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<font size="-1"><font face="Georgia">Richard,<br>
<br>
You are perfectly right, of course. In my desire to be pedagogical, I
tend to neglect exceptions, but they do exist – especially in those
cases where B (or rather b) really is mobile.<br>
<br>
As to what you write about the final, yes. My own claim that there are
four (pairs of) modes because the system is tetrachordal could be
faulted on the basis that the number of eight modes predates the
tetrachordal description in Christian theory. And the fact that the
modes already were numbered in tonaries, etc., must have a reason. So
yes, you are right on this point as well and these ideas were there
before Hucbald. Theory is not entirely an artificial construction. The
tetrachordal principle, for instance, probably must be considered a
feature of diatonism; it is there, whether or not it is recognized in
theory.<br>
<br>
You are right also – to some extent – about the synemmenon producing
two diatonic scales. This is a question of how we define diatonism. The
idea of two intermingled scales, one durum/naturale, the other
naturale/molle, does not really get momentum before the 16th century, I
think (where it materialize in the durum and molle systems, the "chant
par bécarre" and the "chant par bémol", etc.). The situation is less
clear in the middle ages, as you certainly know, among others because
the synemmenon tetrachord is not repeated in other octaves.<br>
<br>
Thanks for your remarks,<br>
Yours,<br>
<br>
Nicolas<br>
</font></font><br>
<br>
Richard Porterfield a écrit :
<blockquote cite="mid:BLU113-W4958DADC94FD9B37CC05D4D5780@phx.gbl"
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Dear Nicolas Meeus, <br>
Thank you for your valuable paper! I will have more to say about it
later. Below are a few comments on your latest reply to Eyton Agmon. <br>
<br>
Richard Porterfield<br>
Instructor, Mannes College <br>
Ph.D. candidate in Music Theory, CUNY GC<br>
<a moz-do-not-send="true" href="mailto:porterfr@hotmail.com">porterfr@hotmail.com</a><br>
<br>
Date: Fri, 17 Apr 2009 22:39:12 +0200<br>
From: <a class="moz-txt-link-abbreviated" href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a><br>
To: <a class="moz-txt-link-abbreviated" href="mailto:agmonz@012.net.il">agmonz@012.net.il</a><br>
CC: <a class="moz-txt-link-abbreviated" href="mailto:smt-talk@societymusictheory.org">smt-talk@societymusictheory.org</a><br>
Subject: Re: [Smt-talk] rationalizing the octenary system<br>
<br>
<font size="-1"><font face="Georgia"><big>... Hucbald's readers were
familiar with the chant repertory, but they had no idea of the diatonic
system, nor of ways of comparing the melodies between themselves from
an intervallic point of view; they did not even have note names, nor
any clear notion of the modal final. Hucbald's purpose, therefore,
cannot have been to discuss which degrees of the system could serve as
finals, as none of these notions was available.</big></font></font><br>
<font face="Arial" size="4"><big><font style="font-size: 16pt;"
size="4">It seems possible that the notion of the modal final was in
circulation already (Aurelian is uncomfortable with chants that seem to
begin in one mode and end in another: with this we have at least
the final <em>phrase</em> being of a mode, if not the final note).
Even if in oral pedagogy and/or a treatise now lost these finals had
already been recognized as discrete tones occupying successively
higher modal degrees -- and their names protus, deuterus, tritus,
tetrardus being in tonal order cannot have been accidental -- it would
then have been Hucbald's theoretical contribution to locate those
finals in a tone-system for western chant adapted from ancient Greek
instrumental models, itself no small feat.</font> </big></font><br>
<font size="-1"><font face="Georgia"><big>What he tried to show is
that, if the melodies were considered in terms of their inner intervals
(to the description of which he devotes a lot of space), it is possible
to align them all along one single general scale (the diatonic
system) ...</big></font></font><br>
<big><font style="font-size: 16pt;" face="Arial" size="4">Two scales,
that is, including that of the <em>synemmenon</em> allowing for soft
b. </font></big><br>
<font size="-1"><font face="Georgia"><big><br>
A and C were not rejected as possible finals, they merely were not
deemed necessary in Hucbald's highly pedagogical description because
modes on D and F respectively could be written with a B flat. As a
matter of fact, melodies ending on F almost always have a B flat, so
that strictly speaking it are the modes on F that do not exist, not
those on C. <br>
<font face="Arial" size="4">Many F-mode melodies have both hard and
soft b (Gradual <em>Viderunt</em>, e.g.); many melodies in protus,
deuterus, and tetrardus do as well. </font><br>
It would theoretically have been possible to write melodies on E with B
flat (corresponding to modes on B), but these merely do not exist. <br>
<font style="font-size: 16pt;" face="Arial" size="4">They certainly
do exist. <em>Credo </em>1, for example (<em>LU </em>64-66). </font><br>
As to melodies on G with B flat, they can as easily be written on D
without.<br>
<font face="Arial" size="5"><font style="font-size: 16pt;" size="4">Some
alternate between a ditone and semiditone (M3 and m3) above the final,
such as the antiphon <em>Missus est gabriel</em> (which Hucbald cites,
by the way); unless this chant is notated on G it goes outside the
notational system.</font> </font><br>
</big></font></font><font color="black" face="Courier New" size="2"><span
style="font-size: 10pt;"> </span></font><br>
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