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<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>
<br>
<br>
<br>
<br>
</font></font>Eytan Agmon a écrit :
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<p class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;">Nicolas,</span></font></p>
<p class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<p class="MsoNormal"><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 class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<p class="MsoNormal"><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 class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<p class="MsoNormal"><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 class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<p class="MsoNormal"><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 class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<p class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;">Yours,</span></font></p>
<p class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;">Eytan</span></font></p>
<p class="MsoNormal"><font color="black" face="Arial" size="3"><span
style="font-size: 12pt; font-family: Arial;"> </span></font></p>
<pre style="margin-left: 36pt;"><font color="black" face="Courier New"
size="2"><span style="font-size: 10pt;"> </span></font></pre>
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