Practicing in public -- Gb Lydian exercise

Hello, everyone, and what I have to share isn't so much a composition
as a keyboard borrowed from various sources, mostly medieval European,
to help me master a skill which must seem pretty basic: actually
learning to play in all the transpositions on a conventional 12-note
keyboard.

Of course, a generalized keyboard would be more efficient and
versatile, but at least, after 35 years and more of musicmaking based
mostly on medieval and Renaissance/Manneristic styles, I'm actually
realizing that getting familiar with the more "remote" transpositions
has its benefits.

This little exercise in Gb Lydian, and the general learning process
I'm describing, have their catalyst in a temperament I devised about
two years ago, actually with eight of the 12 notes identical to those
in Gioseffo Zarlino's famous regular 2/7-comma meantone of 1558, the
first known European meantone temperament to be described in
mathematical terms.

The fifths F-C# are tuned as in Zarlino's temperament at 2/7 sytonic
comma or about 6.14 cents narrow, while the remaining four fifths are
tempered equally _wide_, about 6.42 cents each, to close the circle
and produce a circulating temperament. In my exercie in Gb Lydian,
these wide fifths and the intervals they help generate take a showcase
role:

<http://www.bestii.com/~mschulter/GbTry001.mp3>

What especially excited me was being able to get some septimal types
of sonorities in a circulating 12-note system. Zarlino's tuning, as it
happens, yields a diminished fourth of about 433.52 cents, only about
1.56 cents narrow of a pure 9:7; this interval is here available at
C#-F (or Db-F in the setting of a neo-medieval style where it's used
as a regular major third). The smallest minor thirds of the
circulating version, F-Ab and Bb-Db, are about 274.86 cents, or about
7.99 cents wide of 7:6.

Here these intervals are featured along with others on the spectrum
between Pythagorean and septimal. Note that while the graduation of
intervals, or "modal color" as one moves around the circle, is as a
result of the irregular tempering, Zarlino's original tuning provides
not only the near-9:7 third at C#/Db-F, but the two excellent 25:24
semitones at F-F# and C-C# (or, in this context, F-Gb and C-Db, two
vital cadential steps in Gb Lydian).

Another curious facet of this circulating version inspired the final
cadence of my exercise as a musical tribute to Paul Erlich: the
sonority Bb-F-Ab-C (about 0-708-983-1404 cents) happens to combine the
best approximations of 7:4 (Bb-Ab) and 7:6 (F-Ab) with a near-just 9:4
major ninth at Bb-C to give a nice approximation of 4:6:7:9, a
sonority to which you introduced me, Paul. Here the trick is that that
in the chain Bb-F-C, the first fifth is about 6.42 cents wide and the
second about 6.14 cents narrow -- so that they "average out" to
something very close to a just 9:8 or 9:4. Of course, let me add,
22-equal provides more accurate septimal intervals, and in lots more
locations.

Anyway, I'm posting this bit of keyboard practice in order to post
a recording of something other than ASCII keystrokes <grin>, with
caution that it _is_ practice rather than a finished performance.
Most of the material is medieval, with special homage to the two-voice
setting _Verbum bonum et suave_ and the _Missa Tournai_, plus a
progression that George Secor should recognize (to be documented in
our forthcoming articles in _Xenharmonikon 18_).

For the curious, I'll add a Scala file of this circulating 12-note
variation on Zarlino's 2/7-comma meantone, and also the intervals in
rounded cents for the Gb Lydian I use in this piece.

! zarte84.scl
!
Temperament extraordinaire, Zarlino's 2/7-comma meantone (F-C#)
12
!
70.67243
191.62069
287.43104
383.24139
504.18965
574.86208
695.81035
779.05173
887.43104
995.81035
1079.05173
2/1

Gb Ab Bb C Db Eb F Gb
0 204 421 625 696 913 1129 1200
204 217 204 71 217 217 71

Most appreciatively,

Margo Schulter
mschulter@...