<p class="MsoNormal">Hello Eytan, hello Nicholas,</p>
<p class="MsoNormal"> Yes, Hucbald is clear that there are alternative finals for
each tone, alternatively <i>lichanos hypaton</i><span style="font-style:normal">
[D] or </span><i>mese </i><span style="font-style:normal">[a], </span><i>hypate
meson </i><span style="font-style:normal">[E] or </span><i>paramese</i><span style="font-style:normal"> [hard-b], </span><i>parhypate meson</i><span style="font-style:normal"> [F] or </span><i>trite diezeugmenon</i><span style="font-style:normal"> [c], and </span><i>lichanos meson</i><span style="font-style:normal"> [G] to </span><i>paranete diezeugmenon</i><span style="font-style:normal"> [d].<span style="mso-spacerun: yes"> </span></span></p>
<p class="MsoNormal">Then, in the passage I cited earlier, Hucbald insists that
the lower notes are suitable for placing the beginnings, not endings, of
chants:</p><p class="MsoNormal"></p>
<p class="MsoNormal">Hucbald’s text (p. 202 of Chartier’s edition):</p><p class="MsoNormal"></p>
<p class="MsoNormal">Cum inferioribus quoque quartis et in quibusdam quintis,
parem quodamodo obtinent [hae quattuor finales] habitudinem, quamuis non fini
sed initiis deputentur: usque ad has enim metam inchoandi declinant. Hae sunt.
Proslambanomenos: ad lichanos hypaton…</p><p class="MsoBodyText"></p>
<p class="MsoBodyText">What follows is what I
cited earlier: A is associated with D, B with E (rarely), C with F, D with G.</p>
<p class="MsoBodyText"><span style="font-style:normal"><span style="font-style:normal">The crucial phrase is </span>qamuis
non fini sed initiis depetuentur<span style="font-style:normal">: these [lower
notes] should be assigned not to the end but to beginnings.</span></span></p>
<p class="MsoBodyText"><span style="font-style:normal">So, I think that literally
B (the lower element) cannot be a </span>finalis<span style="font-style:normal">,
but the higher hard-b, can so serve. I agree with Nicolas that our 21<sup>st</sup>-century
notions blind us to some of these distinctions, above all octave equivalence.</span></p>
<p class="MsoBodyText"><span style="font-style:normal">Nicolas, I see your latest
post has arrived before I have finished this one. I will say that yes, the four
</span>maneriae<span style="font-style:normal"> suffice to include the higher
notes in the system, a and c, and hard-b, via </span>socialitas<span style="font-style:normal">, so in medieval terms there was no need for six, agreed.
As to the meaning of the Hermannus Contractus phrase, I’ll have to digest your
article. I notice you discuss Crocker, which is where I derive my understanding
of that treatise, and that may be outmoded, so to speak. But, since Eytan asked
about post-Hucbald developments, I note that you begin with this from Guido
(which I don’t take exception to): “Puisqu’il n’y a que sept notes, car les
autres, comme nous l’avons dit, sont les mêmes, il suffit d’en expliquer sept,
qui diffère par le mode et par le qualité.” Your article goes deeply into
issues of mode and quality. But already there is more recognition of seven note
names of a diatonic system (Guido also quotes Vergil: </span>septem discrimina
vocum<span style="font-style:normal">). This would seem to be getting closer to
Eytan’s query. </span></p>
<p class="MsoBodyText"><span style="font-style:normal">Best,</span></p>
<p class="MsoBodyText"><span style="font-style:normal">David Clampitt</span></p>
<p class="MsoBodyText"><span style="font-style:normal">School of Music</span></p>
<p class="MsoBodyText"><span style="font-style:normal">The Ohio State University</span></p>
<span style="font-size:12.0pt;font-family:Times;mso-ansi-language:EN-US"><i><<a href="mailto:david.clampitt51@gmail.com">david.clampitt51@gmail.com</a>></i></span>
<br><br><div class="gmail_quote">2009/4/17 Nicolas Meeùs <span dir="ltr"><<a href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div bgcolor="#ffffff" text="#000000">
<font size="-1"><font face="Georgia"><big>Dear Eytan,<br>
<br>
I really do believe that your interpretation is not in line with what
Hucbald means. You understand that a melody may end a fifth above its
own final or, in other words, that the final is not necessarily the
last note of the melody but rather some abstract reference note. Such a
view rests, in my opinion, on presuppositions about modality/tonality,
or about the link between the melodies and the underlying diatonic
system, that cannot fit the situation in the late 9th century.<br>
<br>
My own view is largely inspired by a paper by R. Weakland, "Hucbald as
Musician and Theorist", <i>MQ</i> 42/1 (1956), to which you might
refer. <br>
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. 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) – the alignment,
as we today can realize, really is a matter of adjusting the pitches to
a single standard; but they had no notion of that.<br>
Hucbald further says that if the alignment is done correctly, one
discovers that all the melodies in the repertory can be adjusted so as
to have their final note on D, E, F or G. Why he chooses that
particular tetrachord is unclear, but may result from the fact that the
modes already were numbered and that these finals fitted their
numerical order. He immediately adds that the same melodies could also
be adjusted to end on other degrees of the underlying system: so doing,
he is trying to describe aspects of the structure of the diatonic
scale, but he is not discussing differences in the structure of the
melodies. When he states that <u>many</u> (<i>plera</i>) melodies may
end a fifth above D E F G, he does not mean that these cannot end on D
E F G, but well that they can <u>also</u> end on A B C D.<br>
The reason to think so is that this remains a constant doctrine for
centuries after Hucbald. The theory of the <i>affinitas</i> (or <i>socialitas</i>)
is a theory of the structure of the diatonic scale, which states that
notes a fifth (or a fourth) apart are surrounded by the same intervals.
Guido's hexachordal theory is a theory of the extent to which <i>affinitas</i>
is true. In solmization terminology, the four modal finals are <i>re</i>,
<i>mi</i>, <i>fa</i> and <i>sol</i>. Until late in the middle ages,
some theorists state that the melodies of the protus end on <i>re</i>
– that is, any <i>re</i>, be it D, G or A –, those of the deuterus on
(any) <i>mi</i>, of the tritus on <i>fa</i>, of the tetrardus on <i>sol</i>.<br>
I wrote a paper on Jacques of Liège and the practice of partial
transposition (<i>Revue belge de musicologie</i>, 1995), in which I
discuss Jacques's statement that, in some churches of Liège, when the
melody lingered too long in the high, singers mistakenly end it a fifth
too high: it is not that they end on the "fifth above the final" in the
way you seem to imply, but rather that they end, say, on the wrong <i>re</i>,
on A<i>re</i> instead of Dre – not realizing, in other words, that they
had shifted their pitch standard.<br>
<br>
The number of melodies notated with A or C as final was higher in the
middle ages than today: it is because the 19th-century normalization of
the chant reduced all these melodies to their theoretical final
whenever possible. The very fact that this was possible shows that the
question of the <i>affinals </i>in many cases merely is a matter of
notational convenience, not of a structural difference in the melodies.
Note also that changing from the regular finals to the <i>affinals</i>
a fifth above merely involves replacing the F-clef by the C-clef on the
same line.<br>
<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. 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. As to melodies on G with B flat, they can as easily be written
on D without.<br>
<br>
Glarean cannot be considered the "inventor" of the modes on A or C:
they existed from the start. What he did is normalize the notation,
considering that modes written with a B flat were transpositions. This,
by the way, happened not so long after another, more important
invention, that of pitch standards (Arnolt Schlick, 1511).<br>
<br>
Yours,<br>
<br>
Nicolas<br>
</big>
<br>
</font></font>Eytan Agmon a écrit :
<div class="im"><blockquote type="cite">
<div>
<p><font color="black" face="Arial" size="3"><span style="font-size:12pt;font-family:Arial">Nicolas,<span class="Apple-style-span" style="font-size: 13px; -webkit-text-stroke-width: -1; "> </span></span></font></p>
<p><font color="black" face="Arial" size="3"><span style="font-size:12pt;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><font color="black" face="Arial" size="3"><span style="font-size:12pt;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><font color="black" face="Arial" size="3"><span style="font-size:12pt;font-family:Arial"> </span></font></p>
<p><font color="black" face="Arial" size="3"><span style="font-size:12pt;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><font color="black" face="Arial" size="3"><span style="font-size:12pt;font-family:Arial"> </span></font></p>
<p><font color="black" face="Arial" size="3"><span style="font-size:12pt;font-family:Arial">Glarean, by the way,
rejects a B-mode, due to the
diminished fifth above the final.</span></font></p>
<p><font color="black" face="Arial" size="3"><span style="font-size:12pt;font-family:Arial"> </span></font></p>
<p><font color="black" face="Arial" size="3"><span style="font-size:12pt;font-family:Arial">Yours,</span></font></p>
<p><font color="black" face="Arial" size="3"><span style="font-size:12pt;font-family:Arial">Eytan</span></font></p>
</div>
</blockquote>
</div></div>
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