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<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>Hello All,</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>I guess that Nicolas, David, and I will have
to agree to disagree on our readings of Hucbald. I read him as saying “look,
the note a fifth above the final is so closely related to the final, that one
can even end a melody on that note <i><span style='font-style:italic'>as if it
were</span></i> the final!” Quoting Hucbald in David Cohen’s translation from
his CHWMT article (p. 322): “many melodies are found to end in them [the notes
a fifth above the final, EA] as if by rule… and to run their course perfectly
according to the same mode or trope [as that of the true final, DC].” This statement
should be read in the context of an earlier one (also quoted in Cohen’s
translation): “Thus every melody… is necessarily led back to one of these four
[notes]. Therefore they are called “finals,” because anything that is sung
finds its ending (<i><span style='font-style:italic'>finem</span></i>) in [one
of] them.” I don’t believe Hucbald uses any <i><span style='font-style:italic'>finem</span></i>-related
word in describing upper-fifth endings.</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>On the other hand, as David observes, the
three of us do seem to be getting closer to the spirit of my original query.
David essentially acknowledges that the octenary system can only be
rationalized as a subset of the dodecachordal, and Nicolas</span></font> <font
color=black face=Arial><span style='font-family:Arial;color:black'>states that
“Glarean cannot be considered the "inventor" of the modes on A or C:
they existed from the start.”</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>Perhaps, then, we can close this very
fruitful discussion with two points for further thought. First, if the modes on
A or C indeed existed from the start, then the recognition of six finals by
Glarean is probably the most extreme case in the history of music theory of
theory lagging behind practice. Second (and here I guess that Nicolas and
others would strongly disagree), if the modes on A or C indeed existed from the
start, then are we really doing service to medieval <i><span style='font-style:
italic'>music</span></i> and musicians by being (trying to be!) “emic” rather
than “etic”? I am stressing “music” rather than “culture” in some broad sense.
Of course the doctrine of the eight modes is part of “medieval culture” in some
broad sense. Indeed, it was probably very difficult, from a medieval point of
view, to openly contradict a doctrine so closely associated with the authority
of the Church. But rather than succumbing to the intellectual pressures of
medieval culture ourselves, shouldn’t we be voicing what Hucbald, Guido, and
other great medieval musicians, seem to have understood perfectly well, but
were prevented from stating explicitly?</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>Eytan</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=2 face=Tahoma><span
style='font-size:10.0pt;font-family:Tahoma'>-----Original Message-----<br>
<b><span style='font-weight:bold'>From:</span></b> </span></font><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>David Clampitt</span></font><font
size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>
[mailto:david.clampitt51@gmail.com] <br>
<b><span style='font-weight:bold'>Sent:</span></b> </span></font><font size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>Saturday, April
18, 2009</span></font><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma'> </span></font><font size=2 face=Tahoma><span
style='font-size:10.0pt;font-family:Tahoma'>2:05 AM</span></font><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'><br>
<b><span style='font-weight:bold'>To:</span></b> Nicolas Mee<span lang=HE
dir=RTL>ש</span>s<br>
<b><span style='font-weight:bold'>Cc:</span></b> </span></font><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>Eytan Agmon</span></font><font
size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>; </span></font><font
size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>smt-talk@societymusictheory.org</span></font><font
size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'><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
face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>Hello Eytan, hello
Nicholas,</span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'> Yes, Hucbald is
clear that there are alternative finals for each tone, alternatively <i><span
style='font-style:italic'>lichanos hypaton</span></i> [D] or <i><span
style='font-style:italic'>mese </span></i>[a], <i><span style='font-style:italic'>hypate
meson </span></i>[E] or <i><span style='font-style:italic'>paramese</span></i>
[hard-b], <i><span style='font-style:italic'>parhypate meson</span></i> [F] or <i><span
style='font-style:italic'>trite diezeugmenon</span></i> [c], and <i><span
style='font-style:italic'>lichanos meson</span></i> [G] to <i><span
style='font-style:italic'>paranete diezeugmenon</span></i> [d]. </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>Then, in the passage I
cited earlier, Hucbald insists that the lower notes are suitable for placing
the beginnings, not endings, of chants:</span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>Hucbald’s text (p. 202 of
Chartier’s edition):</span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>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…</span></font></p>
<p class=MsoBodyText style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>What follows is what I
cited earlier: A is associated with D, B with E (rarely), C with F, D with G.</span></font></p>
<p class=MsoBodyText style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>The crucial phrase is
qamuis non fini sed initiis depetuentur: these [lower notes] should be assigned
not to the end but to beginnings.</span></font></p>
<p class=MsoBodyText style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>So, I think that
literally B (the lower element) cannot be a finalis, 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></font></p>
<p class=MsoBodyText style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>Nicolas, I see your
latest post has arrived before I have finished this one. I will say that yes,
the four maneriae suffice to include the higher notes in the system, a and c,
and hard-b, via socialitas, 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. </span></font><span
lang=FR>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.” </span>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:
septem discrimina vocum). This would seem to be getting closer to Eytan’s
query. </p>
<p class=MsoBodyText style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>Best,</span></font></p>
<p class=MsoBodyText style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>David Clampitt</span></font></p>
<p class=MsoBodyText style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>School</span></font> of
Music</p>
<p class=MsoBodyText style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>The </span></font>Ohio State
University</p>
<p class=MsoNormal style='margin-right:0cm;margin-bottom:12.0pt;margin-left:
36.0pt'><i><font size=3 face=Times><span style='font-size:12.0pt;font-family:
Times;font-style:italic'><<a href="mailto:david.clampitt51@gmail.com">david.clampitt51@gmail.com</a>></span></font></i>
</p>
<div>
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>2009/4/17 Nicolas Meeùs
<<a href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a>></span></font></p>
<div bgcolor="#ffffff" text="#000000">
<p class=MsoNormal style='margin-left:36.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>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><span style='font-style:italic'>MQ</span></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><span
style='font-style:italic'>plera</span></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><span
style='font-style:italic'>affinitas</span></i> (or <i><span style='font-style:
italic'>socialitas</span></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><span style='font-style:italic'>affinitas</span></i> is true. In
solmization terminology, the four modal finals are <i><span style='font-style:
italic'>re</span></i>, <i><span style='font-style:italic'>mi</span></i>, <i><span
style='font-style:italic'>fa</span></i> and <i><span style='font-style:italic'>sol</span></i>.
Until late in the middle ages, some theorists state that the melodies of the
protus end on <i><span style='font-style:italic'>re</span></i> – that is, any <i><span
style='font-style:italic'>re</span></i>, be it D, G or A –, those of the
deuterus on (any) <i><span style='font-style:italic'>mi</span></i>, of the tritus
on <i><span style='font-style:italic'>fa</span></i>, of the tetrardus on <i><span
style='font-style:italic'>sol</span></i>.<br>
I wrote a paper on Jacques of Liège and the practice of
partial transposition (<i><span style='font-style:italic'>Revue belge de
musicologie</span></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><span style='font-style:italic'>re</span></i>, on A<i><span
style='font-style:italic'>re</span></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><span
style='font-style:italic'>affinals </span></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><span style='font-style:
italic'>affinals</span></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>
</span></font><font size=2><span style='font-size:10.0pt'><br>
</span></font> </p>
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