Running with meantone Wolves

Hello, there, everyone, and here's an example with another kind of
Wolf: the augmented third or "Wolf fourth" in 1/4-comma meantone, a
16th-century European tuning featuring pure major thirds at 5:4.

While meantone tunings are standard for Renaissance and
Xeno-Renaissance styles, they also offer certain "odd" augmented or
diminished intervals which can invite excursions in a 13th-14th
century neo-Gothic style. This kind of excursion led me to the
progression that follows.

One "odd" interval in meantone that deserves more enthusiastic use is
the "Wolf fourth" or augmented third, for example Eb-G#. Here's a
cadence in which this interval sounds very pleasing and "jazzy" to me:

MIDI example: <http://value.net/~mschulter/mnqwf001.mid>

In 1/4-comma meantone with pure 5:4 major thirds, the tuning for this
example, the Wolf fourth has a size of ~462.36 cents, right around the
zone of transition between a very large major third and a very small
fourth, but sounding a bit more "fourthlike" to me. Here's the
progression, with C4 as middle C:

Bb4 A4 G#4 A4
F4 E4 Eb4 E4
D4 C4 B4 A4

The active cadential sonority B4-Eb4-G#4 features a meantone
diminished fourth at 32:25 (around 427.37 cents), in neo-Gothic terms
a quite respectable major third which expands in the usual manner to a
fifth.

Part of the fun with this kind of tuning is the possibility of
shifting between a Renaissance style and a neo-Gothic style in the
same piece, making use of the different intervals the scale has to
offer.

In peace and love,

Margo

Hello, everyone, and a special welcome to Brian McLaren, who now
shares his extraordinary contributions in practice and theory with
us.

Thank you especially for your very important point that the "mood" of
a tuning is determined not only by the tuning's structure, but by the
style of a given composition of improvisation. Your example of
Debussy's Impressionistic approach to 12-tET really brings this point
home.

Based on my own much more modest scope of practice and experience, I
might add a few comments about certain tunings you mentioned, and
offer an example of one of the "moods" of 22-tET.

For me, there are at least three main factors in this "mood" equation,
all of which you mention:

tuning
style
timbre

For example, I have found that the question of whether 23-tET has
anything like a "perfect fifth" is a very timbre-dependent question.
In the right kind of timbre, I've found that 13/23 octave or 678 cents
can take part in a sonority of 0-678-1200 cents that sounds like a
stable neo-Gothic concord to me.

With 17-tET, I would say that both style and timbre shape my feeling
for the "mood" of this tuning. Since in a Gothic or neo-Gothic setting
I _expect_ usual major and minor thirds to be complex and unstable,
the main question is just _how_ complex or tense?

Here the way I would express things is to say that 6/17 octave or
423.53 cents is a very _rich_ major third, and that downplaying the
beats a bit allows me to relish the richness and the delightful
expansion to a fifth, while finding the third itself _relatively_
concordant, its stylistically proper role.

As I remarked in earlier posts here with musical examples, the neutral
intervals of 17-tET have a "mysterious" or "Impressionistic" quality
for me; there I focused especially on the neutral seventh or augmented
sixth of 15/17 octave or about 1059 cents:

/crazy_music/topicId_99.html#99
/crazy_music/topicId_105.html#105

The neutral thirds or sixths have a similar quality for me, and I hope
soon to post on this with more examples.

Now we come to 22-tET, which I have found a very pleasant neo-Gothic
tuning. Usual diatonic progressions and spellings are all there, but
with some nice touches to make the mood a bit "different."

One feature of 22-tET is that the regular major and minor thirds have
sizes close to simple ratios of 9:7 and 7:6, so that a usual sonority
like G3-B3-D4-E4 (with C4 as middle C) at about 0-436-702-927 cents is
not too far from a JI tuning of 14:18:21:24. This expands very nicely
to F3-C4-F4, with three strong interval resolutions (major sixth to
octave, major third to fifth, and upper major second to fourth):

E4 F4
D4 C4
B3 C4
G3 F3

MIDI example: <http://value.net/~mschulter/22tei002.mid>

The diatonic semitone at 1/22 octave or about 54.55 cents, actually a
kind of "diatonic quartertone," is something I find pleasant and
recognizable without any problem, a point I was curious about when I
first tuned this scale. I'm fascinated by how melodic semitones of
this size can sound convincing as regular diatonic steps, and how
they've become something I much treasure in various scales.

One neat touch of 22-tET gives what might be called a subtly different
quality to another typical neo-Gothic progression:

F4 E4 D4 C#4 D4
C4 B3 A3 G#3 A3
A3 G3 F3 E3 D3

<http://value.net/~mschulter/22tei001.mid>

Here each upper voice outlines the descending melodic interval of a
diminished fourth: F4-C#4 or C4-G#3. However, in 22-tET this interval
actually has the size of a kind of large minor third, around 327.27
cents! The result is a special kind of melodic flavor for this type of
cadence.

One point I would make is that style can affect not only how one
describes the "mood" of a tuning, but how one defines and spells its
intervals. The spellings I routinely use for 17-tET and 22-tET, for
example, fit at least my kind of neo-Gothic style; for a different
style, a different spelling system might be much more convenient.

Again, these are only my own opinions, but the topic of tuning,
timbre, and style has room for lots of views, and lots of creative
comparing of notes.

Most appreciatively,

Margo Schulter
mschulter@...

Hello, there, everyone, and here are a few random reflections on the
"xenharmonic bias" of a scale, along with a curious MIDI example in
17-tET.

While composers and theorists such as Ivor Darreg and Brian McLaren
have spoken of the bias of a tuning "toward melody" or "toward
harmony," this raises an interesting question: "_What kind_ of melody
or harmony might be assumed here?"

For example, if a microtonalist were to take the view that the seventh
harmonic is an essential ingredient in "good harmony," then any tuning
without a close approximation of 7-based ratios would be "biased
toward melody." Someone taking a different approach to vertical or
harmonic style might reach a very divergent conclusion.

A different approach might be to ask, "What types of melodic or
vertical style might this scale favor?"

For example, 5-tET might have a melodic bias toward a style like that
associated with the slendro scale of gamelan; while every gamelan has
its own tuning, with lots of intonational nuances, 5-tET is a fairly
close representation.

Vertically, 5-tET might be said to have a bias toward rather complex
and shimmering fifths and fourths at 720 cents and 480 cents, also a
feature of gamelan textures.

These aren't necessarily the only biases of 5-tET, just some obvious
ones to illustrate the "two-dimensional" approach of looking both to
melodic and vertical possibilities for any given tuning.

The fun of comparing notes and biases -- whether of the scales, or of
the xenharmonicists <grin> -- might get especially exciting with a
tuning like 17-tET.

If we're looking at Western European compositional styles, for
example, then 17-tET with its fifths and fourths quite close to pure
and its very active regular thirds and sixths seems to have a bias
toward quintal/quartal harmony (medieval or 20th-century).

The contrast between the large whole-tones at 3/17 octave (~211.76
cents) and the small diatonic semitones or thirdtones at 1/17 octave
(~70.59 cents) suggests a bias toward brilliant diatonic melody.

This isn't exactly the latest news: Ivor Darreg was writing about
17-tET in more or less these terms two decades or more ago. However,
we now run into an interesting question: what kind of timbre do we
want?

A neo-Gothic microtonalist might say, "Let's Sethareanize a bit to
make those active thirds a bit more blending, or less 'dissonant,' so
that they can sound like partial or imperfect concords. They should be
intriguing and unstable, but also relatively euphonious."

A "modernist" familiar with Darreg and McLaren, however, might
suggest, "Why not let those major thirds serve as outright discords,
resolving down to seconds? -- we can rewrite the historical rules for
15th-19th century suspensions, and have the third resolve down to the
second instead of the fourth to the third."

The result might be something like this:

MIDI example: <http://value.net/~mschulter/17tet008.mid>

Then, again, a style treating the neutral thirds of 17-tET as primary
concords might be said to have a "nontraditional tertian or triadic
bias." Here's an open question: what kind of melodic bias why this
type of style invite?

Yet again, if we use a pentatonic melodic style with fifths and
fourths as the main concords, that's another kind of melodic bias
nicely mixing with a vertical "quintal/quartal" bias.

A possible conclusion: take one tuning plus two xenharmonicists,
and you're likely to get at least three biases.

Most appreciatively,

Margo Schulter
mschulter@...

Hello, there, George Zelenz, and thank you for sharing with us an
experience which moves me to send the most benevolent wishes for a
full healing of hand and spirit, along with a bit of music.

Here's an opening sketch for a piece in 20-tET I call "Stern-Brocot
Treehouse," maybe something with a calm kind of energy sort of swaying
in the breeze:

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

You've shared with us a moment of hurt, pain, and vulnerability,
something for all of us to reflect on, and to honor your trust in
making us a part of the healing process.

In friendship,

Margo

Margo!

Wow.

I'm so touched, i'll say it backwards. woW.

I am so very honored to be gifted with your music.

Presciently, you've created a mood i'm familiar with. As a kid, i spent much
time making tree houses for my sister and myself. On summer afternoons,
feeling melancholy over a less than ideal childhood, i would often feel a
bit sad, but ok. Basically happy. Resigned.
Swaying high among the shimmering leaves, i've heard this music before.

What a flood of memories do i happily drown through.

Margo, your the best.

George Zelenz

In-Reply-To: <Pine.BSF.4.20.0107082031200.50006-100000@...>
Margo wrote:

> Here's an opening sketch for a piece in 20-tET I call "Stern-Brocot
> Treehouse," maybe something with a calm kind of energy sort of swaying
> in the breeze:
>
> MIDI example: <http://value.net/~mschulter/20tgz002.mid>

I like this! It sounds at home with the GM timbres, which is a rare
thing. Ends abruptly, but that comes with the territory.

Graham

Hello, there, everyone, and here's a JI example featuring thirdtones
at 28:27 (~62.96 cents), the "7-flavor semitone" as it's called in
neo-Gothic music.

While I posted a similar example of "circumambulation" by a chain of
whole-tones last month, this one features an "expansive/intensive"
quality, with major thirds expanding to fifths, major sixths to
octaves, and major seconds to fourths, by way of ascending 28:27
semitones. One melodic step in each voice gets altered by a
Pythagorean comma in order to make the octave an even 2:1 -- not to
exclude other possibilities!

MIDI example: <http://value.net/~mschulter/sesci002.mid>

In the music of Gothic Europe around 1200-1400, cadences of this
general kind occur based on a standard Pythagorean tuning, but here
the "7-flavor" JI (ratios of 2-3-7, e.g. thirds at 9:7 and 7:6) and
the extra-compact 28:27 semitone maybe give the music a different
nuance.

As I hear them, 13th-14th century cadences are as compelling and
beautiful as anything in later European styles, and they seem open to
many intonational variations, from pure Pythagorean or 2-3-7 JI to
some wild Sethareanized tunings.

However, one the most appealing ways of approaching these progressions
is through just intonation, and the 28:27 semitone or "thirdtone"
feels to me very congenial to the character of this music.

Peace and love,

Margo

Hello, there, everyone, and I'd like warmly to thank Brian, Graham,
and others for some responses to my remarks about xenharmonic "moods"
or "biases" of different tunings.

First, from what has been explained, I would now regard "xenharmonic
bias" as a style-specific concept relating to styles like those of
Western Europe in the later 17th-19th centuries where harmony is based
on major/minor keys and progressions such as I-IV-V-I.

For other styles, this concept may not really apply: that goes for the
Gothic music of 13th-14th century Europe, for example, as well as
Javanese gamelan, Japanese gagaku, Thai or Burmese music based on
or approximating 7-tET, or the traditional ensemble music of Georgia
or the Solomon Islands, etc.

My enthusiastic response to what I call "Sethareanism" (see next
paragraph) is based on musical experience: I try a combination of
tuning and timbre, play some music in 13th-16th century European
styles, and often find myself amazed, delighted, and overwhelmed with
a new beauty.

Brian, thank you for a vitally important point: the approach of
adjusting timbre to scale indeed goes back to John Pierce, and is
something discussed by Ivor Darreg in his _Xenharmonic Bulletins_
going back two decades or more, not to mention others such as Wendy
Carlos. It's your historical writing and documentation that made me
aware of this, and frequent reminders about such foundations for
"Sethereanizing" place the achievements of Bill Sethares in a richer
perspective.

For the kind of neo-Gothic or Xeno-Renaissance music I play, Setharean
timbres can have a truly revolutionary effect. Of course, with other
styles including later European ones, your mileage -- or kilometrage --
may vary.

For example, last night I tried a certain mixture of timbres with
23-tET, and found the effect with a 14th-century style at once
eccentric, offbeat, zany, and somehow at some level an ultimate
refinement of fashion. I'd almost call it a kind of "intonational
syncopation," like the rhythmic intricacies of the period.

It was a wild interpretation, with lots of zing and zonk. The fifths,
fourths, and cadences were recognizable -- and exhilarating, in an
"over the top" kind of way.

I also tried a familiar three-voice Italian piece in what seems to be
a 13th-century style, and found it quite recognizable, also.

Possibly the style of Gothic or neo-Gothic music, with an exuberant
contrast between stable and unstable sonorities, takes more kindly to
Setharean "bending" than some other kinds of music -- anyway, I call
it a revolution, at least for me.

While Renaissance music has a very different and more delicate
approach to concord/discord, I've found that under certain conditions,
Sethareanized fifths well outside the range of 680-720 cents can serve
both as vertical intervals and as direct melodic intervals. While
directed medieval progressions most typically favor stepwise or
thirdwise motion in all voices, Renaissance music typically mixes bass
motions by seconds, thirds, fourths, and fifths.

Here I'd want to emphasize that medieval and Renaissance styles are in
many ways radically contrasting, as are the standard tuning systems of
medieval Pythagorean and Renaissance meantone.

What the two kinds of music may have in common is an often fluid and
flexible sense of modality, in contrast to the tonality of the 18th
and 19th centuries. Might this fluidity permit more Setharean "leeway"
in the stretching or compressing of intervals, as long as sensory
"consonance" or smoothness is maintained?

For example, I find a usual Renaissance semitone of around 117-120
cents in a typical meantone tuning as quite normal, although many
listeners are reported to find it too large or "dull," and composers
such as Darreg have specifically urged the use of a narrower cadential
semitone. Is it possible that 16th-century modality with its "pastel"
colors and delicate shades invites large semitones, but that people
accustomed to later styles like them smaller?

At the other extreme, I find a diatonic semitone of 54.55 cents in
22-tET quite normal, also, for neo-Gothic music -- note that this is
only one interpretation of semitones in that scale, of course.

Maybe one conclusion might be that I'm not only on the cutting edge of
"Sethareanizing," but I've gone _off_ the edge, and should enjoy the
music now that I'm there, but not necessarily expect anyone else to
share my taste <grin>.

Anyway, now that I've maybe learned how to solve a minor technical
glitch with making a tape of some of this music, I look forward to
sharing "Sethareanization" in action -- with lots of gratitude to
Pierce, Darreg, Carlos, McLaren, and all the others who have
contributed to this fascinating dance of tuning, timbre, and style.

In peace and love,

Margo

Ms. Margo,

--- In crazy_music@y..., mschulter <MSCHULTER@V...> wrote:
> Anyway, now that I've maybe learned how to solve a minor technical
> glitch with making a tape of some of this music, I look forward to
> sharing "Sethareanization" in action...

I'm not sure where you are at, with your mention of "glitch", but if
you are able to get a piece onto tape (but no further) I would be
more than happy to digitize it and encode it to mp3 like all the
other kids around here do, and upload it for you. Either that, or
assist you in gathering the tools to do that yourself. Whichever
direction you decide to take, an email will get me to spring into
action.

Not for just anybody, mind you, but you are a bit special in my book!!

Cheers,
Jon

Hello, there, everyone, and I'd like to offer a composition with JI
quartertones, as suggested by Brian McLaren, as a tribute to my
wonderfully creative and intrepid sister in music Mary Beth Ackerman,
and as an invocation for peace within our community.

Please let me express my appreciation to you, Brian, for effectively
commissioning this piece; and to you, Mary, for your powerful example
of all-encompassing art and technical expertise in composing and
making music, and your generosity in sharing it.

Thanks also to you, Joe Monzo, amiable oracle of many labyrinth-like
lattices, for providing inspiration through our shared fascination
with the music and theory of Marchettus of Padua.

The title of this piece is: "Salutation for Mary Beth Ackerman,
envision'd as Lysistrata." It's in a 24-note tuning I call the
"Pythagorean enharmonic," of which more below.

MIDI composition: <http://value.net/~mschulter/mary002.mid>

Before dealing with tuning and style, maybe I should join you, Mary,
in addressing something just as vital: the process of our commmunity.
The active peacemaking of Lysistrata has its counterpoint in various
times and places, and here and now is one of them.

One story I've reflected on a lot these past hours is a special gift
of the Great Turtle Island, one Indigenous name for the continent also
named by its invaders "the Americas."

It is said that maybe sometime around 1600 by European reckonings --
the age of meantone with pure or near-pure 5:4 and 6:5 thirds on
keyboards, maybe an idyllic revery for you, John deLaubenfels -- wars
were devastating the great Confederation of peoples known as the
Haudenosaunee or "Long House," and also as the Five Nations, later the
Six Nations, and sometimes also as the Iroquoian peoples.

As the name "Long House" suggests, the communities and Nations within
this Confederation were as families living within one house; but
conflict was threatening that house from within, as it can threaten
our smaller community.

Then the women declared that since only they knew the secret of birth,
there would be no more children until peace prevailed. Peace did
prevail.

Our community, also, needs what is known among the Six Nations as a
Law of Great Peace -- not necessarily a written law, but a union of
harmonious consensus and sometimes even a friendly concord of
discords.

Mary, how appropriate it is that my first complete composition made
available in digital form, however modest, should be addressed to
you. When Maddalena Casulana pubilshed her first madrigal collection
in 1566, she dedicated it to Isabella de' Medici, a musician and
likely also a composer -- but here the roles are reversed, for you are
the established composer and I the one who seeks to follow your
example.

The scale is what I call Pythagorean enharmonic, with two 12-note
Pythagorean tunings a 459:448 apart, about 41.99 cents.

Brian, when I saw your call for a JI quartertone piece, I realized
that this might be just the tuning for it; and Monz, I couldn't resist
also the chance to share another possible keyboard model for something
that just might approximate the scheme of our beloved Marchettus.

My original idea for this 24-note system was to combine a basic
Pythagorean tuning with pure sonorities at 14:17:21 (around 0-336-702
cents), what I'd call a division of the pure fifth into "supraminor"
and "submajor" thirds at 17:14 and 21:17.

Additionally, Monz, this tuning happens to feature a division of the
regular Pythagorean diatonic semitone or limma at 256:243 or around 90
cents into the 42-cent diesis between the keyboards, plus a neat
48-cent "quartertone" more precisely at 114688:111537 (~48.23 cents).

Both you and Jay Rahn have proposed that at least some of the dieses
of Marchettus had a monochord size of 37:36 (~47.43 cents), or almost
the same size.

Please let me explain that while my "17-flavor" sonorities seem to be
a feature of _neo_-Gothic music rather than known medieval practice or
theory, the use of extra-narrow cadential "dieses" and extra-wide
major thirds before fifths and major sixths before octaves is how many
people including Rahn and I read Marchettus himself.

The opening and closing three-note progressions in this piece have the
outer two voices borrowed from examples in Marchettus. For example,
here's the final cadence, with C4 as middle C, and an asterisk (*)
showing a note on the upper keyboard raised by a 42-cent diesis:

C#*4 D4
G#*3 A3
E3 D3

Here the upper voices ascend by 48-cent "quartertones," with the
cadential major third and sixth at about 450 cents and 948 cents --
the rounded values suggested by Rahn.

A related kind of cadence not described by Marchettus uses 48-cent
quartertones in descending motion, with an extra narrow minor third
and minor seventh at around 252 cents and 954 cents contracting
respectively to a unison and fifth:

F4 E*4
Bb3 A*3
G*3 A*3

There's also a very nice "2/3-tone" at 68:53 (~132.20 cents) that
occurs in this piece in a "17-flavor" progression where a pure
14:17:21 sonority resolves with the 17:14 supraminor third contracting
to a unison and the 21:17 submajor third expanding to a fifth:

C#4 D*4
A*3 G*3
F#3 G*3

By the way, Brian, this tuning has some extra goodies that especially
remind me of you. By adding a 42-cent diesis to a Pythagorean
augmented second or schisma minor third at 19683:16384, we get
intervals in three positions of 9034497:7340032 or about 359.59 cents,
only differing by about 0.12 cents from another interval you've
mentioned recently, 16:13 (about 359.47 cents). An example would be
F4-G#*4 or Bb4-C#*5.

Anyway, enough math for the moment -- but congratulations, Brian, on
that JI tuning with 19 pure 5:4 thirds, something that wouldn't have
occurred to me, and your 19-tET comparison is really neat. It's
amazing all the ways out there to pet a cat and get those ratios
purring, so to speak.

Thank you Mary, Brian, Marchettus, and Monz, among others, for your
ideas, inspirations -- and the opportunity to share with you in a
common community.

Above all, I want to say through this piece what peace activist
Barbara Deming has said: "We are all part of one another."

In peace and love,

Margo

Hello, there, everyone, and I'd like at least to offer a prompt
correct correction both to the post I sent a few minutes ago, and to
the title of my composition:

"Salutation for Mary Beth Ackerley, envision'd as Lysistrata"

How strange that I checked a CD of your music today to confirm the
spelling of your name -- but that somehow I still got it wrong, and
realized this immediately after posting.

Curiously, I find on checking that I spelled your name correctly in my
crude "score" -- the Scala MIDI definition file.

Maybe compositional excitement, concern over events here, and a bit of
tiredness contributed to this most embarrassing mistake for me; but
then, knowledge of one's own fallibility and its sometimes humorous
aspects can be an important ingredient for peace, inner or communal.

Most apologetically, with deepest appreciation,

Margo

Dear George Zelenz, thank you so much for your generous and moving
words in response to my sketch for the opening of "Stern-Brocot
Treehouse," prompting me in reply to send more healing encouragement.

Thank you also, Graham Breed, for your response, to Brian McLaren for
much appreciative incitement to new music, and to Joe Monzo for
mentioning a choral piece I much look forward to hearing, maybe on
cassette or CD.

This kind of generosity is all the more reason why I need to find out
where the rest of "Stern-Brocot Treehouse" is going, something I may
learn through some more improvisation.

There are lots more messages to answer and thanks to share, but at
least this is a start.

Most appreciatively,

Margo Schulter
mschulter@...

>
> "Salutation for Mary Beth Ackerley, envision'd as Lysistrata"
>
> I'm traveling and have have stolen five minutes here on a 28k
laptop I share with my partner who is getting ready for tomorrows
trades. I can't wait to listen to the piece but the speakers aren't
working and I'm too tired to figure that out.

However my partner is having a good time describing his recollections
of Aubrey Beardsley in association to the name Lysistrata Such
memories.

I can't wait to hear it.

And John thank you for your kind review. I am starting the second CD
and welcome the encouragement.

Mary

Hello, there, everyone, and I'd like respectfully and ardently to
affirm that, as Mahatma Gandhi and Barbara Deming among others have
affirmed, peace and nonviolence are the options of the strong.

Through the ages, women have had to stand up to bullying of all kinds,
not least women composers such as Maddalena Casulana and Vittoria
Aleotti, to mention only two in the Western European tradition.

The enemy is not any human being, but it is _bullying behavior_ in
which humans sometimes engage. Women ranging from Fannie Lou Hamer in
Mississippi, USA, to Leyla Zana in Kurdistan have endured violence and
risked their lives in order to resist such behavior without emulating
it.

Cordially but passionately dissenting from some views expressed here,
I'd like to suggest that "spanking a bully" can be viewed as itself a
kind of "bullying behavior," because it involves physical violence
against a subdued person, exactly what we want to stop rather than to
emulate. If you reword that: "Bullying behavior tends to go on until
it is resisted and restrained," then I have no problem.

Normally I would tend to post about these things in some newsgroup or
other discussion forum on creative nonviolence or the like rather than
this one, which is mainly about making "crazy_music" and maybe
philosophizing a bit about one's methods or theoretical outlook in
doing so. (Yes, I regard myself as a theorist.)

What I'd like to suggest are some possible approaches to civility
which may be at once "pro-crazy_music" and "anti-bullying." The idea,
as I see it, is to keep focused on sustaining each other's music
making, and celebrating our positive worldviews behind or shaped by
the music.

1. ERV WILSON'S ADVICE: "Talk about what you're doing, not
about what you're not doing."

2. FOCUS ON OUR MUSIC. While any strict or rigid rule would
be counterproductive, I try to keep theoretical comments
focused mainly on what I'm doing, or at least on what
I'm planning on doing -- or what might be helpful feedback
or background for what someone else is doing or plans on
doing.

3. RECOGNIZE ROOM FOR DIVERSITY AND DIFFERENCES. As it
happens, I find 20th-century pantonal music such as
Schoenberg's or Berg's easier listening than some
19th-century European music -- and if 99.9% of the
people in some psychoacoustical survey show different
tastes, that doesn't bother me.

4. CELEBRATE OUR KOOKINESS. As a self-proclaimed devotee
of the high art of microkookality, I take the view that
to compose, improvise, or celebrate unconventional
music is to be a "kook," and I'm out to make the most
of it. After all, it's called "crazy_music."

5. BOYCOTT BULLYING BEHAVIOR. In a forum like this, one
effective method for resisting verbal assault without
emulating it is the boycott: not responding, but
continuing with our positive musical lives online
and offline.

Finally, since I suspect that we may share many musical discoveries
here that may contradict or at least qualify the opinions of some
great musicians and theorists, I might suggest as a model the words of
Albert Einstein:

"Newton, forgive me. You found the only way
which, in your age, was just about possible
for a [person] of highest thought and creative
power."

I'm not aware of anyone here claiming that Vicentino, Helmholtz,
Schoenberg, Schlesinger, or Partch -- to mention five vital figures --
has given us the last word on music in practice or theory.

However, I would suggest that any new outlook have the charity to
recognize their beautiful music and their conceptual contributions,
which have value both in offering us more perspectives and in
inciting creative controversies leading to more new music.

Here, I would suggest, "new music" should indeed be our main focus,
and mutual affirmation and encouragement our paramount process.

Most appreciatively,

Margo Schulter
mschulter@...

Beautifully said, as usual, Margo.

JdL, let me just extend a hand of friendship to you
as you are being slammed for absolutely nothing that
I know of.

I've successfully downloaded music and heard some very
good stuff from Brian. I also listened to some very
nice 15 and 17 from Jacky. Monz, I have your Bulgarian
piece and will be getting to it. Margos and Mats mids
have been simpler to download and have been illuminating.
Its unfortunate that we can only share these snippets but
its a lot better than nothing.

The music AND the discussion is always inspiring.

thanks all

Bob Valentine

[Bob Valentine wrote:]
>Beautifully said, as usual, Margo.

Yes, thank you Margo.

>JdL, let me just extend a hand of friendship to you
>as you are being slammed for absolutely nothing that
>I know of.

Thanks, Bob, I really appreciate that.

Part of being a big boy is learning not to dwell on such things; life
goes on. If I were to hold onto anger over it, _I_ would be the loser.
Wars are fought because neither side is willing to let go. One of the
really important powers we have as individuals is to act unilaterally
in non-violence, no matter what the provocation.

JdL

Hi Margo,

> From: mschulter <MSCHULTER@...>
> To: <crazy_music@yahoogroups.com>
> Sent: Friday, July 13, 2001 12:17 AM
> Subject: [crazy_music] Re: Nonviolent anti-bullying for crazy_music
>
> ...
>
> Cordially but passionately dissenting from some views expressed here,
> I'd like to suggest that "spanking a bully" can be viewed as itself a
> kind of "bullying behavior," because it involves physical violence
> against a subdued person, exactly what we want to stop rather than to
> emulate. If you reword that: "Bullying behavior tends to go on until
> it is resisted and restrained," then I have no problem.

I'm really glad you called me on that one! I had second thoughts
about what I wrote there after having already clicked the "send"
button, and wanted to post a revised and amended version, but
resisted because I felt it was somewhat off-topic.

As a pacifist, I must agree with you that the only ultimate way
to *stop* bullying behavior is to continue to resist it, until
the death if necessary. I suppose I got a little queasy about
that aspect and backslid a bit. But you're right.

Your guidelines for maintaining both civility and topicality
are excellent, and I fully endorse them.

> Finally, since I suspect that we may share many musical discoveries
> here that may contradict or at least qualify the opinions of some
> great musicians and theorists, I might suggest as a model the words of
> Albert Einstein:
>
> "Newton, forgive me. You found the only way
> which, in your age, was just about possible
> for a [person] of highest thought and creative
> power."

I find it *very* interesting that you brought Einstein into this,
because I was going to mention him the other day in my response
to Dan Stearns about Mahler's maintenance of a childlike naievete
about the universe around him... Einstein was another genius
who came to mind in this respect.

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

------------------------------------------
The Bright Side of Mary Beth Ackerley:
A review of _Intervals of Motion_
------------------------------------------

In her music, Mary Beth Ackerley shares with us both her own spiritual
journey and her vision of a planetary transformation, as is suggested
by the momentous and fateful title of the last piece of her CD
_Intervals of Motion_, "PostAtomic Light."

A medical doctor as well as a composer, Mary expresses what I might
call in my own medieval European tradition _Musica humana_, the
concept of the human body and soul as the expression of a divine
harmony and also as the mirror of a cosmic harmony or _Musica
mundana_. Other traditions such as Tibetan Buddhism also draw such a
parallel between universal macrocosm and human microcosm.

With Mary's music, as with much beautiful music of 14th-century
Europe, for example, a sophisticated mathematical and philosophical
basis doesn't exclude passionate feeling and intimate communication,
but can guide it in certain directions.

Here I will attempt to share my impressions of some of these
directions, however imperfectly, and to suggest some possible
connections -- connections drawn in the eye of the beholder, or the
ear of the listener, like ecumenical difference tones.

I

In 1558, the great Italian theorist Gioseffo Zarlino compared a
composer's apprenticeship to that of a physician, with practical
experience the key to true expertise. Mary seems to take this metaphor
a step further: her microtunings relate to "different aspects of the
body's education." Her purpose is "Evolutionary music that moves
bodies and heals souls..."

Such a purpose is common to various spiritual traditions: consider,
for example, manifestations ranging from the sacred music of Tibet to
the music and dancing of Miriam, David, and Judith in the Hebrew
tradition.

However, Mary's message is not only one of peace and healing, but of
power, sometimes awesome power. People familiar with a range of
microtonal musics have described some of her pieces as eerie or even
scary, although I might prefer to say "subterranean."

I must admit that I was somewhat daunted when first reading an
"Advisory" notice appearing on the back of her CD cover:

"ADVISORY: Warning! This music will penetrate
deeply held belief systems

"Listen only if you are willing to release
social consciousness."

Upon consideration, I concluded that my best response would be to
listen in an ecumenical spirit (both theological and musical),
affirming my own tradition and vows while honoring and respecting the
spirituality and sacred creativity of a precious sister.

At the same time, I realized that my musical impressions might be
profoundly influenced not only by my cultural and spiritual
perspectives, but by a factor possibly of interest to Mary from her
viewpoint as a medical doctor: the state of my hearing and its
psychological ramifications.

For the past 21 months, I have experienced constant tinnitus in my
right ear -- literally a "ringing," but actually for the most part,
fortunately, mainly just a quiet kind of background "white noise."
Happily, I'm often quite unaware of it unless I happen to focus on it.

While it's well to take this opportunity to caution that tinnitus is
often associated with exposure to excessive sound levels -- musical or
otherwise -- in my case the constant tinnitus started after a minor
accident I had when I tried to move a box fan from a window very early
in the morning, and it hit the right side of my head above the ear.

Fifteen years earlier, in 1983, I had been mugged in San Francisco,
and was struck in the same area, with tinnitus persisting a few weeks
and then going away, although occasionally returning. I can only guess
that the fan incident, itself a minor injury, may have aggravated an
earlier problem.

Anyway, an audiology exam revealed (as I had noticed after the
accident) some mild high frequency hearing loss in my right ear. Last
fall I was tested again, and the good news was no significant change.

However, it's not the tinnitus or the mild high frequency hearing loss
that's the most difficult part: it's something that hasn't yet in my
case been officially diagnosed, but might possibly be described as
some kind of "recruitment" or very mild "hyperacusis," coupled with
what's known as "phonophobia," or fear of intense sound levels.

Whatever the correct diagnosis, what it means is that I become
uncomfortable around everyday noises that I took for granted two years
ago, and avoid most public meetings or concerts where any kind of
sound amplification is involved in which I don't have control over the
volume. Sadly, this includes microtonal or early music events,
including local ones where generous people have made transportation
very easily available.

While prudence might suggest that I'm not so overcautious to use ear
plugs or protective ear muffs, for example, when leaf blowers are
being run outside my apartment, the question is how far to carry this.
The balance between real hearing conservation concerns and nervousness
about any moderately loud sound can be a delicate one. Defining and
nurturing a safe space between "inaudible" and "threatening" is a
psychological imperative.

Maybe my mild aural imperfections, however trivial compared to more
serious hearing loss problems not to speak of other medical and human
complications endured in a world filled with violence and poverty, can
at least defuse one topic of musical polemics.

To me, the idea of a "defective ear" is not an insult or a putdown:
it's a simple medical fact. Sometimes I wonder: has my accident
somehow channeled my musical experiences in directions different from
those they might otherwise have taken? Was this a gift of a very
special and unpredictable kind?

Whatever the answers, I must explain the impact in listening to a CD
such as _Intervals of Motion_, or indeed any CD with large dynamic
contrasts of a kind also found, for example, in European classical
music of the 18th century (where _pianoforte_ describes a very
relevant characteristic of the instrument in question).

Confronted by music mixing loud and soft dynamic levels in a sometimes
unpredictable way, I have a simple response: turn down the volume to a
level that feels safe for the highest actual or anticipated level.

With Mary's music, I started with the volume at 18, and found myself
adjusting it downward to 12, then to 8, and eventually to 6. This
reflects mainly my own distorted sense of sound intensity, and
suggests to me that my caution caused me likely to miss at least the
fine points of many quieter sections.

Although with a beautiful piece such as "Phi harmonics" (#15) there is
for me the solution of confirming that the sound level is very
moderate through the piece, and then going back and hearing it again
at a higher volume, my literally defective ear is a factor which can
and should be disclosed in this kind of review.

Please let me add the commonsense advice for more typical listeners
that with this or any other recording, you should adjust the volume as
appropriate in a safe and sane way to promote aural health as well as
listening enjoyment.

II

The opening piece "Perception of Veils" started with what I found a
"spacy" quality, maybe a bit like the music from a science fiction
film of the 1950's; the music seemed now a bit efforvescent, now
lower, and now again "bubbling."

Maybe this association with science fiction or horror genres of my
childhood is part of what makes people describe Mary's music as
"scary," but her evident purpose is not to terrify but to enlighten.
Thus the Tibetan tradition speaks of "Wrathful Deities" -- reflecting
aspects of the observer's consciousness on the path toward love --
while Christian mystics such as St. John of the Cross speak of a "Dark
Night of the Soul."

The second piece, "Flow," also enters this territory: it seems for a
moment to a sound a vertical fifth, an interval for me representing
the quintessence of consonance and spaciousness, then moving through
space, and becoming more low and brooding.

As moods, timbres, and possible allusions to various world musics come
and go in rapid succession, the result is a curious kind of flow of
global scope, at once encompassing many traditions and communicating a
meditative style of its own.

The third piece, "Dead Zone Blues," mixes high and low sounds with a
sense of tension: I was reminded at one moment of a Tibetan sacred
orchestra, or possibly an Indian raga, followed by a kind of
"high-tech" string timbre mixed with high sounds.

The next piece, "Harmony of Center," had a gliding-up kind of feeling,
with a bit of "sliding"; at the conclusion, I wrote, a "very
penetrating sound."

With all this diversity, there is also a subtle mathematical and
intonational unity based on what Mary describes as the "Lambdoma
Matrix of Pythagoras." Apparently quite different than the kind of
tuning by pure fifths often termed "Pythagorean," this system is based
on what she neatly terms a series of "wavelength ratios" taking the
form 1/n, also known as a "subharmonic series."

In the booklet accompanying the CD, there is a multicolor chart of
these subharmonics through five octaves, and their relationship to
different pieces on the CD. The booklet also gives a URL for the
complete chart: <http://www.elucida.com/harmonics3.html>.

Looking at this chart in the booklet version, which reminds me maybe a
bit of a periodic table of the elements, I reflect on the statement of
St. Thomas Aquinas that "whatever is received is received according to
the mode of the receiver."

While St. Thomas was making the point that in the process of human
development, the intellect is informed by the impressions of the
senses, his statement suggests to me also the ways in which spiritual
experience may draw upon cultural forms and images for its expression.
Mary's chart, like a Tibetan mandala or the iconography of a Gothic
cathedral, expresses a spiritual message of love in the language of a
given cultural setting.

At times, the interactions between the composer and the receiver of
the music -- the listener -- can take on joyously unpredictable
patterns. For example, with "Joy Spark" (#8), I experienced a moment
of Monteverdi, remembering a telling suspension discord in the opening
madrigal of his Book IV (1603).

In "Spacious" (#10) I felt a "curious reverberation, or resonances,"
with an effect "a bit like Tibetan chanting," almost a kind of
conversation between voices in some unfamiliar language. This
impression reminded me of the Tibetan practice of in fact distorting
the syllables of certain texts for the compassionate purpose of
protecting listeners not prepared to negotiate their perilous wisdom.

In "Abundance Symphony" (#12), I heard percussion and a melodic theme,
whose pleasing qualities I noted, with a moment recalling for me a
great composer and theorist of the 20th century, Schoenberg. One side
of Mary's music, like Schoenberg's, is a kind of creative chaos, at
once recognizing the ominous or apparently random qualities of the
modern world, and making this chaos part of an ordered musical
universe.

One luminous piece definitely among my favorites is "Phi Harmonics"
(#15), with a spacious and floating feeling, based as Mary explains
on Phi, the "Golden Ratio" of around 0.618 or 1.618 derived from the
Fibonacci series, and also the square of the second form of this ratio
at around 2.618.

Another lyric moment is "Joy" (#17) with a melody and an impression of
vertical fifths or fourths which reminded me of one of my favorite
instruments, the mouth organ called a _khene_ in Laos and a _sheng_ in
China.

The closing two pieces incorporate a kind of vocal music very familiar
to me, Gregorian chant.

"The Missing Gene" (#18) may reflect Mary's fascination with the human
genome as a basis for music, as well as a part of a larger reality.
Her chart in the CD booklet, for example, identifies one wavelength
ratio in "Octave 3" (n/53, if I read correctly): "Stimulates the
transference of information from galactic center to energetic light
channel on DNA."

This piece has a lyric quality, with moments about two minutes into
the music with enticing fifths and fourths.

The final piece, "PostAtomic Light" (#19), has a floating feeling with
voices, chanting, stringlike timbres, and percussion.

Quite apart from my known aural idiosyncrasies, I would caution that
simply by attempting to write a review of this music, I may have been
placing myself in a frame of mind rather different than that of an
ideal listener. Inevitably, in attempting to verbalize my experience,
I must describe and categorize rather than simply abandon myself to
the total experience.

What I can say is that Mary is an artist who draws on many sources and
traditions to share her spiritual vision and express her message of
transformation. The diverse places and cultures which have shaped her
life also interact in her music.

While microtunings play a central role in this music, they are one
part of a whole which might be described as protean, flowing,
shifting, sometimes looming or even ominous, and sometimes placidly
luminous and lyric.

Although I hope that most listeners won't have to deal with the
personal aural complications that I do, I would invite each to find
her or his own sense of beauty and awe in this music.

Mary Beth Ackerley, M.D.
_Intervals of Motion_
Galaxia Studios (1998)
P.O. Box 8282
Longboat Key, FL 34228 USA
http://www.elucida.com

Most appreciatively,

Margo Schulter
mschulter@...

Hi Margo

I was overwhemled with gratititude, after a full day of moving to a
new home in 105 degree heat, to read your review late last night.
Although I must make this quite brief due to one telephone line
shared by two people occupied with "practical" matters there are
several points which really struck me.

One - whatever your ear, it is clear that you listened with your
heart and spirit, and wrote the most insightful review I have ever
read of IOM. Perhaps that is the gift of this physical shortcoming

> A medical doctor as well as a composer, Mary expresses what I might
> call in my own medieval European tradition _Musica humana_, the
> concept of the human body and soul as the expression of a divine
> harmony and also as the mirror of a cosmic harmony or _Musica
> mundana_. Other traditions such as Tibetan Buddhism also draw such a
> parallel between universal macrocosm and human microcosm.

May I quote this? I really appreciate the most beautiful way in
which you have expressed something which just seems intuitive to
me , "as above, so below"
>
>
> Maybe this association with science fiction or horror genres of my
> childhood is part of what makes people describe Mary's music as
> "scary," but her evident purpose is not to terrify but to enlighten.
> Thus the Tibetan tradition speaks of "Wrathful Deities" --

Thank you Margo. Again this is incredibly insightful of you. The
wrathful deity is that which clears so that new growth can come
about, like a forest fire. And in my music there is an overriding
desire, beyond entertainment, to clear old psychic wounds and
baggage, first my own, and then anyone else who is willing to let go
and move forward. One of the most profound mysteries to me in human
psychology is how to get beyond denial and blindness. How can you
possibly change something you cannot see in your behavior(and usually
something which is quite obvious to others). So much of human
interchange is run from what I call "dead" thoughts - perceptions
and filters formed by a young child's reaction to trauma it could not
control, or by resentments, angers and wounds never resolved and
continually recreated in each new encounter.

To be fully present in the moment is the state of the fool and
radical innocence, and is I think the best place to be for creating a
life (our most profound composition) that is enjoyed and savored, not
endured.

I have found for myself again and again that the more I can see "my
stuff" and let go of it (almost more difficult than seeing it) the
more I really enjoy being alive. And in my music I am always looking
for ways to make this process easier, faster, and more efficient.

I am no saint and this is all a process. But I have found that many
perceive this willingness to clear and release as terrifying,
although I tend to find it exhilerating :-)

Anyway I am going to get to go practice these wonderful words on
moving day 2 , 108 degree heat, already irritated partner. I kinda
doubt i'm gonna get beyond endurance today.....

So must end but thank you again very much for you willingness to
enter the journey also. (and I very much like the midi clip you
dedicated to me. When I have a chance i would like to remix it in
Reaktor and Virus and see where it goes with a thoroughly electronic
whine)

Peace,
Mary

Hello, there, Mary, and everyone.

First, Mary, thanks for your most gracious words about my review, and
please feel free to quote anything there. I still have some musical
reparations to make, and hope that I can get to them soon.

Also, I'd like to thank all the people with helpful responses to my
hearing situation. If I were the person who sets the gardening policy
for my apartment building, I would indeed say "Let's use natural
low-noise methods." As a tenant, I guess that protecting my ears is an
imperfect solution -- although your action, Mary, is the best policy,
and a moral victory which I relish reading about.

Peace and love to all,

Margo

Hello, there, everyone, and this is a quick post about what happened
this weekend when a friend came over and I played a bit of neo-Gothic
music in 23-tET using what I loosely call "Sethareanized" timbres.

First, please let me clarify that what I freely term "Setharean"
means simply picking a timbre that sounds right, or at least
"interesting," from among the voices built into the Yahama TX-802
synthesizer. It's also possible to program various timbres with
inharmonic partials using the FM algorithms, but here I've simply been
experimenting with some of the preset voices.

Anyway, for 23-tET, two voices I like are "Piccolo" (A27) and "Whisper
B" (A64), and these are what I used this weekend.

"Piccolo" seems to me like a metallophone or the like with a sustained
more flute-like component, while "Whisper B" might suggest to me a
vocal kind of effect, or some stately instrumental timbre.

What I played was more or less in a 14th-century style, with a stable
three-voice sonority at a pure 2:3:4 in a Pythagorean tuning (a
rounded 0-702-1200 cents) often realized as 0-678-1200 cents, using
the narrow 23-tET fifth at 13/23 octave and the wide fourth at 10/23
octave.

I used a three-voice texture with "Piccolo" for the lower parts, and
"Whisper B" for the upper voice-like melody.

Without getting into technicalities, I should explain that in this
kind of style, melodic motion in the different voices is mostly
stepwise, with major thirds and sixths typically expanding to fifths
and octaves, for example.

Anyway, when I had played in this kind of neo-14th-century style, my
friend said that she found it "scary," reminding her of a science
fiction or horror movie.

She added that while someone might possibly associate this kind of
music with a medieval style, she mostly found it "eerie," some kind of
music "from an alternate universe."

I hope to produce a tape of this kind of style in 23-tET, which would
let people draw their own conclusions.

More generally, at least this kind of "Sethareanizing" may increase
smoothness while leaving a tuning with a quite distinctive "mood."

Peace and love to all,

Margo

Margo wrote...

> First, please let me clarify that what I freely term "Setharean"
> means simply picking a timbre that sounds right, or at least
> "interesting," from among the voices built into the Yahama TX-802

BTW... Off topic, but do you program any of your own patches on this synth?
I have a couple of TX802s myself... I mostly use my own patches, not the
built-ins.

Rick

---------------------------------------------------
Peace through self-moderation on crazy_music
One participant's questions
---------------------------------------------------

Hello, there, everyone, and at this very important time for
crazy_music, I would like to emphasize that I speak only for myself,
but would invite others to comment or ask their own questions in
response to some questions I raise here.

First, if the declared purpose of crazy_music is to promote the
_creation_ of new xenharmonic music, does this imply that we maintain
certain creative and nurturing attitudes not only toward the music and
concepts we share, but toward each other?

Secondly, if our focus is on creation, should not our threads reflect
this focus both by placing new music in the forefront, and by
celebrating our positive goals and values, however diverse or even
sometimes amicably dissonant?

Third, if we feel that a focus on musical creation and mutual
friendship and support is the main theme of this group, then might we
use our discretion so as to respond to those messages and threads
which promote this theme and sustain our community?

To post to crazy_music is an open invitation;
To respond is each user's sovereign choice.

Might I suggest that the purpose of our group be fostered by our free
and communal consensus to reply to messages and threads which serve
two purposes:

1. "Keeping it real," closely related to creating music;
2. "Keeping it friendly," building trust and community.

Both purposes might suggest a positive and constructive focus for
messages and threads. Is it not desirable that people should not only
share their enjoyment and exciting musical ideas here, but leave with
a feeling of comradeship and friendly encouragement to create more
beautiful music?

One possible metaphor for a shared ethos of friendship might be
"emotional Sethareanization." By keeping our tone or emotional timbre
a peaceful and mutually respectful one, we can have lots of lively
conceptual dissonance while still maintaining spiritual concord and
community.

There is enough conceptual and musical space for Graham Breed to
espouse schismic temperaments, for Joe Monzo to explore JustMusic
systems with higher limits and intricate lattices (with generous
helpings of Aristoxenian pragmatism), for Mary Beth Ackerley to
perambulate about her lambdoma and Phi-based scales, for Joe Pehrson
to bring a practiced composerly craft to new intonations, for Brian
McLaren to share exquisite music in once-disparaged tunings, and for
me to approach music as sonorous number and alternate history.

Of course, there are many others, for example our famous resident
numerologist Jacky Ligon with his Prime Directive.

By responding to posts which promote friendship and respect among
participants, which recognize and affirm diversity, and which
encourage people to pursue their own musical ideals in an active and
creative way, can we not better build our crazy_music community
through free choice and self-moderation?

If self-moderation appeals to us as a community of mutual concern,
then it may have one special advantage.

Self-moderation focuses on the present, on what is being posted now,
and invites each participant to offer new threads or replies which
promote our themes of creativity and friendship.

Most respectfully,

Margo Schulter
mschulter@...

Margo,

Thanks for sending this quiz!

> First, if the declared purpose of crazy_music is to promote
> the _creation_ of new xenharmonic music, does this imply that
> we maintain certain creative and nurturing attitudes not only
> toward the music and concepts we share, but toward each
> other?

I think that is an effective way to go about it. There
appears to be an opposing system of belief that people
are lazy and stupid and thus the only way people can be
motivated to do their work is by threats and
intimidation. This theory was soundly debunked tnhrough
extensive research, which is summarized in the
excellent 1963 book "Motivation and Productivity" by
Saul. W. Gellerman.

That has not stopped people, particularly those who see
themselves in the roles of managers or leaders, from
using these tactics, which tend to always spell doom
for the group and resentment among those subjected to
them. As an example, we have just come off an enormous
tech boom characterized by outlandish work hours,
demeaning and dangerous work conditions, and bullying
and intimidation by bosses who ran their best engineers
like they were running a sweatshop. The result?
Exhausted, dismotivated people, extremely poor, perhaps
psychotic decisions being made, enormous turnover and
undelivered, sabotaged, or completely unusable
products. And yet there was enormous potential to
succeed and a will to do so, and general positive
outlook and enthusiasm to begin with. Even a very very
poor manager should have been able to put these things
together to create success, but we are talking about
instead a complete and total incompetance regarding the
ability to motivate others, coupled with an uncanny
genius at demotivational techniques, being pandemic in
the industry.

> Secondly, if our focus is on creation, should not our threads
> reflect this focus both by ** placing new music in the
> forefront **, and ** by celebrating our positive goals and
> values, however diverse or even sometimes amicably dissonant?
> **

Margo, this is self-evident to myself and many others.
And it has historically yielded positive, repeatable
results that are maintainable over time, especially
when used with creative, intelligent and/or highly
skilled citizens.

> Third, if we feel that a focus on musical creation and mutual
> friendship and support is the main theme of this group, then
> might we use our discretion so as to respond to those
> messages and threads which promote this theme and sustain our
> community?

This makes sense to me and is of course the free choice
of each person to choose or reject. Not just here in
this group, but throughout life! Always ask "what do I
hope to accomplish by taking the action I am about to
undertake". Many people will also try to understand us
by asking the same question.

> To post to crazy_music is an open invitation;
> To respond is each user's sovereign choice.

Correct.

> Might I suggest that the purpose of our group be fostered by
> our free and communal consensus to reply to messages and
> threads which serve two purposes:

> 1. "Keeping it real," closely related to creating music;

Yes, that is exactly the meaning.

> 2. "Keeping it friendly," building trust and community.

Well, I suppose the system can handle a little bit of
turf wars or such. It's when they get personal that
damage is done. I like the idea of a 'vicious war'
being conducted between competing composers with music
their only weapon that scores points!! Others may
choose to cooperate with each other. Spectators can
cheer or boo and take votes to determine thumbs up or
thumbs down. Not in every case, but when challenging
music is brought out, such as Chris' excellent
composition which put to rest the concerns many of us
had about John's algorithms.

Dare I say it? Even *heated* debates about what someone
on the list has DONE or accomplished can be very
productive, educational and inspiring ... as long as
they do not resort to puerile name calling or off-track
derailments, resulting in the train of thought
plummeting down the embankment towards the rocks below,
to be dashed to smitheereens and destroying everyone on
board the train.

> Both purposes might suggest a positive and constructive focus
> for messages and threads. Is it not desirable that people
> should not only share their enjoyment and exciting musical
> ideas here, but leave with a feeling of comradeship and
> friendly encouragement to create more beautiful music?

Or feel challenged not by contentious words, but by
challenging music that has been thrown down, as if a
gauntlet.

Men and women do differ here, and I think there is room
for both types of energy. Some masculine energies like
to challenge one another. I think that is fine and very
productive as long as it does not get personal.
Certainly trying to drag another's uninvolved family
members into the fray would cross the line.

I suppose there could be 'staged events' like they have
in wrestling, where a couple of people put on a phoney
fight in order to amuse and entertain, but that should
be done between people who know each other and are
doing so by mutual consent.

> encourage people to pursue their own musical ideals in an
> active and creative way, can we not better build our
> crazy_music community through free choice and
> self-moderation?

Good summary.

> If self-moderation appeals to us as a community of mutual
> concern, then it may have one special advantage.

> Self-moderation focuses on the present, on what is being
> posted now, and invites each participant to offer new threads
> or replies which promote our themes of creativity and
> friendship.

Everyone should really consider themselves responsible
for their own behavior at the very least, particularly
before presuming to dictate the behavior others.

Thanks!

Oh -- as an afterthought, I noticed on another list
that when people spend a lot of time talking about
theory, it seems as if the seldom have anything to show
for it, yet they get a lot of friendly encouragement
from others to continue, so they continue with theories
and never get down to the business of music. So we see
an example where encouragement can reinforce
dysfunctional (in this group that means non-musical)
behavior.

I propose that if someone is posting about theories and
never has any music to show for it, that we not give
them any feedback at all, except to perhaps ask if they
have any music demonstrating their theories (each
responsible for his own theories, rather than dictating
that others provide proof), or offer technical help to
get to that point, and then not responding to them
until they can provide evidence and get on topic with
the group. If there is a strong need to post and
discuss theory, detached from real-life empirical
examples, it would be better to create a new group for
that or perhaps use one of the existing other groups
where it may be more on topic.

I believe this will also help keep down the non-musical
noise level and help the group focus on its charter --
the active creation of music.

Jeff

Hello, there, everyone, and here's a MIDI version of a composition
that I'm posting around, with much appreciation to all the creative
energy here that has lent me inspiration in actually putting this
piece into a settled form and making it available on the 'Net:

<http://value.net/~mschulter/invoc4a.mid>

For Brian McLaren, especially, I'll take note that this piece uses a
certain technique strongly advocated by Ivor Darreg, one that
interestingly goes back to another very justly famed xenharmonicist.

As a very playful and unscientific "survey," I might invite anyone to
identify this technique before I reveal it.

Thanks to all of you for bringing together energies which can this a
forum for sharing music, ideas, and information in a friendly and
enthusiastic community.

Peace and love to all,

Margo

Hello, there, everyone, and please let me thank Brian and Kraig and
Mary and Bob and others for a dialogue on musical style and small
integer ratios which suggests to me that a bit of historical
background might put this "debate" in a different perspective.

Of course, since sharing new music is a major theme of this group, I
can't resist the opportunity to include a piece I wrote back in 1985,
in a 13th-century European kind of style: _Homage to Joyce Ball_, then
a librarian at the local university library.

The piece is actually a setting for three voices of one version of a
typical closing announcement: "May I have your attention please: The
library will be closing in ten minutes. Please collect your belongings
and prepare to leave the building." The lowest of the three parts is
the principal one; here I use a standard Pythagorean tuning:

MIDI: <http://value.net/~mschulter/library1.mid>
Score in PostScript: <http://value.net/~mschulter/library1.ps>

One of my reasons for including this piece, apart from keeping to the
main theme of new music for at least a token introduction <grin>, is
to suggest that an understanding of the diversity of intervals and
sonorities used in Gothic music can play an important role in any
debate concerning "harmonic evolution."

What I'd like to try is a somewhat different method for suggesting
some overview of stylistic change -- one with a focus on xenharmonic
developments.

First, I'll try summing up a few of my general opinions and biases in
this debate, and then move to my main presentation.

I

As someone who often uses Pythagorean tuning, or Pythagorean-based JI
systems combining ratios of 2-3-7, I obviously see a role for integer
ratios, both large and small.

At the same time, as someone who loves meantone for Renaissance or
Xeno-Renaissance styles, and regular tunings with fifths wider than
pure for neo-Gothic styles -- not to speak of 20-tET now and then -- I
regard temperament as another very useful option.

Maybe it's not so surprising, then, that I find myself on both "sides"
of this debate, possibly from a certain historical perspective not so
often articulated.

Looking first from the angle of Kraig's "side," we find indeed that in
most known traditions of medieval European polyphony, fifths (3:2) and
fourths (4:3) are the main stable concords. Together with the octave
(2:1), these intervals form complete or "perfect" three-voice
sonorities which in English I call trines (expressing the _trina
harmoniae perfectio_ or "threefold perfection of harmony") with pure
ratios in Pythagorean tuning of 2:3:4 (e.g. D3-A3-D4, with C4 as
middle C).

In Renaissance-Romantic styles of this same region, however, major and
minor thirds ideally tuned at or near ratios of 5:4 and 6:5 are the
primary concords. The new stable three-voice sonority, known as
_harmonia perfetta_ or _trias harmonica_ (English "triad"), has a
ratio in 16th-century just intonation systems of 4:5:6, approximated
rather closely in familiar meantone tunings of the era.

Thus an advocate of "harmonic series evolution" can argue that the
shift from medieval trine (2:3:4) to _harmonia perfetta_ or triad
(4:5:6) represents historical movement "up the harmonic series," an
outlook of the kind Kraig has suggested.

However, as Brian has very correctly emphasized, when we look at the
totality of musical style (or as much as we can describe and analyze,
however imperfectly), then both practice and theory suggest the
limitations of such a model, especially in its popular and stereotyped
versions based on the notion of "progress from the simple to the
complex."

Specifically, for example:

(1) As early as around 1030, Guido d'Arezzo recognizes
the use of vertical major seconds (9:8) and major
thirds (81:64) as cadential intervals resolving
to a unison, and recommends the use of these
intervals along with stable fourths (4:3).

(2) Major seconds or ninths (9:4) and minor sevenths (16:9)
are often mixed with fifths and/or fourths in Gothic
and other world polyphonies to form relatively
concordant sonorities such as 6:8:9 (e.g. C3-F3-G3)
or 4:6:9 (e.g. G3-D4-A4) -- sonorities treated more
freely in 13th-14th century European music than in
Renaissance-Romantic styles based on stable thirds
and sixths;

(3) Around 1300, Jacobus of Liege notes that the major
ninth serves as a pleasing partial concord in a
three-voice sonority where it is mixed with two
fifths (i.e. 4:6:9), and suggests that the interval
of a major 23rd (triple octave plus whole-tone) at
a ratio of 9:1 is a "perfect concord" -- the ninth
harmonic, as many current JI theorists might say.

(4) Composers of the era of around 1200-1400, such as
Perotin and Machaut, use bold sonorities featuring
minor thirds and minor sevenths, for example, which
resolve to stable trines or fifths -- contrasting
with the much more cautious treatment of such
sevenths in 15th-16th century styles.

(5) Gothic theorists often recognize a subtle continuum
of concord/discord with four, five, or six categories,
and describe a range of cadential resolutions and
sonorities featuring unstable intervals (seconds,
thirds, sixths, and sevenths).

Around 1200, for example, Perotin boldly uses sonorities featuring the
major seventh (243:128, ~1110 cents), a complex interval and an
acutely tense one in this kind of setting. While "evolution up the
harmonic series" may not provide an obvious explanation for this, a
love of dramatic contrasts between concord and discord, plus melodic
factors, do offer a ready musical motivation.

In this debate, I consider it important to recognize that most
European music history over the past two centuries or a bit more has
been written from an explicit or implicit perspective: "The Origins of
18th-century Harmony." Stylistic traits that seem irrelevant or even
"counterproductive" from the viewpoint of this paradigm tend to be
ignored, or even denigrated as "crude dissonances" or the like.

Certain world musics, or eras of European composition, may not fit in
with the established models -- any more than a tuning such as 11-tET
does. Striving to follow the example of Ivor Darreg, I would argue
that each cultural tradition and style may have its own valuable
"mood," and that appreciating the range of moods may enrich dialogues
or debates on topics such as "harmonic evolution."

II

Here I would like to take the approach of considering the history of
Western European composition from the earliest recorded polyphony to
the present as a single day of music. While the focus here will be
mainly on Western Europe, I will mention other world traditions, not
only to avoid total Eurocentricism but to note some patterns
placing certain features of some historical European styles in a
larger perspective.

Although the first known treatises documenting the art of polyphony,
or music for two or more simultaneous voices, seem to date from around
850-900, let us arbitrarily start our "day" a bit earlier, at the
convenient year 800.

Thus our day will cover a rounded 1200 years, with each century
lasting for two hours. Here I'll be concerned mainly with the first
two-thirds of this day, from midnight to 4 p.m., or 800-1600.
As we'll see, "High Noon" (1400) is a significant point in the history
of intonation.

----------------------------------------------------------
1. Midnight (800): The dawn of recorded European polyphony
----------------------------------------------------------

As we start our clock at midnight in 800, the era of Charlemagne in
Western Europe, it is possible that the sophisticated orchestral
tradition of Japanese gagaku music with its complex "clusters" built
from superimposed fifths or fourths is already established.

In 814, ecclesiastical authorities are recognizing linguistic reality
by moving from a strategy of "educating" parishioners in "correct"
Latin to one of calling for sermons in the _lingua Romana rustica_,
the language of the people, now known as Old French.

Around 850 or so, writers start recording what might well represent a
traditional style of polyphony based mainly on fifths and fourths,
intervals favored in many world cultures: they speak of _organum_ or
"organized music," and write in a manner suggesting that this practice
is already well known. While these stable intervals, plus octaves and
elevenths (8:3) or twelfths (3:1), are central to the style, unstable
intervals including major seconds or thirds appear now and then in
certain examples involving oblique or contrary motion.

--------------------------------------------------
2. Four a.m. (1000): Cadential practice and theory
--------------------------------------------------

By around 1000, or 4 a.m., at places such as Winchester and Chartres,
this kind of largely improvised style has given rise to compositional
traditions where the melodies added to a chant are recorded.

Around 1030, Guido in his _Micrologus_ offers what may be the first
known presentation in this tradition specifically recommending the use
of unstable major seconds (9:8) and major or minor thirds (81:64,
32:27) as elements of style.

Our sources for this era seem to suggest a typical style around 1000
centering around motion from unison to fourth and eventually back
again to a concluding unison, with unstable second and thirds often
lending both melodic grace and vertical tension to the texture.

Interestingly, Richard Hoppin has offered an example of traditional
Chinese polyphony where there is an interplay between vertical octaves
at the opening or conclusion of phrases and parallel fourths in
between, suggesting a possible kinship between various world
traditions (whatever the "explanations").

As the 11th century (4 a.m.-6 a.m.) continues in Western Europe,
musicians and composers move toward a style of two-voice improvisation
or writing using _all_ intervals from the unison to the octave,
bringing into play unstable intervals such as sixths and sevenths.
Around 1100, John of Afflighem (or "John Cotton") remarks that
different people treat organum in different ways (he may be the first
to derive this term from the instrument of the organ, one of several
meanings for _organum_), but that he favors an approach centered on
the idea of contrary motion.

-----------------------------------------------------
3. The flowering of polyphony -- a Georgian interlude
-----------------------------------------------------

During the 12th century (6 a.m.-8 a.m.), a style often especially
favoring contrary motion while featuring all types of motions and
intervals gets established in Western Europe -- but its exponents are
by no means alone.

At the same time, in Georgia, theorists are documenting three-voice
singing, notably also based on fifths and fourths as the most favored
concords, while featuring a variety of other intervals. By the end of
the century, three-voice polyphony will also become the new and
exciting trend in the West.

Maybe a bit after 7 a.m., or 1150, Leonin is writing his most prolific
collection of two-voice polyphony, music sometimes featuring acutely
tense intervals such as major sevenths resolving to octaves, as well
as the usual stable concords and "compatible" unstable intervals
(e.g. M2, m3, M3, M6, m7).

------------------------------------------
4. Eight a.m. (1200) -- the Perotinian era
------------------------------------------

By around 1200 -- 8 a.m. -- Perotin and his colleagues are writing
exquisite pieces for three and four voices, featuring a rich variety
of stable and unstable sonorities of the kind also found in traditions
such as those of Georgian singing and of Kirghiz instrumental music.

One feature shared in common not only between these traditions, but
among many world traditions ranging from Japanese koto music to the
khene or "mouth organ" music of Laos, is the use of sonorities
superimposing fifths or fourths with major seconds or ninths or minor
sevenths. Such sonorities have a kind of "relatively concordant"
quality quite different from that of either a bare fifth or fourth, or
a bare major second or ninth or minor seventh: thus combining three or
more voices opens up new musical possibilities.

At the same time, the relatively concordant but complex and unstable
major and minor thirds of Pythagorean tuning -- as treated in this
Gothic tradition -- play a vital musical role, often impelling
directed cadential action and also providing a resource for sheer
vertical color.

Often an interval is defined not only by its degree of concord or
discord, of blend or tension, but how it may typically resolve: major
seconds expanding to fourths by contrary motion, or contracting to
unisons by conjunct motion (highly recommended by Guido around 1030);
thirds contracting to unisons or expanding to fifths; major or minor
sixths expanding to octaves, or sometimes obliquely resolving to
fifths; and major or minor sevenths contracting to fifths, or
expanding obliquely to octaves.

This "musical geometry" uniting vertical and melodic dimensions shapes
much of the Gothic repertory of progressions -- with arguably somewhat
analogous patterns playing a role in Georgian music, for example,
although each tradition has its own logic.

------------------------------------------------------------
5. Ten a.m. (1300): Multi-voice theory -- and a new practice
------------------------------------------------------------

By around 1300, or 10 a.m., theorists such as Johannes de Grocheio and
Jacobus of Liege are writing about the ideally harmonious qualities of
the complete three-voice trine, and Jacobus also describes and
sanctions a range of unstable sonorities for three or more voices.

As he points out, for example, the Pythagorean tradition of the four
hammers or strings with ratios of 12:9:8:6 lends a certain degree of
"concord" to the pure 9:8 major second, and he endorses 4:6:9 as a
pleasant three-voice sonority. As noted, this type of sonority occurs
in many world cultures, with or without this kind of mathematical
approach.

Jacobus also describes a three-voice sonority called the _quinta
fissa_ or "split fifth" where a fifth is divided into a major and
minor third (e.g. G3-B3-D4 or D3-F3-A3), 64:81:96 or 54:64;81 as
expressed in modern frequency ratios. He recommends these sonorities
as pleasing when aptly resolved.

In medieval Europe, as elsewhere, tastes could vary: both musical
pieces themselves and theoretical evidence document a penchant in
parts of England and Scandanavia for major and minor thirds as "the
best concords," to borrow the words of a scholar writing maybe around
1275 and now known as Coussemaker's Anonymous IV.

Very possibly this penchant for more fully concordant thirds may have
favored simpler ratios at or near 5:4 or 6:5. The English theorists
Theinred of Dover (12th or 13th century?) and Walter Odington
(c. 1300) explain the relatively concordant effect of thirds by noting
that the Pythagorean ratios are close to these simple ones, with
Odington adding that apt singers can make them sound fully
concordant.

At the same time, Odington asserts that contrary to the opinion of
some musicians, major seconds (9:8) and ninths (9:4) are not
"compatible" -- Jacobus, in contrast, describes these same intervals
as "imperfect" or "intermediate" concords, and describes the use of
6:8:9 or 8:9:12 as well as his favored 4:6:9.

This era around 1300 marks not only some fascinating theoretical
analyses of 13th-century practice, but the advent of a new and
"modern" style: the _Ars Nova_, or "New Art."

Composers such as Philippe de Vitry introduce new notational systems
to handle duple as well as triple time, bringing into play techniques
such as syncopation which will develop into more and more complex
styles of polyrhythmic music as the century progresses.

Jacobus, for one, loves the music of his youth in the late 13th
century, but dislikes the new style, citing a kind of psychoacoustical
survey in which some listeners were given a chance to hear pieces in
both the old and new styles, and preferred the old.

The Ars Nova style nevertheless prevailed, but with composers of the
modern style such as Guillaume de Machaut (1300-1377) often availing
themselves of traditional 13th-century liberties such as the use of
sonorities involving minor sevenths or major ninths, intervals
endorsed by Jacobus but excluded from the basic vocabulary of some
"modern" 14th-century counterpoint treatises.

While typical 14th-century styles nicely fit the standard system of
Pythagorean intonation, one xenharmonicist deserves special mention:
Marchettus (or Marchetto) of Padua.

Completed in 1318, his _Lucidarium_ may well call for use of cadential
major thirds and sixths defining in effect new classes of intervals: a
large major third at around 453 cents, or about midway between the
usual Pythagorean major third and fourth; and a major sixth which he
describes as equally distant from 3:2 fifth and 2:1 octave, or around
951 cents, about midway between usual major sixth and minor seventh.

His special emphasis is on the principle of "closest approach," in
which thirds expanding to fifths or sixths to octaves should be
"colored" or made major in order to make the resolution to a stable
concord more efficient. While other theorists find the usual
Pythagorean intervals ideal for this purpose, Marchettus appears to
carry it yet further, advocating the use of a cadential semitone or
"diesis" of possibly somewhere around 41-48 cents, in contrast to the
usual Pythagorean diatonic semitone of 256:243 (~90 cents).

Both this style of accentuated intonation apparently favored by
Marchettus, and more conventional Pythagorean approaches, focus on a
directed contrast between stable trines and unstable sonorities --
often involving thirds or sixths, and in some musical dialects also
seconds or sevenths.

Various types of more or less conclusive cadences are used to provide
larger-scale organization for forms such as French ballade or virelai
of Machaut and the Italian ballata of Francesco Landini (1325-1397).

Near the end of the 14th century, the _Ars subtilior_ or "more subtle
art" achieves rhythmic and polymetric refinements not again equalled
until the 20th century, with the vertical and formal patterns of Ars
Nova trinicism providing a basis for elaborations with subtlety and
beauty perfectly allied.

--------------------------------------------------------------
6. "High Noon" (1400): A stylistic and intonational transition
--------------------------------------------------------------

Around our symbolic "high noon," or the year 1400, we encounter a kind
of intonational demarcation line -- or actually a fuzzy era of
transition in which Pythagorean tuning on the Continent is first
modified and then gradually yields to meantone as the standard
paradigm for keyboard instruments.

While this era has been viewed by some historians (e.g. Knud Jeppesen)
as a "springtime" of harmony, and by Richard Crocker as a kind of
blurring of the clarity of 14th-century vertical organization, we
might best approach it as a transition between a Gothic style based on
a high level of vertical contrast and a Renaissance style based on
more muted contrasts.

In a typical Gothic style of the kind prevailing in Continental
Europe, both the treatment of intervals and the qualities of
Pythagorean tuning emphasize a contrast between stable fifths and
fourths with pure ratios, and mildly unstable thirds with complex
ratios.

By around 1500, however, the new Renaissance textures tend to flow
smoothly between sonorities featuring thirds and sixths as the most
favored intervals, and indeed the emerging standard of stable
saturation. Here the concept of a "smooth" flow means not only the
pervasive use of thirds and sixths, but the rather cautious and
restricted use of seconds or sevenths -- in contrast to their more
prominent role in Gothic styles.

In the epoch from around noon to 1 p.m., or 1400-1450, two trends
provide a kind of bridge from the old style to the new: modified
Pythagorean keyboard tunings, and a genre known as fauxbourdon.

Possibly sometime around 1370 or 1380 in regions such as Florence, and
by around 1400-1420 over a wider area of Europe, keyboard tuners often
adopted a technique of tuning a 12-note instrument so that the keys
for written sharps were actually placed at the flat end of the
chain. This meant that written thirds spelled with sharps -- e.g. the
major thirds D-F#, E-G#, and A-C# -- would actually be played as the
diminished fourths D-Gb, E-Ab, and A-Db, and similarly affected minor
thirds as augmented seconds.

In Pythagorean tuning, as it happens, a diminished fourth has a ratio
very close to 5:4, and an augmented second to 6:5. Through much of the
early 15th century, it would appear, these altered and acoustically
"smoother" thirds were used side-by-side with the traditional and more
active ones (e.g. F-A, G-B, C-E).

While this trend seems to have taken root in some parts of Continental
Europe by 1415, it may have been reinforced by an event of that year:
an all-too-literal English invasion of France, contrasting in its
martial violence to the gentler transoceanic incursion of the Beatles
in 1964. The Battle of Agincourt not only inspired a famous carol, but
may have the famous English composer John Dunstable to France along
with the Duke of Bedford.

In any event, by around 1440 a French poet notes that composers such
as Dufay and Binchois follow the "English countenance" of Dunstable,
and looking back in 1477, Tinctoris regards these composers as the
font and origin of the new style.

One aspect of the new style introduced by composers around 1420-1430
such as the young Guillaume Dufay (c. 1397-1474) is a genre which may
well have been derived at least in part from English sources:
fauxbourdon.

In some 14th-century Continental compositions, a typical cadence with
major third expanding to fifth and major sixth to octave is preceded
by a set of sixth sonorities in parallel motion: in 1357, Johannes
Boen says that in this type of cadence, the imperfectly or partially
concordant thirds and sixths serve as "forerunners and handmaidens" of
the resolving fifths and octaves.

In England, starting around the epoch of 1300, such sixth sonorities
often make up much of the bulk of a piece in a style sometimes called
_cantilena_, and the post-Agincourt influence of this tradition would
serve as one source for the fauxbourdon of Dufay and his colleagues.

A fascinating intonational aspect of such fauxbourdon is that at least
to my ears, it can sound very pleasing in Pythagorean intonation with
complex thirds and sixths, or for that matter in 22-tET with thirds
and sixths near 9:7 and 12:7, for example, as in this example:

F4 E4 D4 C#4 D4
C4 B3 A3 G#3 A3
A3 G3 F3 E3 D3

<http://value.net/~mschulter/22tei001.mid>

While the term fauxbourdon can refer generally to this type of late
Gothic or early Renaissance texture, more specifically a fauxbourdon
was often a type of composition in which only the outer two parts,
moving mostly in sixths with standard cadences to the octave, were
actually noted. An unwritten middle part was understood to follow a
fourth below the upper voice, or a third above the lower one.

Here the parallel unstable concords can be heard as a kind of
cadential "free fall" in which the expected resolution is prolonged or
delayed: Pythagorean tuning, as Mark Lindley has noted, can nicely
express the tentative or "sinuous" quality of these partial concords.

----------------------------
8. One p.m. (1450): Meantone
----------------------------

However, by around 1450, or 1 p.m., the altered or "odd" thirds of the
modified Pythagorean tunings had come into such vogue that they were
defining a new intonational norm in which as many thirds as possible
should have this smoother quality.

Meantone temperament was the result, likely reflected first in
practice by the style of pieces by an organ composer such as Conrad
Paumann, and then in theory by an evident description of a meantone
keyboard by Ramos (1482), and a more explicit statement by Gaffurius
(1496) that fifths on the organ are narrowed or tempered
(_participata_) by "a certain small or hidden amount."

Here I might add, to place my own mathematical tendencies in some
balance, that musicians were likely tuning keyboards in meantone for a
century or so before Zarlino (1558) came up with a mathematical model
based on fractions of the syntonic comma. It was done by practice, and
by ear, as some early 16th-century instructions for the aspiring lay
reader indicate.

While treated in a more cautious manner in typical Renaissance styles
than in the often exuberant Gothic tradition, seconds and sevenths
play a subtle and indeed vital role as suspensions, with a suspended
6:8:9 sonority (e.g. C4-F4-G4, the fourth resolving to a third,
e.g. C4-E4-G4) for example often serving as a cadential "marker."

Thus the diverse and often dramatically contrasting sonorities of the
Gothic era give way to the rather smooth and homogenous textures of
the Renaissance.

In 1555, or 3:06 p.m., this Renaissance style serves as the setting
for one of the great xenharmonic statements of all time, _Ancient
Music Adapted to Modern Practice_ by Nicola Vicentino. The meantone
diesis or "fifthtone," not too far from the size of the enharmonic
diesis of Greek theory, opens a new world of melody and verticality
still largely to be explored in the 21st century.

---------------------------------------------------
9. Four p.m. (1600): "high contrast" again in vogue
---------------------------------------------------

By around 1600, or 4 p.m., trends in the overall balance of the
intervals are again changing, with bold seconds and sevenths again
coming vogue -- now resolving to the stable sonorities dubbed "triads"
by Johannes Lippius (1610, 1612), rather than to Gothic trines.

The use of a systematic contrast between stable and boldly unstable
sonorities is thus a feature of 13th-14th century Gothic style, and
also of the key system which was established by around the time of
Corelli and Werckmeister (c. 1680), the latter taking much of its
material from the more fluid modal music of the era around 1600 with
its "poetic dissonances."

------------------------------------------------
10. Some possible viewpoints and interpretations
------------------------------------------------

It is noteworthy that the bold use of minor sevenths in either
13th-14th century or 17th-18th century music does not necessarily fit
a simple "harmonic series" scenario, since during these eras the usual
tunings generally yield ratios at or near 16:9 (Pythagorean), or
somewhere between 16:9 and 9:5 (meantone or well-temperament).

A ratio of 7:4, representing the "seventh harmonic," is recommended by
Euler in 1764, for example, as a tuning for this interval, and the
augmented sixth of meantone curiously offers a close approximation of
this ratio.

However, it is interesting that even the acceptance in some
20th-century styles of the minor seventh as an element in _stable_
sonorities may be tied to tuning systems such as 12-tET, where this
interval is some 31 cents wider than 7:4, although quite close to the
Pythagorean ratio of 16:9 formed from two pure fourths.

How might a person taking the "side" of a "harmonic series" outlook
approach this information?

One possible interpretation might be to say that various "partials"
have played a role in assorted world musics, with the "third and ninth
partials," for example, featured in traditions mixing fifths or
fourths (3:2, 4:3) with major seconds or ninths or minor sevenths
(9:8, 9:4, 16:9). From the Gothic music of Europe to the koto music of
Japan, these intervals often happily combine.

In contrast, the Renaissance styles of Europe would place the "fifth
partial" at center stage.

Taking this kind of approach, it would be possible to note the
relevance of small JI ratios without excluding larger ones. For
example, one might argue that the complex major and minor thirds of
Pythagorean tuning represent a rather "inaccurate" representation of
the simplest 5-based ratios, thus offering a great artistic potential
realized in the "imperfect" or partial concords of the Gothic era.

However, there's also the other side: is "justness," even if presented
in this more sophisticated kind of way, really a central feature of
world musics? The traditions of tuning in pure fifths and fourths in
various cultures, and of "5-limit" tunings in Renaissance Europe and
the sruti system of India, suggest that JI ideals are _one_
significant approach -- but are they _the_ prevailing approach?

Here such phenomena as 720-cent fifths and 1215-cent octaves, as well
as pragmatic rather than mathematically precise tunings used in many
world cultures, present "the other side of the coin."

Also, even within the much narrower scope of the historical European
compositional tradition, to "just" or "equal" tunings we should add
such important categories as meantones (some of which may happen to
define equal divisions of the octave) and unequal well-temperaments.

Here we might also delve into various Near Eastern currents of
practice and theory where conceptual Pythagorean ratios often mix with
instruments and performance traditions approximating something like
17-tET, for example.

What I would urge mainly is that both "sides" in this debate -- or
maybe, for some of us, different and not necessarily antagonistic
"sides" of our own musical experience -- can take on a richer and more
musically satisfying quality as they are informed by the diversity of
world traditions and practices.

In peace and love,

Margo

> From: mschulter <MSCHULTER@...>
> To: <crazy_music@yahoogroups.com>
> Sent: Friday, July 27, 2001 9:16 AM
> Subject: [crazy_music] A composition -- with Ivor Darreg connection
>

>
> <http://value.net/~mschulter/invoc4a.mid>
>
> For Brian McLaren, especially, I'll take note that this piece uses a
> certain technique strongly advocated by Ivor Darreg, one that
> interestingly goes back to another very justly famed xenharmonicist.
>
> As a very playful and unscientific "survey," I might invite anyone to
> identify this technique before I reveal it.

Well, I've figured it out!

But I think I'll keep quiet and see if anyone else gets it.
(Meantime, my response goes to Margo privately.)

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In crazy_music@y..., mschulter <MSCHULTER@V...> wrote:

/crazy_music/topicId_210.html#768
>
> What I'd like to try is a somewhat different method for suggesting
> some overview of stylistic change -- one with a focus on xenharmonic
> developments.
>
> First, I'll try summing up a few of my general opinions and biases
in this debate, and then move to my main presentation.
>

Many thanks to Margo Schulter for including this fascinating post
about the evolution of tuning. It's a "Ulysses" of tuning post...
one "day" encompassing many styles and trends...

___________ _________ ______
Joseph Pehrson