[Smt-talk] rationalizing the octenary system

[Ildar Khannanov]

Dear Nicolas,
 
in support of your statements about melodic character of modes, in addition to Arabic reference, I would mention the neumatic notation. Although theorists were dealing with the division of the octave in one or another fashion, musical practice of the 9th century and on operated with neums (pneums). Neums do not reflect the pitch. Neither they denote rhythmic proportion. Rather, they indicate the trajectory and the shape (phrasis) of speech intonations. The fact that the Eastern tradition used Oktoikhos was not the matter of choice. The same problem, the lack of precise notation system, appeared in the West. There was no other way to operate with modes than through memorization of numerous neums (popevkas) and placing them in groups. The ikhos had no modal definition. I know, for example,  that the funeral music should use the 6th ikhos. 
 
My teacher, late professor Yuri Kholopov, attempted creating the modal system for the Russian oktoikhos using the Obikhod scale. He realized that the modes are three ( greater, smaller and diminished) and there are two levels of transposition possible. So, he came up with the term Hexaikhos as a modal system of 6 modes of Znamennyi chant. (He has presented this topic at the AMS 1998 in Phoenix). It is obvous, however, that it is difficult to reconcile the two principles: grouping of melodic patterns and actual division of the octave.
 
 
Best,
 
 
Dr. Ildar Khannanov
Peabody Institute of Music
Johns Hopkins University
solfeggio7 at yahoo.com


--- On Mon, 4/20/09, Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr> wrote:


From: Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr>
Subject: Re: [Smt-talk] rationalizing the octenary system
To: "Richard Porterfield" <porterfr at hotmail.com>
Cc: "smt-talk smt" <smt-talk at societymusictheory.org>
Date: Monday, April 20, 2009, 4:29 AM


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

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.
    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.

Cordialement,

Nicolas Meeùs
nicolas.meeus at paris-sorbonne.fr
http://www.plm.paris-sorbonne.fr

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