[Smt-talk] rationalizing the octenary system

David Clampitt david.clampitt51 at gmail.com
Fri Apr 17 06:54:12 PDT 2009

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

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
> Ramat-Gan
> Israel, 52900
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