, but not A or C, may be “passed over” as finals.


My question, therefore, is this. In the centuries between Hucbald and Glarean, was the question ever posed, and if so, was an answer provided, as to why A and C are a priori unfit to serve as finals, relative to the “white-note” system (cantus durus)? It is understood, of course, that “the Carolingian clergy regulated the relationship in the Franco-Roman Gregorian chant by using the borrowed system of the oktoechos” (Powers, “Mode,” NG, p. 382).    


Eytan Agmon

Dept. of Music

Bar-Ilan University


Israel, 52900




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