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<big>Let me add two short answers to Eytan's questions:<br>
<br>
1) 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.<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>Dialogus</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 class="moz-txt-link-abbreviated" href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a><br>
<a class="moz-txt-link-freetext" href="http://www.plm.paris-sorbonne.fr">http://www.plm.paris-sorbonne.fr</a><br>
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