[Smt-talk] rationalizing the octenary system

[David Clampitt]

Hello Eytan,

Agreed. B is out of the running on these grounds. And I think Hucbald
is clear that B is not to be assigned at the end of the chant, but it
can be to the beginning--perhaps this is the sense in which Nicolas
understands that no note as such is excluded as final. If you read on
p. 202 of Chartier's edition and on p. 39 of Babb and Palisca, he
writes (after Babb): "These [beginnings and endings] are:
proslambanomenos [A] to the lichanos hypaton [D]; hypate hypaton [B]
to the hypate meson [E], but this is rare; parhypate hypaton [C] to
the parhypate meson [F]; ..." So A, B, and C are finals, albeit
alternative ones. But in the conception I set forth, which follows the
later Hermannus's rule: "Take any tetrachord you wish, add a tone at
both ends, you then have the limits of the tonal patterns which form
the basis for the modes [sedes troporum]." Ellinwood's translation.

So, I mostly agree with your statement: "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." It is clear that B cannot be
principalis, in Hucbald's terms, because it can't form the authentic
form.

David

David Clampitt
School of Music
The Ohio State University

<david.clampitt51 at osu.edu>



On 4/17/09, Eytan Agmon <agmonz at 012.net.il> wrote:
>
>
>
>
> 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.
>
>
>
> Best,
>
> Eytan
>
>
>
>
>
>
> -----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
>
> Ramat-Gan
>
> Israel, 52900
>
>
>
>
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