Re: Xeno-Gothic (reply to Joseph Pehrson)

Hello, there, and while a project prevents me at the moment from
participating in some Tuning List threads as much as I would like,
please let me offer a brief reply to some questions from Joseph
Pehrson about the nature and purpose of "Xeno-Gothic" music.

(The question of 9:12:16 is something I look forward to addressing
after I finish this stage of my project -- and greetings to George
Kahrimanis, with whom I might exchange some reflections about the
close temporal proximity between Ugolino of Orvieto's proposal for a
17-note Pythagorean octave and Nicholas of Cusa's favorable view of
the Pythagorean paradigm of a heliocentric solar system.)

First of all, Joseph, I very much agree with the view that Pythagorean
or similar tunings can be used for many varieties of music, not only
for European medieval or derivative styles. The various Pythagorean
systems of China, Persia, and other musical cultures quite distinct
from those of Gothic Europe should confirm this point.

Further, I consider it a point very much worthwhile making "early and
often," because I would not want to leave people with a certain tacit
impression that Gothic or neo-Gothic is the one "correct" way to use a
Pythagorean tuning -- even in the context of European and derived
styles, let alone that of world musics generally.

The importance of this point becomes all the more clear when I see
statements which seem to make categorical assumptions that anyone
tuning Pythagorean -- or more likely the almost identical 53-tone
equal temperament (53-tet) -- is taking 5-limit just intonation (JI)
as their model. I would be equally ill-advised to invite the
impression that a Gothic or neo-Gothic style is inherent in tunings
which lend themselves to many purposes.

Indeed, 5-limit JI schemes based on 53-tet and the like are a very
healthy antidote to any impression that a Pythagorean or similar
tuning structure implies a medieval or neo-medieval style. I hope that
discussions of Xeno-Gothic or more generally neo-Gothic music may
likewise help to illustrate the diversity of styles possible.

Please let me emphasize that the reason I use Pythagorean tunings, or
tunings such as 22-tet for that manner, to play in Gothic or
neo-Gothic styles is that I love Gothic music and have played this or
improvised in similar styles for over 30 years, on keyboards of
various kinds (yes, often by default in 12-tet).

This certainly doesn't mean that because I use these tunings for
medieval European and related styles, this is what everyone else
interested in these tunings should do also. In fact, if other people
use these tunings for whatever music captures their passion and seems
to fit the intonational structure more or less, that would be a most
desirable consequence, quite apart from my own desire to promote
enthusiasm for Gothic and neo-Gothic styles.

Now we come to an important question you have raised: why the label of
_Xeno_-Gothic to describe a 24-note Pythagorean tuning which may seem
closer to original medieval practice than to a "strange" or "alien"
departure from it?

Possibly this label may reflect my historical orientation, which
prompts me to caution that indeed a 24-note Pythagorean tuning
designed for rendering certain intervals a Pythagorean comma wider or
narrower than usual, at the performer's discussion, is something "new"
or "strange" when set against the known period practice.

As far as I know, a 17-note Pythagorean tuning is the limit of
medieval theory, and it remains an open question whether keyboards of
this kind were actually built in the late 14th or early 15th
century.

Above all, the use of Pythagorean tuning to obtain major intervals
a comma wider than usual and minor intervals a comma narrower than
usual in "closest approach" resolutions (m3-1, M3-5, M6-8, m7-5, M2-4)
is a "new" and "strange" nuance, even if the often elusive remarks of
Marchettus of Padua (1318) about cadential intonation may provide some
scintilla of historical rationale.

The modified Pythagorean tunings of the early 15th century producing
"smoothed" major and minor thirds involving written sharps -- actually
diminished fourths and augmented seconds -- offer another partial
precedent, and I consider the use of these intervals for the music of
this epoch to be a "standard" performance practice rather than "Xeno."
Even when I lean toward a more "experimental" approach, say a tuning
of 15 or 16 notes permitting discretionary use of both C# and Db, for
example, I would call this "an adventurous interpretation" but not
quite "Xeno."

However, going beyond 17 notes and using a major third or sixth a
comma wider than the regular 81:64 or 27:16 is for me "Xeno," whatever
aesthetic inspiration Marchettus may lend; here my theoretical source
is not any medieval treatise, but the modern theorist John Chalmers,
who called to me attention the fact that Pythagorean can approximate
7-limit intervals. Given my orientation to Gothic music, it may not be
surprising that I quickly associated these intervals with Marchettus
and medieval cadences.

Thus I call the music both Xeno, to emphasize this _is_ a modern
development, and Gothic, to emphasize the grounding in such
traditional 3-limit musical assumptions as the principle of "closest
approach."

Also, Xeno-Gothic style can involve some novel progressions which I
wouldn't immediately associate with Gothic music but may be based on
kindred if slightly altered musical patterns. For example, consider
this progression in regular Pythagorean intonation, shown in a
MIDI-like notation with C4 as middle C, with the rhythmic signs at the
top showing a 2/2 or 2/4 meter:

1 2 |1 2 | 1
F4 E4 F#4 G4
D4 C#4 D4
B3 A3 G3
G3 A3 G3

Here the first sonority G3-B3-D4-F4 suggests a resolution to the
stable fifth A3-E4, like this, a progression with at least close
analogues in the 13th century:

F4 E3
D4 E3
B3 A3
G3 A3

(m7-5 + M3-1 + m3-5 + m3-1)

The progression of the outer minor seventh to a fifth might be
taken as the "guiding" two-voice resolution, with the three unstable
thirds resolving in the usual manner to unisons or fifths. The
diminished fifth B3-F3, regarded as a strong dissonance, adds tension
and color, and behaves typically like a "counterfeit" fifth, often
progressing by parallel or similar motion to a concordant fifth (as
here) or fourth.

In our actual progression, however, this resolution is both delayed
and diverted. The minor seventh indeed contracts to a fifth, but
instead of A3-E3 we have what is called a _quinta fissa_ or fifth
"split" by a middle voice into two thirds, A3-C#4-E4. The major third,
especially in connection with the accidental alteration, suggests
resolution to a fifth, and this is what happens -- after the upper
voice accentuates this expectation by moving to F#4, a major sixth
inviting expansion to the octave.

This brings us to the complete trine G3-D4-G4, a point of repose.
While the opening G3-B3-D4-F4 could have been resolved in a "standard"
13th-century fashion, and the last two measures alone have a
characteristically 14th-century sound, the juxtaposition seems to me
"new," and maybe "Xeno."

Note that here the "Xeno" aspect involves the musical progression
itself, not the intonation, which could be achieved on a standard
12-note Pythagorean keyboard in Eb-G#.

In other instances, the music may be standard Gothic but the
intonation "Xeno" -- as when a major third before a fifth is made a
comma wider than the regular 81:64. Even here, note that the medieval
concept of "closest approach" may give a better idea of what is going
on than the simple intonational label "near-9:7."

To sum up, I might define Xeno-Gothic and more generally neo-Gothic
music as involving an interaction between Gothic or Gothic-like styles
and new tunings -- with 24-note Pythagorean being a new tuning in
relation to known medieval practice based on 17 or fewer notes per
octave.

In celebrating and indeed promoting a practice, I do have concerns in
more than one direction.

First, I am concerned that it be clearly understood that Gothic,
Xeno-Gothic, and neo-Gothic styles are only _one_ possibility for the
tunings I discuss: 24-note or larger Pythagorean, 17-tet, 29-tet,
22-tet, etc.

Secondly, I would like often to emphasize that I play in Gothic or
Xeno-Gothic and Neo-Gothic styles because I love the music, a taste
that goes back long before my awareness of the richness that
alternative intonations have to offer.

Finally, having offered these cautions and comments, I do also hold to
the opinion that Gothic music has not yet gained full recognition as
one great historical practice based on 3-limit JI, a practice with its
own vocabulary of vertical progressions which suggest musical
possibilities maybe not so often considered.

Most appreciatively,

Margo Schulter
mschulter@value.net