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<big><font size="-1"><big><font face="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 class="moz-txt-link-freetext" 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>Quatuor a primis tribus...</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>Quatuor
a primis tribus </i>[...] <i>quatuor modis vel tropis </i>[<i>...</i>]<i>
perficiendis aptantur, ita ut singulae earum quatuor chordarum geminos
sibi tropos regant subiectos, principalem, qui autentus, et lateralem,
qui plagius appellatur</i>). The reason why he passes the first </font></big></font></big><big><font
size="-1"><big><font face="Georgia">three </font></big></font></big><big><font
size="-1"><big><font face="Georgia">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>socialitas</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>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.</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>socialitas</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>Dialogus</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>modus vocum</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>
Yours,<br>
<br>
Nicolas<br>
<a class="moz-txt-link-abbreviated" href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a><br>
<br>
<br>
<br>
</font></big></font><br>
Eytan Agmon a écrit :</big>
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<p class="MsoNormal"><font face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;">Dear Collective Wisdom,</span></font></p>
<p class="MsoNormal"><font face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<p class="MsoNormal"><font face="Arial" size="3"><span
style="font-size: 12pt; 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 face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<p class="MsoNormal"><font face="Arial" size="3"><span
style="font-size: 12pt; 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 face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<p class="MsoAutoSig"><font face="Times New Roman" size="3"><span
style="font-size: 12pt;">Eytan Agmon</span></font></p>
<p class="MsoAutoSig"><font face="Times New Roman" size="3"><span
style="font-size: 12pt;">Dept. of Music</span></font></p>
<p class="MsoAutoSig"><font face="Times New Roman" size="3"><span
style="font-size: 12pt;">Bar-Ilan</span></font> University</p>
<p class="MsoAutoSig"><font face="Times New Roman" size="3"><span
style="font-size: 12pt;">Ramat-Gan</span></font></p>
<p class="MsoAutoSig"><font face="Times New Roman" size="3"><span
style="font-size: 12pt;">Israel</span></font>, 52900</p>
<p class="MsoNormal"><font face="Times New Roman" size="3"><span
style="font-size: 12pt;"> </span></font></p>
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