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<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'>Quoting Nicholas Meeùs:</span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<div>
<p class=MsoAutoSig><font size=4 face="Times New Roman"><span style='font-size:
13.5pt'>Hucbald cannot be meaning that melodies at times end a fifth above
their final, because that would imply that the "final" is not their
last note. One would have to assume that "final" somehow means
"reference note". There are notes in chant melodies that can be
considered "references" of some kind – e.g. the reciting note, tenor,
etc. But none of these could ever be a fifth below the last note; as a matter
of fact, reference notes other than the final one always are higher than the
final.</span></font></p>
<p class=MsoAutoSig><font size=3 color=black face="Times New Roman"><span
style='font-size:12.0pt;color:black'> </span></font></p>
<p class=MsoAutoSig><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>Isn’t it possible, however, that Hucbald
is referring not to the <i><span style='font-style:italic'>entire</span></i>
melody, but rather to a phrase within it? Immediately following the discussion
of upper-fifth endings (Babb, bottom of p. 39), Hucbald states that melodies in
any mode (authentic and plagal are not distinguished) may begin up to a fifth
above or below the final. Not only does Hucbald seem to refer to <i><span
style='font-style:italic'>endings</span></i> as well (in Babb’s translation: “…
The endings and beginnings are confined within these series of eight—or sometimes
nine—notes, be the mode authentic or plagal”), the fifth <i><span
style='font-style:italic'>protus</span></i> example (Babb, p. 40), the first
phrase of the antiphon <i><span style='font-style:italic'>Ecce nomen Domini</span></i>
(see <i><span style='font-style:italic'>LU</span></i>, p. 294), begins on the
final D but ends on A (D-D-C-F-G-F-G-A-A; the antiphon as a whole end, of
course, on D).</span></font></p>
<p class=MsoAutoSig><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'> </span></font></p>
<p class=MsoAutoSig><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'>I think it is important to keep Hucbald <i><span
style='font-style:italic'>first</span></i> statement on finals always in mind:</span></font><font
color=black face=Arial><span style='font-family:Arial;color:black'> “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” (David Cohen’s
translation). Surely he cannot state so emphatically that D-G are finals, and
then immediately contradict himself saying that a-d are also finals. </span></font></p>
<p class=MsoAutoSig><font size=3 color=black face="Times New Roman"><span
style='font-size:12.0pt;color:black'> </span></font></p>
<p class=MsoAutoSig><font size=3 color=black face="Times New Roman"><span
style='font-size:12.0pt;color:black'>Eytan Agmon</span></font></p>
<p class=MsoAutoSig><font size=3 color=black face="Times New Roman"><span
style='font-size:12.0pt;color:black'>Dept. of Music</span></font></p>
<p class=MsoAutoSig><font size=3 color=black face="Times New Roman"><span
style='font-size:12.0pt;color:black'>Bar-Ilan University</span></font></p>
<p class=MsoAutoSig><font size=3 color=black face="Times New Roman"><span
style='font-size:12.0pt;color:black'>Ramat-Gan</span></font></p>
<p class=MsoAutoSig><font size=3 color=black face="Times New Roman"><span
style='font-size:12.0pt;color:black'>Israel, 52900</span></font></p>
</div>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=2 color=black
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma;color:windowtext'>-----Original
Message-----<br>
<b><span style='font-weight:bold'>From:</span></b> smt-talk-bounces@societymusictheory.org
[mailto:smt-talk-bounces@societymusictheory.org] <b><span style='font-weight:
bold'>On Behalf Of </span></b>Nicolas Mee?s<br>
<b><span style='font-weight:bold'>Sent:</span></b> Monday, April 20, 2009 12:30
PM<br>
<b><span style='font-weight:bold'>To:</span></b> Richard Porterfield<br>
<b><span style='font-weight:bold'>Cc:</span></b> smt-talk smt<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 color=black
face="Times New Roman"><span style='font-size:12.0pt'> </span></font></p>
<p class=MsoNormal style='margin-left:36.0pt'><font size=4 color=black
face="Times New Roman"><span style='font-size:13.5pt'>Let me add two short
answers to Eytan's questions:<br>
<br>
<br>
Hucbald also cannot have meant that some melodies were sung
a fifth higher <u>in pitch</u>, because melodies were sung at any convenient
pitch anyway. As the pseudo Odo, the author of the <i><span style='font-style:
italic'>Dialogus</span></i>, clearly states, the modes do not differ from each
other by their pitch.<br>
For Hucbald, the diatonic scale is a mobile yardstick for
the measure of the melodies. What he says is that the yardstick can always be
adapted to the melodies so that the last note falls in the tetrachord D E F G,
and that it usually also is possible to shift it so that the last note is in
the tetrachord A B C D. He is not trying to explain properties of the melodies
here, but to stress the structure of the diatonic system – because it is the
system that needs justification, not the melodies.<br>
<br>
2) As Richard already explained, the modes cannot be reduced to scales. They
must also be considered sets of melodic formulas. One (oversimplified) way to
look at these is to consider the underlying pentatonism which, in the usual
notation of Gregorian chant (resulting from Hucbald's choice of D E F G as
finals), is the scale F G A C D. <br>
(This convention also left a trace in the modern notation of
Arabic music, with the equation Rast = C. As a result, the mobile degrees of
Arabic music are mainly the two notes missing in this pentatonic scale, B and
E, which can be flattened or half-flattened.)<br>
The underlying pentatonism of the D-mode is D F G A C, with
the possibility of either B or B-flat. The pentatonism of the A-mode would be A
C D F G which, transposed on D for purposes of comparison, would give D F G Bb
C – the true A-mode is one without strong 5th (which may be the reason why it
is rare). Many medieval melodies written with A as final are transposed D-modes
rather than true A-modes.<br>
The same reasoning applies to the F- and C-modes. The F-mode
is articulated on F G A C D, with a strong 3d and without strong 4th degree,
while the C-mode is articulated on C D F G A, without 3d and with a strong 4th.
Many medieval secular melodies are written in C and sound "major"
because they are articulated on C E G; but that points to the F-mode. Our major
mode did not evolve from the C-mode, pace Glarean and others, but from the
F-mode.<br>
The E-mode is rare, because its final falls on a weak degree
of the scale. In the Arabic tradition, this very weakness makes it one of the
favored modes, maqam sikah, with its "reference note" (final, or
tonic) on E half-flat.<br>
<br>
Contrarily to what Harold Powers once thought, mode is real.<br>
<br>
Cordialement,<br>
<br>
Nicolas Meeùs<br>
<a href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a><br>
<a href="http://www.plm.paris-sorbonne.fr">http://www.plm.paris-sorbonne.fr</a></span></font></p>
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