[Smt-talk] Gravity (Was: Car names)
Nicolas Meeùs
nicolas.meeus at paris-sorbonne.fr
Fri Aug 3 14:13:57 PDT 2012
Dear Thomas,
Your MTO article begins with a quotation of Taruskin,
Where actual musical practice is concerned, the relevant historical
fact is that people have evidently internalized the diatonic pitch
set—carried it around in their heads as a means of organizing,
receiving, and reproducing meaningful sound patterns—as far back as
what is as of now the very beginning of recorded musical history,
some three and a half millennia ago.
a statement that seems highly questionable. I suppose that 'the diatonic
pitch set' refers to what I'd call 'Pythagorean' diatonicism, a scale
that can be generated by a cycle of (pure) fifths, and producing a
pattern of tones (T) and semitones (S) of the type TST T TST (two TST
tetrachords separated by a disjunctive T). There are other (Antique)
definitions of diatonicism, but let's agree that this is the strict one.
Oriental ('Arabic') modality makes an extensive use of another
scale, the 'scale of Zalzal', with major (T) and neutral (N) seconds,
for instance in the arrangement NNT T NNT (NNT tetrachords and a T of
disjunction). This scale, which may be the chromatic system of the
Greek, seems to have been used also in early Christian chant. It cannot
be fully produced by a cycle of fifths and the degrees that are not in
fifth-relation with the others often are of imprecise intonation.
The link between Pythagorean diatonic and the 'actual musical
practice' mentioned by Taruskin is unclear, to say the least. The
earliest descriptions of the Pythagorian diatonic scale in the West
(after Boethius who may not have been much concerned with practice) are
those by Hucbald and the Enchiriadis group of treatises, c900. This is
too close to the beginnings of polyphony to be a mere coincidence.
Handschin's idea of the character of tones is convincing, but he may
have been mislead (by ideas common in the earlier 20th century) in
believing that it depended on the cycle of fifths. Medieval theorists
described 'qualities' of tones, the 'modi vocum', at least from Hucbald,
c900, to Hermannus contractus in the later 11th century. They described
four qualities, corresponding to the four degrees of the tetrachord and
determining four pairs of modes; the modal final shared the same quality
as the fifth above and the fourth below (which is the origin of the
theory of species of fifths and fourths); etc. See my paper on /Modi
vocum/, available on
http://paris-sorbonne.academia.edu/NicolasMee%C3%B9s/Papers. What you
call 'Guidonian affinity' (why Guidonian?) obviously has to do with this
(but this may not always have been properly understood).
Medieval theory was torn between a tetrachordal (or hexachordal) and a
heptachordal conceptions of the diatonic system. The medieval
equivalents to your height and width cannot be dimensions of the same
degrees, as there are so to say seven 'heights' and four 'widths'. And
neither can be assimilated with pitch, as pitch is not a relevant
category in medieval theory – as the pseudo Odo of Cluny clearly stated,
modes do not differ from each other by their pitch. The 'quality' of the
notes (your 'width') depends exclusively of their intervallic
surrounding: they may be described as systemic functions. What you
describe as 'height' concerns what might be described as a modal
function, without necessary link with 'pitch' properly speaking.
Your description of the height-width duality forms and interesting
modern view of diatonic scales. I have no objection against your dubbing
these scales 'modes'. I am not sure, however, that it does explain
medieval (or oriental) modality... To say it in other words: your
expression "Guidonian modes" may make sense today, but what does it mean
for medieval theory?
Nicolas Meeùs
Université Paris-Sorbonne
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