Re: the sound of a distant horn: entropy emancipated

Hello, there, everyone, and here are some comments on the thread that
Dan Stearns has started.

First of all, borrowing a leaf from the turn of the last century in
European music, I'd like to join such composers as Ivor Darreg and
Brian McLaren in calling for what I might call an "emancipation of
concord/discord/entropy," the recognition of equal citizenship, so to
speak, for all points on the interval continuum.

Maybe my viewpoint on this is a bit curious. My main orientation is to
Western European music -- but music written before the shifts which
led by the late 17th century, as Paul Erlich has stated, to what he
considers the most important European element of triadic major/minor
tonality.

Since Gothic music isn't based on stable thirds, and my "modern"
Renaissance music features a variety of modes and progressions derived
in part from the 3-limit Gothic ones and presenting a significantly
different outlook than late 17th-19th century tonality, does this make
me "uncharacteristically European" -- or something else?

Kraig Grady has mentioned the polyphony of the Solomon Islands, and my
reaction to hearing this -- maybe first around 1971 -- was, "This
feels quite at home, another wonderful tradition of polyphony based
mainly on those beautiful fifths and fourths."

Of course it's also different, with various nuances a European
Gothic-oriented era ear might not pick up, so I want to speak here
with due caution. However, this music seems to me more a delight than
an enigma, although the real enigma, "What might a native speaker of
this musical language hear in addition to what I'm relishing?" can be
an occasion for enhanced wonder as well as due humility.

To me, "alternate tunings" mean that all points on the continuum are
open, not just those represented in a "standard" intonation
(e.g. 12-tET, 31-tET, or whatever) or expressed by integer ratios with
a given level of simplicity or complexity.

The valleys, plateaus, and peaks of the entropy charts should all be
open, Ivor Darreq's theme of "each equal temperament has its own
flavor" generalized into an emancipation of tunings of all kinds.

In various world musics, this has already happened, and as William
Sethares has shown, timbre is a vital variable in the equation also.
How interesting that those gamelan fifths and fourths I have relished
turn out to be not so close to 3:2 or 4:3.

It's noteworthy that just intonation or "JI" can mean many different
things to different people, and that is maybe just as it should be,
given the diversity of musical styles and cultures.

For example, if we consider a composition to be "in" a tuning for
which it was likely intended, then most Gothic music is _already_ in
JI: more specifically, 3-limit JI or Pythagorean tuning. Yet this is a
radically different system than the 5-limit or 7-limit systems which
many people associate with the label "JI."

Also, for a composer such as LaMonte Young and also for me, "JI" means
more generally "integer ratios, however simple or complex." This can
lead to a kind of alliance between JI and temperament: complex integer
ratios, like tempered intervals, are more shadings on a continuum than
discrete "locking-in" points.

While it happens that neo-Gothic music follows what may be a typical
European pattern of stability/instability distinctions and directed
tension, I would honor Daniel Wolf (lamentably offlist at this time)
by suggesting that such patterns, also, should not be taken as any
kind of general norm.

The emancipation of entropy includes the possibility that points of
"maximum entropy" or "maximum complexity" as judged by various
measures may serve as very pleasing points of rest or conclusion in
some compelling compositions, improvisations, or general styles.

In the 20th-century, Bela Bartok demonstrated in such pieces as "Major
sevenths, minor seconds," that traditional European concepts of
"concord/discord" were not invariable laws, and today similar kinds of
demonstrations with intervals at "entropy maxima" might be a timely
exercise, as well as a possible germination point for new musics.

Given the variety of world musics, I suspect that such "experiments"
may be honored practice in various cultures, and I would urge that
concepts of "concord/discord" or "entropy" take account of world
musical practices, with representation of cross-cultural views on
these questions. The Setharean analysis of gamelan tunings seems to be
a very laudible step in this direction.

Maybe it's fitting to conclude this article with a tribute to a
theorist and musician whose contribution may go far beyond his
specialty: Ed Foote, who has gotten me fascinated with the whole theme
of different "flavors" of intervals and subtly graduated degrees of
tension.

While Ed has focused on these concepts in the setting of European
music from around 1680 to 1850 or a bit later, the era of unequal
"well-temperaments," more generally they might apply to a range of
other European or world musics -- and to new musics in the making.

Most appreciatively,

Margo Schulter
mschulter@value.net