What is Xeno-Gothic tuning/music?

[Please note that this is a repost to the new Tuning List address, my
original attempt to post to the old address failing. Thanks to those who
helped negotiate the process of finding the List a new home.]

Hello, there.

Recently someone asked about Xeno-Gothic intonation and style, and is
this is (to my best knowledge) a new category, definitions will
necessarily be tentative and not yet informed by the wisdom of
practical experience. However, I can at least offer a definition for
the moment.

To me, _possibly_ the first person to use this term (caution seems
wise on such matters of tuning terminology!), "Xeno-Gothic"
specifically means a 24-note per octave tuning defined as two
otherwise identical 12-note Pythagorean scales tuned a Pythagorean
comma apart.

Typically this would be implemented on a two-manual instrument, with
each manual tuned to an Eb-G# scheme ("Wolf" between these two extreme
notes in the chain of pure 3:2 fifths). It's really arbitrary whether
we take the upper or the lower keyboard as the "standard" or "home"
manual, and in fact this sense of a center might change in the course
of a piece.

Such a tuning produces the standard Pythagorean intervals, plus
variant intervals a Pythagorean comma wider or narrower than the
standard versions. These intervals closely approximate either 5-based
ratios (varying by a regular or syntonic schisma of ~1.95 cents) or
7-based ratios (varying by a septimal schisma of ~3.80 cents).

For example, let's suppose that we take the "standard" keyboard as
Eb-G#, and the "supplementary" keyboard as extending the chain in the
flat direction. Here I'll use a "@" sign to show a note a Pythagorean
comma lower than the version without this sign, maybe easier to grasp
than double flats:

16777216: 8388608:
256:243 14348907 1024:729 128:81 4782969
90.22 270.67 588.27 792.18 972.63
db' eb@' gb' ab' bb@'
_113.7|90.2_90.2|113.7_ _113.7|90.2_113.7|90.2_90.2|113.7_
c@' d@' e@' f@' g@' a@' b@' c@''
531441: 65536: 8192: 2097152: 262144: 32768: 4096: 1048576:
524288 59049 6561 1594323 177147 19683 2187 531441
-23.46 180.45 384.36 474.58 678.49 882.40 1086.31 1176.54
203.91 203.91 90.22 203.91 203.91 203.91 90.22

Keyboard 2: Supplemental
Keyboard 1: Standard

2187:2048 32:27 729:512 6561:4096 16:9
113.7 294.13 611.73 815.64 996.09
c#' eb' f#' g#' bb'
_113.7|90.2_90.2|113.7_ _113.7|90.2_113.7|90.2_90.2|113.7_
c' d' e' f' g' a' b' c''
1:1 9:8 81:64 4:3 3:2 27:16 243:128 2:1
0 203.91 407.82 498.04 701.96 905.87 1109.78 1200
203.91 203.91 90.22 203.91 203.91 203.91 90.22

Note that we get three flavors of popular cadential intervals
characteristically leading to stable 3-limit sonorities. For example,
we have a choice of the usual c-e or c@-e@ (81:64, ~408 cents); the
"smoothed" ~5-based c-e@ (8192:6561, ~384 cents, ~5:4); or the
"accentuated" ~7-based c@-e (43046721:33554432, ~431 cents, ~9:7).

A recent thread on the usual (or "syntonic") and septimal schismas
discusses the theoretical basis for such a tuning.

In my view, "Xeno-Gothic" tends to imply not only the tuning, but a
certain general expectation of a Gothic-like harmonic orientation:
fifths and fourths tend to serve as the favorite stable intervals,
with seconds, thirds, sixths, and sevenths typically resolving to
stable sonorities.

Thus an "accentuated" major third such as f@-a invites a resolution,
for example, to e-b, with a "superefficient" 67-cent semitonal
progression f@-e. Another way of putting this is that our "supermajor
third" needs to expand only a total of about 270 cents to reach a pure
fifth, as opposed to 294 cents with a usual Pythagorean M3. We could
thus view such a resolution as an "exaggerated" version of a standard
Gothic cadential progression. For a possible 14th-century basis for
such wide cadential thirds, people might want to look at recent
threads on the theories of Marchettus of Padua (1318).

A caution: using "7-limit" or "5-limit" in this stylistic context
might be misleading, because I realize that many readers may be more
accustomed to systems treating 7-limit sonorities as stable than to a
system treating them generally in a "Gothic-like" fashion as
combinations inviting resolution to sonorities with fifths and
fourths.

Of course, anyone is free to tune "Xeno-Gothic" (the keyboard
arrangement) and to use it in any way desired; but my implicit context
is the harmonic technique of the 13th-early 15th centuries.

Most respectfully,

Margo Schulter
mschulter@value.net

Since Margo Schulter's Xeno-Gothic tuning is simply a pythagorean
series carried to 24 terms, what essentially seems to define
"Xeno-Gothic" is the arrangement into two sets of twelve and the
set of stylistic conventions. These are very interesting,
especially since these conventions place restrictions on interval
use although the intervals in question are very smooth,
relatively close approximations of just thirds and sevenths.

In designing her constraints, Margo Schulter is clearly working
in the western contrapuntal tradition. Central Javanese _pathet_
presents another example of such stylistic restrictions organized
-- I am tempted to say 'co-evolving' -- in parallel with a tuning
system. South Indian Gamakas might be another example. Can anyone
think of any others?

Daniel Wolf
Frankfurt

Margo : It seems the Xeno-Gotic scale looks like the Indian Scale, with both
the exceptions of the 5-schkismic aprox. and the duplication of the Tonic
and the Fifths.
Isn t it ? Thanks.

Eduardo

Eduardo Sabat-Garibaldi e-mail : esabat@adinet.com.uy
Home:Simon Bolivar 1260 OfficeFAX-PHONE :5 982
900-0353 11300 Montevideo Home Phone : 598 2
708-0952
Uruguay

Yes -- the Indian scale is, ignoring schismic (2 cent) deviations, 22
consecutive notes in a chain of just perfect fifths, while Margo
Schulter's Xeno-Gothic scale is 24 consecutive notes in a chain of just
perfect fifths.

> -----Original Message-----
> From: Eduardo Sabat-Garibaldi [SMTP:esabat@adinet.com.uy]
> Sent: Sunday, February 08, 1998 10:09 AM
> To: tuning@onelist.com
> Subject: [tuning] Re: What is Xeno-Gothic tuning/music?
>
> From: Eduardo Sabat-Garibaldi <esabat@adinet.com.uy>
>
> Margo : It seems the Xeno-Gotic scale looks like the Indian Scale,
> with both
> the exceptions of the 5-schkismic aprox. and the duplication of the
> Tonic
> and the Fifths.
> Isn t it ? Thanks.
>
> Eduardo
>
>
> Eduardo Sabat-Garibaldi e-mail : esabat@adinet.com.uy
> Home:Simon Bolivar 1260 OfficeFAX-PHONE :5 982
> 900-0353 11300 Montevideo Home Phone :
> 598 2
> 708-0952
> Uruguay
>
>
>
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