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<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Dear Collective Wisdom,</span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><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 class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoNormal><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 class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'> </span></font></p>
<p class=MsoAutoSig><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Eytan Agmon</span></font></p>
<p class=MsoAutoSig><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Dept. of Music</span></font></p>
<p class=MsoAutoSig><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Bar-Ilan</span></font> University</p>
<p class=MsoAutoSig><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Ramat-Gan</span></font></p>
<p class=MsoAutoSig><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>Israel</span></font>, 52900</p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> </span></font></p>
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