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P.C./I.C. set complexes [Medieval]

🔗Joseph Pehrson <josephpehrson@compuserve.com>

6/11/2000 12:59:32 PM

Regarding the interesting Margo Schulter article on "convexities and
inversions" in TD 668:

I remember, although it has been some time ago, that during my limited
study of 12-tone set theory, there was significant discussion of the
difference between P.C. (pitch class) and I.C. (interval class)
nomenclature.

I was wondering if that could be applied in any way to Margo Schulter's
Medieval tuning definitions... (??)

The "conversity" would be, of course, an I.C. inversion, "interval
class," as contrasted with a P.C., "pitch class," inversion.

I'm not certain if the chromatic methodology generally used for this
kind of set theory would have any relevance to Medieval tuning theory,
since each semi-tone gets a number, starting with the first pitch = 0.
(i.e. the perfect fifth is I.C. 7, and G4 is P.C. 7 when starting from
C4=0, but the two nomenclatures would not coincide if we were starting
on a different pitch -- for example, obviously, the perfect fifth from
D4 to A4 would have I.C. 7 again, but A4 would be P.C. 9 with C4=0).

Maybe the diatonic nomenclature that Ms. Schulter uses is more pertinent
for this period of music, since there is limited chromaticism (??)

I obviously haven't yet worked out any details... but I was just
thinking that the traditional (and very much emphasized) distinction
between P.C. inversions and I.C. inversions in traditional set theory
might have some relevance to the Schulter work...

Just an idea... (??)
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Joseph Pehrson