Re: "Pitch drift in Binchois" -- someone else's theory(?)

Hello, there, and I'm granting myself an exception from my Tuning List
moratorium in order to clarify a question raised in certain recent
posts about my views on "pitch drift" in the music of Giles Binchois,
a composer flourishing in the second quarter of the 15th century.

Possibly someone else has come up with a theory of "pitch drift" in
music of this era marking the Gothic-Renaissance transition as placed
by many recent chronologies, but my own view simply proposes some kind
of modified Pythagorean tuning -- the general view suggested by Mark
Lindley.

Of course, any fixed-pitch system can only approximately and partially
model what singers or players of flexible-pitched instruments might
do, but maybe I can briefly explain enough so that others can address
the issue of whether any "pitch drift" might be involved, something I
haven't associated with this kind of tuning.

In a popular 12-note keyboard tuning of this era, Gb-B, written sharps
are in fact realized as Pythagorean flats, so that thirds and sixths
involving sharps are performed as "schisma thirds," that is, as
diminished fourths very close to 5:4 or augmented seconds very close
to 6:5.

As Lindley remarks, the contrasting sizes and "colors" of thirds and
sixths in this kind of keyboard or vocal tuning are rather analogous
to those of an 18th-century well-temperament. With due caution, he
presents the attractive hypothesis that composers such as Binchois and
the young Guillaume Dufay around 1420 _may_ have been influenced by
this tuning in their vocal compositions.

In one _possible_ kind of flexible intonation which I approximate with
a Pythagorean keyboard system of 15 or 16 notes (Gb-G# or Gb-D#),
performers might lean toward regular Pythagorean major thirds and
sixths in cadential progressions (M3-5, M6-8), but toward schisma
thirds and sixths for prolonged noncadential sonorities of a kind
often prominently featured in both vocal and keyboard music of the
time.

The only comma involved in this kind of distinction is the Pythagorean
comma between two differently spelled notes in the regular chain of
fifths, for example A3-C#4-F#4 as a cadential sonority expanding to
G3-D4-G4 vs. A3-Db4-E4 as a "schisma third" sonority. This seems more
analogous to me to the diesis of a regular meantone tuning, also
arising between notes in the regular tuning chain such as C#-Db, than
to the kind of syntonic comma issues involved in a system combining
pure vertical ratios of 3 and 5 and using only integer ratios for
melodic intervals also (as in the syntonic diatonic, as opposed to
Vicentino's adaptive JI system based on meantone).

In short, while someone else may have proposed "pitch drift" as a
feature of music by Binchois or other composers of the early to middle
15th century, this is not my theory, nor I am aware of it as a
consequence of the kinds of modified Pythagorean outlook which Lindley
or I have suggested.

Most respectfully,

Margo Schulter
mschulter@value.net