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<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>Hello David,</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>If the existence of a perfect fifth above
the upper and lower <i><span style='font-style:italic'>neighbors</span></i> of
the final is considered an important property, then the existence of a perfect
fifth <i><span style='font-style:italic'>above the final itself</span></i> is
all the more so. It follows that if Guido’s <i><span style='font-style:italic'>affinitas</span></i>
indeed “requires a similar environment above and below the alternative finals, <i><span
style='font-style:italic'>at a minimum the same intervallic neighbors</span></i>”
(emphasis added), then we have a modal <i><span style='font-style:italic'>hierarchy</span></i>
where modes on D-G are a <i><span style='font-style:italic'>subset</span></i>
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.</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>Best,</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>Eytan</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=2 face=Tahoma><span
style='font-size:10.0pt;font-family:Tahoma'>-----Original Message-----<br>
<b><span style='font-weight:bold'>From:</span></b> David Clampitt
[mailto:david.clampitt51@gmail.com] <br>
<b><span style='font-weight:bold'>Sent:</span></b> </span></font><font size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>Friday, April
17, 2009</span></font><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma'> </span></font><font size=2 face=Tahoma><span
style='font-size:10.0pt;font-family:Tahoma'>4:54 PM</span></font><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'><br>
<b><span style='font-weight:bold'>To:</span></b> Eytan Agmon<br>
<b><span style='font-weight:bold'>Cc:</span></b> smt-talk@societymusictheory.org<br>
<b><span style='font-weight:bold'>Subject:</span></b> Re: [Smt-talk]
rationalizing the octenary system</span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>Hello Eytan, </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>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><span style='font-style:italic'>socialitas</span></i> is the
property a final has of possessing perfect fifth above it, but <i><span
style='font-style:italic'>quinta semper loca his singulis quatuor superiora,
quadam sibi </span></i> <i><span style='font-style:italic'>conexionis unione
iunguntur</span></i> 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 <i><span style='font-style:italic'>socialitas</span></i>
is a precursor of Guido’s <i><span style='font-style:italic'>affinitas</span></i>,
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 <i><span style='font-style:italic'>affinitas</span></i>.
(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 <i><span style='font-style:italic'>final</span></i> and perfect fifth
above are surrounded by different intervallic neighbors. This may indeed be <i><span
style='font-style:italic'>a posteriori</span></i> reasoning, and as Nicolas
suggests, Hucbald passes over A B C because he needs them below the finals for
the plagal modes.</span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>David Clampitt</span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>School</span></font> of
Music</p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>The </span></font>Ohio State
University </p>
<p class=MsoNormal style='margin-right:0cm;margin-bottom:12.0pt;margin-left:
36.0pt'><font size=3 face=Times><span style='font-size:12.0pt;font-family:Times'><<a
href="mailto:david.clampitt51@gmail.com">david.clampitt51@gmail.com</a>></span></font>
</p>
<div>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>On </span></font>Wed, Apr 15, 2009 at 10:06 AM, Eytan Agmon <<a href="mailto:agmonz@012.net.il">agmonz@012.net.il</a>>
wrote:</p>
<div link=blue vlink=purple>
<div>
<p style='margin-left:36.0pt'><font size=3 face=Arial><span style='font-size:
12.0pt;font-family:Arial'>Dear Collective Wisdom,</span></font></p>
<p style='margin-left:36.0pt'><font size=3 face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p style='margin-left:36.0pt'><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 style='margin-left:36.0pt'><font size=3 face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p style='margin-left:36.0pt'><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 style='margin-left:36.0pt'><font size=3 face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p style='margin-left:36.0pt'><font size=3 face="Times New Roman"><span
style='font-size:12.0pt'>Eytan Agmon</span></font></p>
<p style='margin-left:36.0pt'><font size=3 face="Times New Roman"><span
style='font-size:12.0pt'>Dept. of Music</span></font></p>
<p style='margin-left:36.0pt'><font size=3 face="Times New Roman"><span
style='font-size:12.0pt'>Bar-Ilan</span></font> University</p>
<p style='margin-left:36.0pt'><font size=3 face="Times New Roman"><span
style='font-size:12.0pt'>Ramat-Gan</span></font></p>
<p style='margin-left:36.0pt'><font size=3 face="Times New Roman"><span
style='font-size:12.0pt'>Israel</span></font>, 52900</p>
<p style='margin-left:36.0pt'><font size=3 face="Times New Roman"><span
style='font-size:12.0pt'> </span></font></p>
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