Re: Response to Joseph Pehrson (Xeno-Gothic, neo-Gothic)

Hello, there, Joseph Pehrson, and thank you for your encouragement. If
my discussion of neo-Gothic music can encourage new experiments and
performances, that would be most rewarding, especially I hope for the
performers and listeners.

Very briefly, I might just propose these possible distinctions, since
I recognize that terms like "Xeno-Gothic" and "neo-Gothic" may often
seem synonymous, and in fact overlap ("Xeno-Gothic" being one approach to
the larger category of neo-Gothic).

--------------
1. Xeno-Gothic
--------------

Xeno-Gothic refers specifically to a 24-note Pythagorean tuning with
two 12-note keyboards a Pythagorean comma apart, as used for music of
13th-14th century Gothic Europe and related derivative styles. Here
I would emphasize that it is not the tuning alone which is
"Xeno-Gothic" -- Euler apparently proposed a similar if not identical
arrangement in 1739 (according to Barbour) for a kind of 5-limit just
intonation -- but the use of this tuning for Gothic or derivative
styles.

More specifically, this implies an outlook where generally the regular
Pythagorean intervals are the usual norm, with a characteristic focus
also on the "near-7-limit" intervals in cadential progressions to
stable 3-limit sonorities. Certainly the "near-5-limit" intervals can
play a role also, especially in early 15th-century idioms and their
offshoots, but the overall outlook is "complex 3-limit, with
interesting variations."

-------------
2. Neo-Gothic
-------------

Generally "neo-Gothic" refers to any kind of tuning or musical style
derived from Gothic music in a reasonably recognizable fashion. Within
this larger category, Xeno-Gothic is one subset.

(1) Xeno-Gothic JI. More specifically, Xeno-Gothic is a just
intonation (JI) system based on 3-prime-limit intervals -- as is
Pythagorean tuning in general. As a matter of convenience, Xeno-Gothic
uses a 24-note chain fitting two standard 12-note keyboards, but the
scheme might be extended to a full and "virtually closed" cycle of 53
notes.

(2) Other JI systems. Another JI approach to neo-Gothic might be the
use of arrays of intervals including pure ratios at higher prime
limits such as 7:6, 9:7, 13:11, 14:11, 17:14, 21:17, and so on.

(3) Neo-Gothic regular temperaments. Neo-Gothic hypermeantone tunings
with fifths larger than Pythagorean, ranging out to around 22-tet and
in some special circumstances to 27-tet, are counterparts of
traditional meantones with fifths narrower than pure. Such tunings,
also like meantones, may be precisely closed (n-tet's) or open.
Familiar examples might include 17-tet, 22-tet, 27-tet, 29-tet,
41-tet, and 46-tet. Note that 53-tet, although not a hypermeantone
since its fifths are minutely smaller than Pythagorean, also serves as
a regular temperament closely approximating Pythagorean JI.

(4) Neo-Gothic irregular temperaments. Like the late 17th-19th century
well-temperaments, these tunings would feature regular fifths of more
than one size. As Paul Erlich has pointed out in a Baroque context,
such tunings need not be limited to 12 notes per octave, although the
historical term "well-temperament" often implies this tuning size.

(5) Adaptive JI systems. As Paul Erlich recently noted, one could use
a tuning such as 1/4-septimal-comma hypermeantone (fifths ~6.82 cents
flat, major thirds at a pure 9:7) or 22-tet as the basis for an
adaptive tuning system making adjustments so that vertical sonorities
might, for example, have consistently pure 3-limit and 7-limit ratios.
Such a scheme would be analogous to that taking 1/4-comma meantone or
31-tet as the basis for adjustments to obtain pure 3-limit and 5-limit
ratios (in the manner of Nicola Vicentino, 1555, and Erlich).

Please feel welcome to ask more questions: I know that it is often
easier for me to use terms such as "Xeno-Gothic" or "neo-Gothic" than
to define them clearly, especially here when one term may represent
the subset of another.

Most appreciatively,

Margo Schulter
mschulter@value.net