Yahoo Tuning Groups Ultimate Backup makemicromusic Practice and theory in 13-tET -- Hi, Jacky

Hello, there, brother Jacky, and everyone.

A couple of days ago I noticed a bit of discussion on "Why be
practical?" and I'd say that practice and theory can go together; but
the theory can be lots more fun, and more fruitful, when it gets
informed by some direct experience.

Yes, I'm all wrapped up in the excitement of getting acquainted with a
new scale, and Jacky, I don't think that my choice of this one is
going to disappoint you <grin>.

I'm not sure if you'd guess this: it's 13-tET, a really neat tuning
for neo-Gothic music that supports a lot of "textbook progressions"
based on inspired by medieval and Renaissance European music, and at
the same time rewrites a few of the rules for things like adding
intervals together.

What's my method? Basically: go to the keyboard, start playing, try
some familiar progressions, find out what sounds similar, or maybe
different, and see how both the similarlities and differences might
lead in new directions -- or give a new kind of color to some favorite
old ones.

To illustrate one humorous kind of relationship between practice and
theory, I'll tell a story that really happened today.

In exploring 13-tET with the TX-802 "Piccolo" timbre (A27) that I
already knew could make 738 cents sound like a stable fifth -- from
the meantone experiment in this issue of TMA -- I quickly found all
kinds of consonances and pleasant progressions.

One of my favorite consonances is something like G3-C4-D4-G4 (C4 here
shows middle C), with a fourth, fifth, and octave above the lowest
note. When I played it in 13-tET, it sounded concordant and beautiful,
just as in Pythagorean or some other accustomed tuning.

Then I looked at the numbers, and counted the steps -- and concluded
that what is "supposed" to be a major second in the middle (C4-D4)
must actually be a 13-tET minor third of 3 steps. In this scale, a
usual fourth plus a minor third makes a fifth (5 + 3 = 8). This led me
to conclude that I had been playing 0-5-8-13, or 0-462-738-1200 cents.

Well, I said to myself, that's fine: 13 just "adds up" a bit
differently, and that's one of the charms of this scale.

"If it sounds nice, don't argue with it."

Well, at least I'll stand by that last conclusion. However, on
reconsidering my arithmetic, I realized that that "major second" was
actually a major second of two steps, something like 184.6 cents --
which meant that something else had to be different. It turned out
that I was playing -- if I got the figures right this time -- a
sonority of 0-5-7-13, or 0-462-646-1200 cents with the "fifth" G3-D4
at around 646 cents instead of the usual 738 cents.

Whatever I played, it sounded like my beloved 6:8:9:12, as I'd say in
JI lingo: here I would sum up, "Enjoy the practice, the theory will
follow even if the math needs a bit of proofreading" <grin>.

Another reason to rely on practice, even if there's already a lot of
great theory out there, is that the people who've written that theory
aren't necessarily coming from _your_ musical viewpoint, and that
viewpoint can make just as much difference as interval sizes or
tuning/timbre interactions.

That means that if you _really_ want to find out about a tuning, you
need to try it -- not to invalidate everything that others have done,
but to contribute a new viewpoint to all that they've accomplished.

For example, I've learned today that 13-tET, in the right timbre,
offers beautiful versions of some "textbook" Gothic or neo-Gothic
progressions -- and also certain Renaissance or Xeno-Renaissance
progressions! -- with some creative "warps" and surprises.

It can be really neat for some slow, note-against-note progressions,
and also for a modal melody against a drone. I can take a drone on D,
improvise above it in Dorian, and feel much as if I were in
Pythagorean. Then a bit of theoretical reflection reveals that the
"fourth" D-G happens actually to be 554 cents insteaad of 462 cents --
so what else is new?

By the way, here's how I arrange my keyboards, with two versions of
"F#," one mapped to each keyboard, and the other notes the same:

92 276 646 831 1015
1 3 7 9 11
C#3 Eb3 F#3(2) G#3 Bb3
C3 D3 E3 F3 G3 A3 B3 C4
0 2 4 5 8 10 12 13
0 185 369 462 738 923 1108 1200
------------------------------------------------------
92 276 554 831 1015
1 3 6 9 11
C#3 Eb3 F#3(1) G#3 Bb3
C3 D3 E3 F3 G3 A3 B3 C4
0 2 4 5 8 10 12 13
0 185 369 462 738 923 1108 1200

Maybe especially for Dan Stearns, here's a look at the pattern of
scale steps in this kind of "diatonic" 13-tET arrangement for a mode,
let's take that D Dorian I mentioned, counting steps or cents from the
final or note of repose D:

2 1 3 2 2 1 2
D E F G A B C D
0 2 3 6 8 10 11 13
0 185 276 554 738 923 1015 1200

It's curious that the F-G step, really a "minor third," can sound more
or less like a "whole-step" -- and sometimes the structure makes the
usual resolution of a sonority sound quite strange or "nondiatonic," a
bit like 20-tET. At other times, it seems quite routine, with the
progressions flowing much as in Pythagorean or 29-tET or whatever --
in it's own way.

Mary, it reminds me of you when I reflect on the nice approximation of
Phi in this scale, actually very close to 21:13 (two numbers in the
Fibonacci series), at around 831 cents. It's funny that the "thirds"
and "sixths" in this scale are all types that I'm familiar with from
other neo-Gothic tunings, but they fit together a bit differently.

Anyway, my two conclusions at the moment are yes, one can make
neo-Gothic music in 13-tET -- and yes, practice has something very
special to offer, not least to theory.

Thanks for _Galunlati_, which I should be reviewing here soon, and for
all your encouragement in friendship and by example.

With peace and love to all,

Margo

🔗nanom3@...

Hi Everyone

I've been playing with Wilson's Scale Tree, Horagram 11, which is 1
phi +0/3 phi +1). I found a lovely scale in his 7th ring, courtesy
of David Finnamore. It is

0 205 332 537 663 868 995

It is extremely soothing and calming (really - even I noticed :-))
and I've been playing it all day . I've included here a small clip,
and my plans are to expand it into a piece for yoga that I have been
commissioned to do.

http://64.224.182.41/Golden_Rings.html

Does anyone know any other of Wilson's scales from the horagrams that
are this soothing. I'm assuming the tranquility has something to do
with its phi properties, and I'm wondering if mathematically there is
someway to find similar scales from the scale tree, without trying
each one. Paul I think this is a question you are well qualified to
answer. I also think it is a practical question since I am planning
on making more music from the scales but don't have the time to try
every one (although I plan to over the next few years) but Jon you
might want to moderate math answers elsewhere.

Also on the very practical side I am using Waves C4 parametric eq and
compressor for the first time for some hiss removal but I've done no
other digital processing (except dither) and though it might serve as
a springboard for discussion about processing audio files for the
web.

Mary

🔗nanom3@...

🔗Paul Erlich <paul@...>

--- In MakeMicroMusic@y..., nanom3@h... wrote:

> Does anyone know any other of Wilson's scales from the horagrams that
> are this soothing. I'm assuming the tranquility has something to do
> with its phi properties, and I'm wondering if mathematically there is
> someway to find similar scales from the scale tree, without trying
> each one. Paul I think this is a question you are well qualified to
> answer.

Perhaps you liked this one because it has "whole
steps" close to 9:8 (204 cents). Blackwood
observed that it is hard to write good melodies
without whole steps. Look for other scales in the
Horagrams with steps around this size. Personally I
don't believe the precise phi properties have any
perceptual relevance -- they just guarantee that
you'll have an infinite series of scales coming out of
each of the horagrams.

Anyway, I'm just guessing about the whole steps --
it may very well turn out that you really like _all_
of the Horagram scales, as well as many other
MOS scales without the phi property. I think they
all work well melodically because there are two
step sizes, which are distributed as evenly as
possible around the scale.

P.S. Don't forget to try all modes of each scale!

🔗nanom3@...

🔗mschulter <MSCHULTER@...>

Hello, there, Mary, and trying to keep this fairly practical, I'd like
to address a very important question you raise: the meaning of calling
an interval a "Wolf," and the usefulness of keeping this in historical
perspective when making new music -- or music using new mixtures of
old styles and new timbres.

First of all, in JI terms, I'd say that 537 cents is around 15:11, and
663 cents around 22:15. One term that Dave Keenan has come up with for
the first type of interval is "superfourth," and 20-tET for example
has a routine diminished fifth the way I arrange it (e.g. B-F) at 540
cents.

You can hear this 540-cent interval in the opening passage for the
"Stern-Brocot Treehouse" piece I started and still need to finish:

MIDI example: <http://value.net/~mschulter/20tgz002.mid>

Now for the term "Wolf": historically, it means an interval that
resembles a regular consonance, but in a given set of styles and
timbres is different enough that it can't be treated as if it were
that consonance.

For example, a standard 12-note Pythagorean tuning based on a chain of
pure 3:2 fifths at around 702 cents will have a diminished sixth or
"Wolf fifth" (e.g. G#-Eb) at around 678 cents, far enough from 3:2 so
that in a typical Gothic harmonic timbre, that narrow "fifth" will
beat very prominently, and sound quite different from a usual one.

Similarly, moving to the Renaissance, in a 12-note version of
1/4-comma meantone we have regular fifths at around 697 cents --
tempered slightly narrow of 3:2 -- and a diminished sixth at around
738 cents. Again, that odd "fifth" such as G#-Eb -- this time wide
rather than narrow -- will sound very different in most timbres from a
usual fifth.

A story tells us that the very prominent beating of either type of
"odd fifth" reminded people of the "howling of Wolves," and thus the
term "Wolf."

By analogy, someone oriented to this kind of style, for example, could
say that 663 cents is a "Wolf fifth" because it's about 39 cents from
3:2, close enough to somewhat resemble a fifth, but far enough that
it's likely to sound radically different than a 3:2 in typical timbres
for traditional Western European compositions.

In other stylistic settings, however, an interval of 663 cents may
have very different meanings: to call it a "Wolf fifth" suggests, at
least to me, that you want to hear it as a stable "fifth" but can't,
at least in a given timbre. However, what if you're using it
intentionally as another kind of interval?

In 20-tET, for example, 660 cents would be for me an ordinary
"augmented fourth" or "tritone," e.g. F-B, and would typically
progress in parallel motion to a 480-cent "perfect fourth."

Also, in just the right timbre, an interval such as 738 cents can
actually sound like the stable concord it's a bit too far from to
substitute for in usual historical practice. Then we can have a
"meantone well-timbrement" where either 697 cents or 738 cents is a
concordant "fifth."

How about 13-tET, for example, a very different tuning in many ways
from either medieval Pythagorean or Renaissance meantone, where an
interval of 8/13 octave or 738 cents (almost exactly the size of the
meantone "Wolf") happens to be the closest approximation of a "fifth"
at or near 3:2?

Here there are two approaches. In lots of timbres, we might take the
attitude that 13-tET doesn't have anything very close to a usual
"fifth," and compose or improvise based on other categories and
patterns. Here 738 cents could have various musical meanings,
different from those of a "fifth" in historical Western European
styles of composition.

Another approach is to choose a timbre where 738 cents can resemble a
"usual" stable fifth closely enough that we tend to hear it as
belonging to the same category, and then using it as a fifth in a
style like neo-Gothic, for example.

In the first case, it isn't a "Wolf," in my opinion, because we're not
trying to make it fill the place of a usual "fifth," only to find that
it doesn't fit.

In the second case, it isn't a "Wolf" because in the right timbre, the
interval actually fits as a stable "fifth," at least in the ear of a
given listener.

One practical way to sum this up is to say that a "Wolf" is the right
interval in the wrong style and timbre -- and even in a musical
setting where an interval is generally considered a Wolf, it can
sometimes be used deliberately as a very telling special effect.

In peace and love,

Margo