Re: [tuning] Digest Number 3457

Re: "Sumer is a coming in" and Pythagoreanism

The English specialized in a semi-improvised form of polyphony called fauxbourdon. It made a predominantly triadic texture, especially 6th (6/3) chords, out of monophonic repertoire. It is hard to imagine that these would have been sung vertically in anything other than simple 5-limit chords. It is easy to imagine the "Sumer" canon within this sme intonational environment.

(Please don't think that my appeals to imagination here are cop-outs: England, and English fauxbourdon, was on the margin of European theory and practice, and the deficits in surviving documents can only be balanced by modest appeals to the imagination!)

It is easy enough to to place the blanket label "pythagorean" over all medieval musical theory and practice, but that is insufficiently granular to describe what is a reather more complex situation, and this is apparently true for pythagoreanism in both of the cultures inheriting the Hellenistic traditions, Christendom and Islamdom.

On the one hand, one can assume that a literal pythagorean practice did exist for some repertoire. However, the is ample evidence in both surviving repertoire and in theory that the pythagorean "project" included trying to reconcile practices beyond the three limit with an intellectual (= rational _and_ theological) committment to the three limit. Extended pythagorean schemes (e.g. schismatic tunings where a pythagorean Fb/C is used to approximate the 5:4 third) were one answer to this problem, quarter-comma meantone was the unique European solution, and the searches for a successful large-number temperament have been perpetual Greece, Turkey, in Arabic countries, and even among some members of this community, however within this community the problem has been generalized to considered the reconciliation of several prime factors, not just three and five.

Re: Lowinsky

Edward Lowinsky (1908-85) was a music scholar, with a decidedly unorthodox bent. His controversial work centered on the "secret chromatic art" of the high renaissance, and especially questions of _ficta_ and the characterization of transitional repertoire as tonal or atonal. Naturally, he touched on some significant intonational issues as well. Lowinsky remains an essential figure for research in music from Ockeghem to Orlando and Vincentino to Gesualdo. His article on Mozart's rhythm is a small treasure, again with a viewpoint that goes against the grain.

As an undergrad, I had a very gracious exchange of letters with Lowinsky, then retired from Chicago, about the disappearance of the enharmonic genera, one of my small obsessions.

Not an idol, but a bit of a hero and a good example of the ability of Academe to sometimes let unorthodox scholars get past the gates to the ivory tower. Not a bit of general knowledge, but certainly a name that should be encountered by anyone with more than a passing interest in music of the Renaissance.

Daniel Wolf