Ongoing adventure (mp3, Wilson-related papers)

Hello, everyone, and I would like warmly to thank Joe Pehrson,
Gioseffo Zarlino, Erv Wilson, Kraig Grady, and Shaahin Mohaajeri for
much inspiration as I write this note sharing a bit about my recent
musical life, with some links both to mp3 files and to some
Wilson-related "paracompositional" papers written and posted to
celebrate a new year.

On MMM, it's appropriate to start with some music, so I'll give links
to pieces written in a new tuning system called Zest-24 I'm now very
excited about -- although the pieces themselves have been posted here
before. First, here's an improvisation from last spring:

<http://www.bestII.com/~mschulter/MMMYear001.mp3>

This was actually based on only 12 notes of what was to become Zest-24
later last year, but shows one side of the tuning: lots of intervals
close to septimal, or generally in the Pythagorean-to-septimal region.
By November, however, I had arrived at a full 24-note set in time to
record this piece in honor of Shaahin's newborn daughter Baran, whose
name means "rain":

<http://www.bestII.com/~mschulter/Baran-GiftOfRain.mp3>

This uses some septimal variations on the Persian dastgah-ha or modal
families of Shur and Nava, and shows one new ingredient of the full
24-note tuning: lots of neutral intervals!

I referred before to some "paracompositional" papers now available:
that is, papers written "around" or "along with" experience in
composing or improvising. Erv Wilson's writings released and made
available at the Anaphorian Embassy site <http://www.anaphoria.com>,
along with related documents there by Kraig Grady and others, have
served as a creative spur.

Early this month, I discovered a paper by Wilson on various topics
including a method for generating a 17-note just scale by
transposition, and was led to a fascinating subset of Zest-24 relating
to the septimal aspects of my adventure that I mention above. Here are
links to Wilson's paper and my paracompositional response:

<http://www.anaphoria.com/genus.PDF>
<http://www.bestII.com/~mschulter/zest24-septendecene.txt>

Also, having recorded the _Baran: Gift of Rain_ piece, I was excited
to find another Wilson paper on a "Rast/Bayyati matrix" using Zalzal's
neutral thirds of 27:22 and 11:9 to generate a just tuning system
which, in its 24-note version, could serve as a kind of theme with
Zest-24 as one tempered variation. Here are links to the Wilson paper
and my curious appreciation of it.

<http://www.anaphoria.com/RAST.PDF>
<http://www.bestII.com/~mschulter/zest24-RastBayyati.txt>

Joe Pehrson's comments on composing in Blackjack -- and I wish I'd
posted in a more timely way to encourage him and promote more dialogue
about his experience and methods, if he's inclined to discuss this
here -- remind me that composing or improvising is indeed an
adventure. Right now I have the partial satisfaction of having
composed a new piece, and the challenge of performing and recording it
so I can make it available here.

To conclude this note, I should give more credit where credit is
due. The Zest in Zest-24 stands for Zarlino Extraordinaire Spectrum
Temperament, and indeed Gioseffo Zarlino's 2/7-comma meantone (1558),
evidently the first known regular European temperament to be described
with mathematical precision, is the basis. Eight fifths (F-C#/Db) on
each keyboard manual are tuned as in this regular temperament, with
the other four tuned equally wide to make a 12-note circle on each
manual; the two keyboards are about 50.28 cents apart, the enharmonic
diesis of Zarlino's regular tuning. Here's a Scala file:

<http://www.bestII.com/~mschulter/zest24.scl>

My paracompositional papers go into more detail: but I did want to be
sure that Zarlino got due credit for his part in all this.

Peace and love,

Margo

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@...>
wrote:

> To conclude this note, I should give more credit where credit is
> due. The Zest in Zest-24 stands for Zarlino Extraordinaire Spectrum
> Temperament, and indeed Gioseffo Zarlino's 2/7-comma meantone
(1558),
> evidently the first known regular European temperament to be
described
> with mathematical precision, is the basis. Eight fifths (F-C#/Db) on
> each keyboard manual are tuned as in this regular temperament, with
> the other four tuned equally wide to make a 12-note circle on each
> manual; the two keyboards are about 50.28 cents apart, the
enharmonic
> diesis of Zarlino's regular tuning. Here's a Scala file:
>
> <http://www.bestII.com/~mschulter/zest24.scl>

It seems to me this is an awfully round-about way to characterize
this scale. I would call it 24 notes of 2/7-comma meantone in a chain
of fifths, from -11 to +12 fifths, or Meantone[24] in a 2/7-comma
tuning. This tuning fixes 25/24 to have its just value; it is
the "eigenmonzo tuning" for 25/24. Nearby is the eigenmonzo tuning
for 9/7, fixing the interval 9/7 to its just value, at 695.6145
cents, and the Wilson fifth, with synchronized beating, at 695.6304
cents. Either of these would make for an interesting alternative to
2/7-comma.

> <http://www.bestII.com/~mschulter/zest24.scl>

> It seems to me this is an awfully round-about way to characterize
> this scale. I would call it 24 notes of 2/7-comma meantone in a
> chain of fifths, from -11 to +12 fifths, or Meantone[24] in a
> 2/7-comma tuning. This tuning fixes 25/24 to have its just value;
> it is the "eigenmonzo tuning" for 25/24. Nearby is the eigenmonzo
> tuning for 9/7, fixing the interval 9/7 to its just value, at
> 695.6145 cents, and the Wilson fifth, with synchronized beating,
> at 695.6304 cents. Either of these would make for an interesting
> alternative to 2/7-comma.

Please let me gently explain that Zest-24 differs from the regular
24-note version of Zarlino's 2/7-comma which you describe because it
consists of two 12-note _circles_ each with eight of Zarlino's
meantone fifths (695.810 cents) plus four wide fifths (708.379 cents)
to close a circle. This is thus an _irregular_ 24-note temperament,
rather than the chain of 23 identical fifths of which you write.

In other words, I had to be "round-about" because this a tuning with
two "roundish" circles -- or ellipses, if you like that figure of
speech.

By the way, for MMM purposes, people might ask, "What difference does
all this make for practical music with either of the tunings you folks
are discussing?"

With greetings to Shaahin, let's consider music in a Persian kind of
style, for example. In a regular 24-note version of Zarlino's
meantone, we'd have two steps in the general "neutral second" area at
around 141 and 171 cents. The first is close to 13:12, and the second
a bit larger maybe than a typical neutral second -- almost identical
to a 7-EDO step, and sort of in its own territory.

In Zest-24, we get these sizes and also some others at around 133,
141, 146, 154, 159, 166, and 171 cents. This means we'll get subtle
variations as we transpose a tetrachord or mode through different
locations. That's why I call it Zarlino Extraordinaire Spectrum
Tuning -- we get a spectrum with lots of interval sizes. It would be
prudent for me to emphasize that while 2/7-comma is Zarlino's tuning,
the irregular temperament and use of two circles is mine.

Maybe this discussion of the mathematics should be moved to another
forum -- but I will include a Scala file so that you and others can
confirm that this is an irregular tuning rather than a regular
meantone. Also, here's a piece for Shaahin's daughter Baran that uses
some of the neutral second steps I mention above.

<http://www.bestII.com/~mschulter/Baran-GiftOfRain.mp3>

! zest24.scl
!
Zarlino Extraordinaire Spectrum Temperament (two circles at ~50.28c apart)
24
!
50.27584
25/24
120.94826
191.62069
241.89653
287.43104
337.70688
383.24139
433.51722
504.18965
554.46549
574.86208
625.13792
695.81035
746.08619
779.05173
829.32757
887.43104
937.70688
995.81035
1046.08619
1079.05173
48/25
2/1

Peace and love,

Margo

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@...>
wrote:

> Please let me gently explain that Zest-24 differs from the regular
> 24-note version of Zarlino's 2/7-comma which you describe because it
> consists of two 12-note _circles_ each with eight of Zarlino's
> meantone fifths (695.810 cents) plus four wide fifths (708.379
cents)
> to close a circle.

Sorry, my mistake; I made a mistake using Scala's "compare scale"
command which made me think they were identical.

To make up for it, I'll mention that I was pointing out to Ozan
recently that 764-edo was one of a number of equal divisions around
704 in size which struck me as more recommendable than 704. 764,
among its other talents, which includes excellent 11- to 17-limit
approximations, does a near-perfect 2/7-comma meantone (443/764.) In
764 Zest-24 goes:

[32, 45, 77, 122, 154, 183, 215, 244, 276, 321, 353, 366, 398, 443,
475, 496, 528, 565, 597, 634, 666, 687, 719, 764]

In terms of 443deg764 generators, that is:

[-379, -202, -190, -13, -12, -11, -10, -9, -8, -7, -6, -5, -1, 0, 1,
2, 3, 4, 5, 6, 7, 184, 196, 373]

We can now use the excellent 17-limit approximations of 764 to give
17-limit interpreations of intervals such as -190 fifths (16/9), -202
(280/153), -379 (85/72), +184 (1989/1232), +196 (80/51), +373
(175/144). 16/9, at least, looks relevant.