Yahoo Tuning Groups Ultimate Backup tuning An exciting new tuning experience

Hello, there, everyone, and in the excitement of exploring for the
first time a tuning which has served as the basis for much creative
music, I would like to celebrate with what is likely one of the more
improbable definitions of "microtemperament" to be posted here.

Anyone who'd like to move directly to my practical experience with
this incredible tuning should jump to Section 2, with the intervening
theoretical musings hopefully providing a diversion for those who like
playful and arcane puzzles.

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1. Can you name this "microtemperament"?
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Some people might argue that my keyboard layout and first crude
attempts at sound design are merely a numerical palindrome on Fokker's
famous organ recently mentioned here.

As a preface to my curious definition, I would emphasize that my
references to Dave Keenan and David Beardsley may mainly show how
ideas posted here might sometimes set things in motion that the
authors may not necessarily have intended <grin>.

However, given that 12-tET might be considered a "microtempered JI"
system for world musics based on stable consonances of 3:2 and 4:3,
maybe there's a certain xenharmonic exuberance about including some
other tunings using irrational numbers also.

Here's my definition to celebrate my first close encounters with a
very exciting scale:

A tuning may be described as "microtempered JI"
if all stable concords are within one cent of an
integer ratio meeting at least one of these tests:

(1) The ratio, a:b, is such that a*b<=104; or

(2) The ratio

(a) is one repeatedly mentioned by David
Beardsley (or an octave complement or
extension of such an interval); and

(b) serves as a stable concord on the given
instrument in a given musical context,
especially a context based on styles
originally developed in a setting of
harmonic timbres and JI ratios under
definition (1).

To introduce the scale suggesting to me this curious definition, I
might term it "Blackwood" both after a famous composer who has used
it, and following the example of names such as "Blackjack" and
"Canasta" on this list.

In view of the recent thread about Bartolomeo Ramos de Pareja, I would
like to observe that "Blackwood" can be generated by using an interval
almost identical to a ratio appearing on his famous monochrord (1482):
135:128 (~92.18 cents). To obtain an equal division of the octave, we
very slightly stretch this same generator to ~92.31 cents, or more
precisely 92-4/13 cents, as Monz has noted.

However, we can also generate the scale using another interval, a
"microtempered" stable concord in my stylistic context serving as the
equivalent for a 3:2, and within one cent of an integer ratio often
mentioned by David Beardsley: 49:32 (~737.65 cents). The "Blackwood"
generator at ~738.46 cents, or 738-6/13 cents, is only ~0.81 cents
wider than this ratio.

The tempered version of the Bohlen-Pierce scale, with its 3:1
"tritave" divided into 13 equal parts, suggests another method for
deriving "Blackwood." Starting with an equal division of 49:16 based
on the next Fibonacci number, 21, we get an interval at step 13 of
~1199.50 cents, and can then very slightly stretch the tuning to
obtain a pure 2:1 octave.

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2. Playing in 13-tET
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Enough for some possibly quite bizarre "microtemperament" theory -- my
main idea, after all, is to celebrate the tuning, known in more
familiar terms as 13-tET or 13-EDO.

Over the last couple of days, I've been designing some custom timbres
on the Yahama TX-802 synthesizer to emulate the remarkable effect of
one of the built-in timbres: a stable quality for the interval of 8/13
octave, or around 738 cents, more or less musically equivalent to that
of a fifth around 3:2.

As described in a recent discussion of "meantone well-temperament,"
this preset "Piccolo" timbre (voice A27) made the "Wolf fifth" of
1/4-comma meantone at ~737.64 cents -- almost precisely 49:32 --
interchangeable to my ears with a usual fifth in this temperament at
~696.58 cents.

Since I knew that the 13-tET fifth at ~738 cents is almost identical,
my next logical step was to tune it up. Here people like Bill
Sethares, Dan Stearns, Jeff Scott, and Jacky Ligon played a catalytic
role both by advocacy and by example.

At first, I was content to thrill that the "Piccolo" timbre made it
possible for me to play neo-Gothic progressions in 13-tET using a
738-cent fifth -- not so surprising, given my meantone experience.
Here I should explain for people unfamiliar with the term that
"neo-Gothic" means inspired by the Gothic music of Europe around the
13th-14th centuries, where fifths are the prime concords.

Then, inspired by the Bill Sethares CD _Xentonality_, I was moved to
take the next step of trying to customize my own 13-tET timbres.

One of my favorite TX-802 voices is "Puff Pipes" (A56), and for
something like 17-tET or even 20-tET in a neo-Gothic style it's fine
"right out of the box." For 13-tET, however, I could hear that I
needed to do some "Sethareanizing" or maximizing of tuning/timbre
consonance.

As a rank beginner, I can't claim to understand the sophisticated
consonance/dissonace models of Sethares, much less to share his
practiced musical judgment and art in the crafting of beautiful new
timbres. This is indeed a new art of orchestration, which people like
Bill Sethares and Mary Beth Ackerley are making one of the most
engaging features of early 21st-century music.

However, I did know that part of the idea, also presented by earlier
writers such as Ivor Darreg and Wendy Carlos, was to adjust the
partials of a timbre to match the intervals of the tuning.

Thus for my 13-tET "Puff Pipes," I would try using FM operators to
define a timbre with partials to fit the 738-cent fifth -- slightly
wider than the usual harmonic ratios of 3:1, 6:1, etc. The TX-802
offered ratios such as 3.06, 6.12, and 12.24 -- in octave-reduced
terms, around 736.24 cents, neatly approximating the tuning.

Using "algorithm 31," the FM equivalent of a drawbar organ, to set up
some partials of this kind, I found that some other qualities of the
timbre changed: while the original "Puff Pipes" reminds me of a
Renaissance chamber organ[1], this sounded maybe more like a larger
pipe organ with a deeper and less brilliant sound.

With these adjustments, which I further fine-tuned today, I found that
the fifths could sound amazingly stable and "solid." It was delightful
to play 13th-14th century progressions and find them recognizable, and
beautiful -- sometimes with striking "paradoxes" and variations.

"Paradoxes" engagingly arise from a perspective of historical Western
European styles of composition, because 13-tET isn't a regular
diatonic tuning, and has different patterns than something like
Pythagorean tuning or 29-tET for the way that intervals "add up."

For example, if we use traditional Pythagorean or similar categories,
two 13-tET "fifths" of 8/13 octave or 738 cents add up not to a major
ninth but to an interval we might call a "minor tenth" at 1477 cents.
Similarly, the difference between an 8-step "fifth" and a 5-step
"fourth" isn't a "major second" (2 steps), but a 277-cent "minor
third" (3 steps).

A bit of experience with this, and some wise counsel from a more
expert musician, have led me to conclude that the best approach is to
"let 13-tET be 13-tET," describing the interval categories in terms of
scale steps rather than nomenclatures that may often tend mainly to
induce conceptual vertigo.

Having seen what can happen when authors attempt to explain
13th-century European vertical style in terms of the presence or
absence of 18th-century traits, I'll try to present 13-tET in its own
terms, or at least make my best effort as a beginner in this
direction.

Of course, this doesn't rule out the use of familiar terms where they
fit the structure of the tuning: for example, "semitone" and "tone"
for the 1-step and 2-step intervals. I also like "sesquitone" for the
3-step interval ("one-and-a-half-tones"), which appears along with the
semitone and tone as basic intervals of my versions of the medieval
diatonic modes in 13-tET.

For example, my diatonic Lydian has the sequitone as the first
interval:

3 2 2 1 2 2 1
0 3 5 7 8 10 12 13
0 277 462 646 738 923 1107 1200
277 185 185 92 185 185 92

By the way, there are a few incongruities of rounding -- using Monzian
fractions (e.g. 276-12/13 cents for the sesquitone) would avoid them.

There's not necessarily any harm in explaining, for example, how the
role of a 13-tET interval in a given neo-Gothic progression parallels
that of a usual Pythagorean interval -- as long as it's understood
that we are talking in useful metaphors.

Above all, as someone often rather historical in approach, I would
emphasize that 13-tET is a tuning with its own structure and patterns,
which might evoke many stylistic "allusions" without being limited to
them, just as Haresh Bakshi has written a fascinating comparison
between the raga system of India and Western European modes.

For now, I'll just share two neat experiences. The first is a really
beautiful pentatonic scale that I play above a vertical 8-step
interval (0-8) as the drone:

3 2 3 2 3
0 3 5 8 10 13

In a timbre where the 8-step interval (738 cents) has a concordant,
"3:2-like" quality, this sounds to me much like a pentatonic with what
Dan Stearns or Paul Erlich would term "2L + 3s" -- here it's the
charming converse pattern of "3L + 2s" (3 large, 2 small intervals).

Tossing in a semitone now and then at 7-8 or 12-13, I had a diatonic
Lydian mode -- and I love both patterns.

It was like a journey through some beloved Chinese and other Asian
musics, and also the 13th-century melodies of the _minnesingers_ or
courtly "love singers" of Germany, often with a pentatonic feeling,
favorite music of my college years, also reminding me of Joseph
Yasser's theory of a "pentatonic" element in Gregorian chant and
"Medieval Quartal Harmony."

Was this a journey at all like the odysseys of Dan Stearns through
landscapes of nature and of scalar patterns, whose stories and
metaphors in turn remind me of my own musical meditations on long
walks?

A curious theme of my pentatonic journey was the role of intervals
having the feeling of my beloved 3:2 and 4:3. Would other people hear
it this way? -- only they can answer that question.

I'll also give one very striking neo-Gothic progression in 13-tET,
raising the basic problem of how I should notate it.

In 13-tET, a usual neo-Gothic trine, the basic three-voice concord --
in JI terms 2:3:4 or a rounded 0-702-1200 cents, is 0-8-13 steps or
0-738-1200 cents. A very rich and spacious version of this sonority
adds a 21-step interval or quasi-3:1, 0-8-13-21 or 0-738-1200-1938
cents.

If I number the notes of this stable sonority as 0-8-13-21, then the
cadence would look like this, with signed numbers showing the
ascending (positive) or descending (negative) motion in steps of each
voice:

20 -- +1 -- 21
12 -- +1 -- 13
10 -- -2 -- 8
2 -- -2 -- 0

The first sonority, on steps 2-10-12-20, has a vertical structure of
0-738-923-1661 cents (or intervals above the lowest voice of 0-8-10-18
steps). This expands majestically, and compellingly, to the stable
0-8-13-21.

I look forward to writing more about the theory, but for now I'll say
that it sounds gorgeous, quite sufficent a reason in itself for a
well-timbred 13-tET.[2]

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3. A philosophical conclusion: musical ambiguities and metaphors
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An issue discussed by Paul Erlich, Joseph Pehrson, and others
is the question as to whether timbres maximizing the sensory
consonance of an interval such as 8/13 octave may tend to "blur" pitch
definition by comparison to usual harmonic timbres.

One reply might be that the concept of "blurring" can come up in many
creative periods of musical transition when familiar stylistic
patterns or sonorous expectations are challenged or "distorted." An
impartial, or at least relatively impartial, assessment, might focus
on the real musical values of the older patterns as well as the newer
ones often applauded in textbook histories of 18th-century or
20th-century European and related traditions as simple "musical
progress."

Of course, the new and innovative can and should be celebrated, but
with an awareness of the validity of the older styles and paradigms
also. A recognization of this point may lend perspective to the
question of harmonic vs. inharmonic timbres.

For example, the style of Dunstable and Dufay in the early 15th
century has been applauded since Tinctoris (1477) as the "font and
origin" of a new era of music, known as the Renaissance.

However, the medievalist Richard Crocker has credibly argued that from
another viewpoint, Dunstable can be seen as blurring or obscuring the
clear organizational patterns of 14th-century music.

Similarly, the innovations of Monteverdi around 1600 were decried by
at least one theorist as demonstrating "the imperfections of modern
music" and unwisely attempting to defy the "natural" categories of
consonance and dissonance. Yet his music did not invalidate the
artistic power of those categories, only their universality as the
_only_ way to compose pleasingly (as 14th-century music, also, does
not follow standard 16th-century patterns).

Around 1900, the innovations of Debussy could be seen as "blurring"
both tonality (sometimes suggesting a freer "neo-modality," for
example) and traditional consonance/dissonance distinctions.
Yet I see this neither as a "flaw" of Debussy's music, nor as a
barrier for people such as Paul Erlich who wish to explore the
possibilities of tonality in new systems such as the decatonic.

In "Sethareanizing" or "Carlosizing" or "Darregizing" 13-tET, I
sometimes need to remind myself that my purpose is not to come up with
a timbre/tuning combination indistinguishable from Pythagorean
intonation, but to seek a new kind of consonance with patterns often
radically different than historical tunings.

Just as visual Impressionism involves some deliberate blurring of
details -- and thus is an alternative to rather than a substitute for
other modes of expression in various world traditions -- so
tuning/timbre "pastelization" or Impressionism is only one stylstic
choice.

Possibly the "probabilistic" qualities of the technique are one of its
special attractions -- to have an 8-step interval in 13-tET, for
example, sound often like a convincing "3:2," sometimes like a kind of
minor sixth, and sometimes somewhere in-between.

Around four centuries ago, in the early 17th century, the use of novel
dissonances in place of expected consonances was described and
sometimes defended against critics as a kind of "poetic metaphor" in
the rhetoric of music, and the art of tuning/timbre may also be one
where intonational metaphors of sensory consonance can suggest
familiar patterns or open the way to new musical languages, possibly
both at once.

-----
Notes
-----

1. The "Puff Pipes" might suggest to me either a "portative organ"
played by a single person operating the bellows with one hand and
negotiating the keyboard with the other, which as its name suggests
can be carried around; or a larger "positive" organ. The latter
category might include Nicola Vicentino's _arciorgano_ or "superorgan"
built of wood and apparently featuring the same basic tunings of 36
notes per octave as his _archicembalo_ or superharpsichord.

2. Incidentally, the stable 0-8-13-21 sonority of this progression
features a set of nonunisonal intervals with sizes of (5, 8, 13, 21)
steps, a portion of the Fibonacci series. Fibonacci or Golden Section
lovers might also note that a 9-step interval at ~830.77 cents, or a
Monzian 830-10/13 cents, is very close to 21:13 at ~830.25 cents, and
not far from Phi itself at ~833.09 cents. In 1981, John Chowning used
a scale based on Phi^1/9, very close to 13-tET, for his composition
_Stria_; see Brian McLaren, "A Brief History of Microtonality in the
Twentieth Century," _Xenharmonikon_ 17:57-110 (Spring 1998), at p. 86.

Most respectfully,

Margo Schulter
mschulter@value.net

An exciting new tuning experience

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