Re: Response to Graham

Hello, there, Paul Erlich and Graham and everyone.

After six attempts to write a reply to this thread so rich with
everything from subtle relationships between commas and schismas to
basic questions of musical style and taste (proverbially not to be
disputed, but often fruitfully to be discussed), I'd like for the
moment quickly to answer one very important question from Graham.

When you ask why I would tend to use a 24-note Pythagorean tuning for
complex 3-limit progressions based largely on 13th-14th century style,
rather than some kind of style based on 9-limit just intonation (JI)
in a typical late 20th-century manner, I would answer simply: "Because
I love medieval music, and Gothic style is what I'm accustomed to
hearing, playing, or improvising on a Pythagorean keyboard."

However, you or someone else familiar with 20th-century styles based
on higher-limit JI may just as naturally consider the same 24-note
Pythagorean tuning, as you point out, "a schismic temperament without
tempering," and use it for 9-limit sonorities and progressions in a
different but equally beautiful musical language.

Similarly, Vicentino's 31-note meantone tuning of 1555 might be used
for music based mainly on the usual 5-limit sonorities and
progressions of the 16th century in various modes, but with some extra
"special effects" intervals; for improvised preludes or fugues in a
Bach-like style; or for 7-limit Blues of the kind which pianist Dave
Hill has actually played on a 12-note meantone piano.

Certainly I would also agree that a given tuning can make available
intervals which historically become associated with potential or
actual changes of style. Thus in the early 15th century, it appears
that keyboard tunings featuring Pythagorean schisma thirds for
sonorities involving written sharps led to the transition to meantone
around 1450-1480; and Vicentino's 31-note meantone tuning could have
led to 7-limit or 11-limit style (he finds the near-11:9 acceptably
"concordant," although evidently unstable or at least unconclusive
judging from his musical examples).

However, a tuning is often open to many musical styles, depending upon
one's tastes or preferences. Thus Prosdocimus espouses a 17-note
Pythagorean tuning while maintaining an often traditional 14th-century
outlook, and Vicentino finds the meantone augmented sixth (~7:4, as it
happens) as decidedly on the dissonant side.

In short, your musical response to a 24-note Pythagorean tuning is
just as valid and beautiful as mine.

Maybe one way of putting this is that a "Xeno-Gothic" style based on
13th-14th century Western European music reflects my own medievalist
tastes rather than any inevitable tendency of such a tuning itself.

Most appreciatively,

Margo Schulter
mschulter@value.net