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<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'>Nicolas,</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'>Thanks for your thoughtful message. I look forward to
reading your paper (hopefully my French is up to it!). In the meantime, here is
a comment and a question.</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'>Hucbald most certainly does <i><span
style='font-style:italic'>not</span></i> say A, B, and C <i><span
style='font-style:italic'>can</span></i> serve as finals. Even though a melody
may end on the upper fifth, there is a clear distinction between the upper
fifth and the final. On the other hand, Hucbald refers to “the four finals” D,
E, F, and G so many times, that the exclusion of A, B, and C (for whatever reason),
can hardly be missed.</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'>In terms of your “emic” theory, why does Hucbald
choose D-G as finals, rather than (say) E to a? The lower fourth that he
supposedly needs will exist, and he will even be using a true tetrachord of the
Greater Perfect System, rather than an arbitrary one.</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'>Glarean, by the way, rejects a B-mode, due to the
diminished fifth above the final.</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'>Yours,</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'>Eytan</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=black
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;color:windowtext'>-----Original
Message-----<br>
<b><span style='font-weight:bold'>From:</span></b> </span></font><font size=2
color=black face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;
color:windowtext'>Nicolas Mee?s</span></font><font size=2 color=black
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;color:windowtext'>
[mailto:nicolas.meeus@paris-sorbonne.fr] <br>
<b><span style='font-weight:bold'>Sent:</span></b> </span></font><font size=2 color=black face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;
color:windowtext'>Friday, April 17, 2009</span></font><font size=2
color=black face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;
color:windowtext'> </span></font><font size=2 color=black face=Tahoma><span
style='font-size:10.0pt;font-family:Tahoma;color:windowtext'>11:27 AM</span></font><font
size=2 color=black face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;
color:windowtext'><br>
<b><span style='font-weight:bold'>To:</span></b> </span></font><font size=2
color=black face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;
color:windowtext'>Eytan Agmon</span></font><font size=2 color=black
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;color:windowtext'><br>
<b><span style='font-weight:bold'>Cc:</span></b> </span></font><font size=2
color=black face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;
color:windowtext'>smt-talk@societymusictheory.org</span></font><font size=2
color=black face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;
color:windowtext'><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 color=black
face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3 color=black
face=Georgia><span style='font-size:12.0pt;font-family:Georgia'>Eytan,<br>
<br>
I wrote years ago a paper that touches upon this question. The publication of
it has repeatedly been promised for "next month", but next month does
not seem to come... In order to make it available for the present discussion, I
deposited it at the URL <a
href="http://www.plm.paris-sorbonne.fr/Modi_vocum.pdf">http://www.plm.paris-sorbonne.fr/Modi_vocum.pdf</a>,
where it can be downloaded. (It is in French.)<br>
<br>
I do not have Babb's translation, but I feel that "passing over the first
three notes" somehow overstresses what Hucbald writes. The latin text
reads: <i><span style='font-style:italic'>Quatuor a primis tribus...</span></i>,
which means "the four [notes] after the first three"; Hucbald
continues saying that these four notes "are adapted to the perfection of
the modes in such a way that each of these four notes rules the pair of modes
subjected to it, both the principal, called authentic, and the lateral, called
plagal" (<i><span style='font-style:italic'>Quatuor a primis tribus </span></i>[...]
<i><span style='font-style:italic'>quatuor modis vel tropis </span></i>[<i><span
style='font-style:italic'>...</span></i>]<i><span style='font-style:italic'>
perficiendis aptantur, ita ut singulae earum quatuor chordarum geminos sibi
tropos regant subiectos, principalem, qui autentus, et lateralem, qui plagius
appellatur</span></i>). The reason why he passes the first three notes merely
is that he needs them <u>below</u> the finals for the plagal modes. But he does
not say that A, B or C cannot serve as finals, and nobody I can think of ever
said so in the centuries between Hucbald and Glarean. (Even B seems a possible
final!)<br>
<br>
The important difference between the medieval conception and ours (or
Glarean's) is that we view the system, the diatonic scale, as a concatenation
of sets of seven pitch classes, while the middle ages (and many other musical
cultures) saw it as a complex concatenation of four classes only, forming
alternating conjunct and disjunct tetrachords. I am convinced that it is
because the system is formed of tetrachords that there are only four (pairs of)
modes – in very much the same way as we (or Glarean) would expect seven modes.<br>
<br>
If I follow you correctly, you seem to understand <i><span style='font-style:
italic'>socialitas</span></i> as indicating that a final must have a perfect
fifth above (and that that excludes B as a possible final). This is not what
Hucbald says: he writes that any note a fifth above D E F G can also serve as
final: "It should not surprise that, neglecting the synemmenon tetrachord,
the degrees a fifth above these said four [notes] link to them in a bond of
connection such that one finds many melodies ending on these so to say regularly,
without any contradiction of reason or sense, and unfolding in the same mode or
trope" (<i><span style='font-style:italic'>Illud nihil attendendum, quod
synemmenon tetrachordo summoto, quinta semper loca his quatuor superiora quadam
sibi connexionis unione iunguntur, adeo, ut pleraque etiam in eis quasi
regulariter mela inveniantur desinere, nec rationi ob hoc vel sensui quid
contraire, et sub eodem modo vel tropo recte decurrere.</span></i>) It
goes without saying that if the synemmenon tetrachord is taken into account,
finals can also be found a fourth above D E F G, etc.<br>
<br>
As I explain in my paper refered to above, Hucbald provides the earliest
mention not only of the <i><span style='font-style:italic'>socialitas</span></i>,
but also of the concept of final itself. And what he means by "the
perfection of the modes", or by "ruling" the modes as
"subjects", etc., is far from simple. "Perfection" is a
heavily loaded term in these times. Guido, a century later, explains that the
final is the note by which we understand the melody as a whole – i.e. as
perfected. And the author of the <i><span style='font-style:italic'>Dialogus</span></i>
(the pseudo Odo of Cluny) states that "mode" is "a rule allowing
to judge the melody as a whole by its final" (what has been misunderstood,
from the middle ages until now, as meaning that mode allows to judge "any
melody").<br>
<br>
My claim is that according to what seems to have been a recurrent doctrine in
the 10th and 11th centuries (and possibly later), each of the four notes in
each tetrachord has a "mode" (called <i><span style='font-style:italic'>modus
vocum</span></i> by Guido of Arezzo). "Mode", in other words, is
first of all a quality of the four degrees of the tetrachord (any tetrachord);
and the melodies ending (attaining perfection) on any of these degrees acquire
the quality (the mode) of their final. I claim also that this has been
misunderstood in recent times (e.g. by Powers in the NG); it also was
misunderstood by Glarean.<br>
<br>
[The question whether A and C are unfit to serve as finals can and must be
asked from an etic point of view, of course, and there remains a lot to discuss
here; but from an emic, medieval point of view, they are not.]<br>
<br>
</span></font><font face=Georgia><span lang=FR style='font-family:Georgia'>Yours,<br>
<br>
Nicolas<br>
</span></font><font face=Georgia><span style='font-family:Georgia'><a
href="mailto:nicolas.meeus@paris-sorbonne.fr"><span lang=FR>nicolas.meeus@paris-sorbonne.fr</span></a></span></font><font
face=Georgia><span lang=FR style='font-family:Georgia'><br>
<br>
<br>
<br>
</span></font><font size=4><span lang=FR style='font-size:13.5pt'><br>
</span></font><font size=4><span lang=FR style='font-size:13.5pt'>Eytan Agmon</span></font><font
size=4><span lang=FR style='font-size:13.5pt'> a écrit :</span></font><span
lang=FR> </span></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3 color=black
face=Arial><span style='font-size:12.0pt;font-family:Arial'>Dear Collective
Wisdom,</span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3 color=black
face=Arial><span style='font-size:12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3 color=black
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 style='margin-left:36.0pt'><font size=3 color=black
face=Arial><span style='font-size:12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3 color=black
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 style='margin-left:36.0pt'><font size=3 color=black
face=Arial><span style='font-size:12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoAutoSig style='margin-left:36.0pt'><font size=3 color=black
face="Times New Roman"><span style='font-size:12.0pt'>Eytan Agmon</span></font></p>
<p class=MsoAutoSig style='margin-left:36.0pt'><font size=3 color=black
face="Times New Roman"><span style='font-size:12.0pt'>Dept. of Music</span></font></p>
<p class=MsoAutoSig style='margin-left:36.0pt'><font size=3 color=black
face="Times New Roman"><span style='font-size:12.0pt'>Bar-Ilan</span></font> University</p>
<p class=MsoAutoSig style='margin-left:36.0pt'><font size=3 color=black
face="Times New Roman"><span style='font-size:12.0pt'>Ramat-Gan</span></font></p>
<p class=MsoAutoSig style='margin-left:36.0pt'><font size=3 color=black
face="Times New Roman"><span style='font-size:12.0pt'>Israel</span></font>,
52900</p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3 color=black
face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p>
<pre style='margin-left:36.0pt' wrap=""><font size=2 color=black
face="Courier New"><span style='font-size:10.0pt'> </span></font></pre><pre
style='margin-left:36.0pt;text-align:center'><font size=2 color=black
face="Courier New"><span style='font-size:10.0pt'> </span></font></pre><pre
style='margin-left:36.0pt;text-align:center'><font size=2 color=black
face="Courier New"><span style='font-size:10.0pt'> </span></font></pre><pre
style='margin-left:36.0pt;text-align:center'><font size=2 color=black
face="Courier New"><span style='font-size:10.0pt'>
<hr size=4 width="90%" align=center>
</span></font></pre><pre style='margin-left:36.0pt;text-align:center'><font
size=2 color=black face="Courier New"><span style='font-size:10.0pt'> </span></font></pre><pre
style='margin-left:36.0pt;text-align:center'><font size=2 color=black
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style='margin-left:36.0pt'><font size=2 color=black face="Courier New"><span
style='font-size:10.0pt'> </span></font></pre><pre style='margin-left:
36.0pt'><font size=2 color=black face="Courier New"><span style='font-size:
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