<p class="MsoNormal">Hello Eytan, </p><p class="MsoNormal"></p>
<p class="MsoNormal">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 <i>socialitas</i><span style="font-style:normal"> is the property a final has of possessing
perfect fifth above it, but </span><i>quinta semper loca his singulis quatuor
superiora, quadam sibi </i><span style="font-style:normal"><span style="mso-spacerun: yes"> </span></span><i>conexionis unione iunguntur</i><span style="font-style:normal"> 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 </span><i>socialitas</i><span style="font-style:normal"> is a precursor of Guido’s </span><i>affinitas</i><span style="font-style:normal">, 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 </span><i>affinitas</i><span style="font-style:normal">. (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 </span><i>final</i><span style="font-style:normal"> and perfect fifth above are surrounded by different
intervallic neighbors. This may indeed be </span><i>a posteriori</i><span style="font-style:normal"> reasoning, and as Nicolas suggests, Hucbald passes
over A B C because he needs them below the finals for the plagal modes.</span></p><p class="MsoNormal"></p>
<p class="MsoNormal">David Clampitt</p>
<p class="MsoNormal">School of Music</p><p class="MsoNormal">The Ohio State University </p><p class="MsoNormal"></p>
<span style="font-size:12.0pt;font-family:Times;mso-ansi-language:EN-US"><<a href="mailto:david.clampitt51@gmail.com">david.clampitt51@gmail.com</a>></span>
<br><br><div class="gmail_quote">On Wed, Apr 15, 2009 at 10:06 AM, Eytan Agmon <span dir="ltr"><<a href="mailto:agmonz@012.net.il">agmonz@012.net.il</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div lang="EN-US" link="blue" vlink="purple">
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<p><font size="3" face="Arial"><span style="font-size:12.0pt;font-family:Arial">Dear Collective Wisdom,</span></font></p>
<p><font size="3" face="Arial"><span style="font-size:12.0pt;font-family:Arial"> </span></font></p>
<p><font size="3" face="Arial"><span style="font-size:12.0pt;font-family:Arial">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” (<i><span style="font-style:italic">socialitas</span></i>)
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.</span></font></p>
<p><font size="3" face="Arial"><span style="font-size:12.0pt;font-family:Arial"> </span></font></p>
<p><font size="3" face="Arial"><span style="font-size:12.0pt;font-family:Arial">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 <i><span style="font-style:italic">a priori</span></i>
unfit to serve as finals, relative to the “white-note” system (<i><span style="font-style:italic">cantus durus</span></i>)? 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 <i><span style="font-style:italic">oktoechos</span></i>” (Powers, “Mode,” <i><span style="font-style:italic">NG</span></i>, p. 382). </span></font></p>
<p><font size="3" face="Arial"><span style="font-size:12.0pt;font-family:Arial"> </span></font></p>
<p><font size="3" face="Times New Roman"><span style="font-size:12.0pt">Eytan Agmon</span></font></p>
<p><font size="3" face="Times New Roman"><span style="font-size:12.0pt">Dept. of Music</span></font></p>
<p><font size="3" face="Times New Roman"><span style="font-size:12.0pt">Bar-Ilan</span></font> University</p>
<p><font size="3" face="Times New Roman"><span style="font-size:12.0pt">Ramat-Gan</span></font></p>
<p><font size="3" face="Times New Roman"><span style="font-size:12.0pt">Israel</span></font>, 52900</p>
<p><font size="3" face="Times New Roman"><span style="font-size:12.0pt"> </span></font></p>
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