[Smt-talk] rationalizing the octenary system

Eytan Agmon agmonz at 012.net.il
Tue Apr 21 07:34:52 PDT 2009

Quoting Nicholas Meeùs:


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.


Isn’t it possible, however, that Hucbald is referring not to the entire 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 endings 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 protus example (Babb, p. 40), the first phrase of the antiphon Ecce nomen Domini (see LU, 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).


I think it is important to keep Hucbald first statement on finals always in mind: “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 (finem) 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. 


Eytan Agmon

Dept. of Music

Bar-Ilan University


Israel, 52900


-----Original Message-----
From: smt-talk-bounces at societymusictheory.org [mailto:smt-talk-bounces at societymusictheory.org] On Behalf Of Nicolas Mee?s
Sent: Monday, April 20, 2009 12:30 PM
To: Richard Porterfield
Cc: smt-talk smt
Subject: Re: [Smt-talk] rationalizing the octenary system


Let me add two short answers to Eytan's questions:

    Hucbald also cannot have meant that some melodies were sung a fifth higher in pitch, because melodies were sung at any convenient pitch anyway. As the pseudo Odo, the author of the Dialogus, clearly states, the modes do not differ from each other by their pitch.
    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.

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. 
    (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.)
    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.
    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.
    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.

Contrarily to what Harold Powers once thought, mode is real.


Nicolas Meeùs
nicolas.meeus at paris-sorbonne.fr

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