[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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