[Smt-talk] rationalizing the octenary system

Eytan Agmon agmonz at 012.net.il
Fri Apr 17 07:37:52 PDT 2009

Hello David,


If the existence of a perfect fifth above the upper and lower neighbors of the final is considered an important property, then the existence of a perfect fifth above the final itself is all the more so. It follows that if Guido’s affinitas indeed “requires a similar environment above and below the alternative finals, at a minimum the same intervallic neighbors” (emphasis added), then we have a modal hierarchy where modes on D-G are a subset of modes on C-A. Modes on C-A are conceptually prior, in exactly the same way that the final is conceptually prior to its neighbors.






-----Original Message-----
From: David Clampitt [mailto:david.clampitt51 at gmail.com] 
Sent: Friday, April 17, 2009 4:54 PM
To: Eytan Agmon
Cc: smt-talk at societymusictheory.org
Subject: Re: [Smt-talk] rationalizing the octenary system


Hello Eytan, 

The response by Nicolas seems mostly correct to me, with its emphasis on the tetrachordal conception. I look forward to reading his paper. As he points out, your question seems to assume that socialitas is the property a final has of possessing perfect fifth above it, but quinta semper loca his singulis quatuor superiora, quadam sibi  conexionis unione iunguntur and what follows says that this “bond of connection” as Nicolas renders it, or even more, “bond of similarity” as you have it, probably following Babb, is a stronger link, allowing melodies to “unfold in the same mode or trope” at either location. So socialitas is a precursor of Guido’s affinitas, which requires a similar environment above and below the alternative finals, at a minimum the same intervallic neighbors. This would justify passing over A and C, which do not enjoy affinitas. (I'm simplifying here, since for Guido, neither did G, but we could also follow Hermannus, who is more consistent.) To put it positively from a more modern point of view, A and C do enjoy what I’ve called double neighbor polarity, where final and perfect fifth above are surrounded by different intervallic neighbors. This may indeed be a posteriori reasoning, and as Nicolas suggests, Hucbald passes over A B C because he needs them below the finals for the plagal modes.

David Clampitt

School of Music

The Ohio State University 

<david.clampitt51 at gmail.com>  

On Wed, Apr 15, 2009 at 10:06 AM, Eytan Agmon <agmonz at 012.net.il> wrote:

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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