Yahoo Tuning Groups Ultimate Backup makemicromusic counterpoint and microtonality

In-Reply-To: <20011221144225.21089.qmail@...>
Brian Szymanski wrote:

> ...
> (perhaps borrowing some "rules" from traditional
> counterpoint, and inventing some new ones that make
> sense for your own scale), and seeing where it goes.
> ...

I have been thinking about an 11-limit redefinition of counterpoint. It's
based on the Miracle/decimal system. See

<http://x31eq.com/miracle.htm>

The first change is obviously to introduce new harmonies. I have
segregated intervals into four levels of dissonance, roughly guided by the
integer limit and interval width. You could think about starting and
ending on perfect consonances, and always moving up or down the dissonance
hierarchy by one step.

Another idea is that intervals within the decimal scale count as "normal"
and most of the melody should be composed of them, even when it uses more
than 10 notes. That's equivalent to only using diatonic intervals even in
chromatic music.

And a less obvious difference is that you have intervals of 8:7 and 7:6
that are somewhere between the steps and leaps of traditional theory, so
you have to blur the rules accordingly.

I've written bits of music like this, but not enough to know present a
finished set of rules. Still, it is an interesting direction, and I plan
to look into it more.

Another thing is that certain progressions which work in 12-equal but not
5-limit JI can be spiced up with 9- or even 11-limit intervals and made
more coherent. That would make more sense with staff notation, using
modifiers to get to the exotic intervals.

Graham

🔗paulerlich <paul@...>

🔗M. Schulter <MSCHULTER@...>

Hello, there, Brian and everyone, and thank you for the stimulating
question and answers concerning counterpoint and microtonality.

Keeping in tune with the practical, "doing is learning" focus of this
group, I'll say a bit about how I tend to approach counterpoint in
various tunings, including new ones I might be trying for the first
time.

Mainly it's a question for me of sitting down at the keyboard, with
the internalized patterns of counterpoint (mostly medieval and
Renaissance, plus some curious "derivatives") I've learned, and my
knowledge of the tuning "in theory" -- and playing some familiar
cadences and phrases, seeing how they sound, and also what new or
modified patterns may emerge from the action of my hands and my
response to the resulting sound.

This isn't necessarily a new approach: if "microtonal" means using
something other than the usual intervals a familiar historical tuning
like Pythagorean or Renaissance meantone in the European tradition,
then Nicola Vicentino was in rather the same situation when he
explored a near-equal 31-note division of the octave in the early
1550's, and published his results in 1555.

Here my focus is not on the technicalities of 16th-century style
("usual" or microtonal), but on Vicentino's evident learning
process. He was a master of the common practice style, and explored
the new types of intervals he encountered, developing a kind of
counterpoint combining new and old. For example, he concluded that the
"proximate minor third" at around 11:9, or 9/5-tone (about 9/31
octave) was rather concordant, but found a "minimal third" of 7/5-tone
(about 7:6) as more dissonant in its leanings. He also developed some
cadences where certain voices shift from their expected notes of
arrival by 1/5-tone.

Now, as in 1555, I guess that "playing around" is the main process for
exploring these things on a keyboard.

Here I might make a few general comments.

First, from a medieval or Renaissance viewpoint, there's no distinct
line between "counterpoint" and "harmony" -- if there is in any era of
European or other world music. Multi-voice cadences are often built by
superimposing two-voice progressions so that they mutually reinforce
each other and lead to a rich stable sonority. There is a distinction
between note-against-note and more ornamented or rhythmically
independent textures, and especially in Renaissance styles a special
kind of feel in imitative textures where the voices share an opening
motive (like a canon, but often much freer).

Secondly, maybe there's a continuum from designing or choosing the
tuning to fit the style, to taking the tuning and shaping the style to
fit it. A 14th-century European style in a regular Pythagorean tuning,
and such a style in 13-tET, might illustrate the more clearly defined
poles of this continuum <grin>.

One fun thing is the way that a "strange" tuning can have some
familiar progressions, as well as vice versa. For example, adapting
standard 14th-century European cadences to 13-tET, we have (in cents):

minor 3rd to unison 277-0
major 3rd to fifth 462-738
major 6th to octave 923-1200
major 2nd to fourth 185-462
minor 7th to fifth 1015-738

These are all progressions in stepwise contrary motion, and the
resolutions from "minor third to unison" and "major sixth to octave"
are quite "down at home," routine and beautiful for a neo-medieval
kind of tuning. However, it turns out that in 13-tET, the interval of
about 462 cents -- 5/13 octave -- can serve either as a stable small
fourth or an unstable large major third! I find it most convenient to
describe the interval either way -- in explaining how the tuning
"maps" to neo-medieval expectations -- depending on what it does.

In view of all the debates since the early 14th century in European
theory on whether the fourth is a "consonance" or "dissonance," we
might find it a refreshing change of pace to consider whether the same
interval is serving as a major third or a fourth <grin>.

Timbre here is very important, as others have discussed, and with
13-tET my usual first item on the agenda is to pick a timbre where
intervals of 738 cents and 462 cents can sound like "stable
consonances" more or less "equivalent" to a usual fifth and fourth.

However, a lot of this kind of counterpoint is metaphor -- it sounds
"right" or "convincing," not necessarily "just like" a more usual
tuning. Thus I'd say that in 13-tET, 0-462-923 cents is a fine
cadential sonority expanding to 0-738-1200 cents -- rather like a
sonority of 0-408-906 cents might do in an historical Pythagorean
tuning, or 0-435-933 cents in simple just intonation based on ratios
of 2-3-7-9 (7:9:12) -- again given the right timbre.

Is this the power of imagination, or historical association, or what?
I'd say that 462 cents is more like a small fourth than a large third
in itself, and yet 0-462-923 cents, with two of these identical
intervals, can "suggest" to me a lower major third and upper fourth.
Or, maybe most judiciously stated, this sonority can very nicely do
the same thing as a more typical medieval or neo-medieval sonority
with the "expected" interval sizes for the "major third" and "fourth"
as well as the "major sixth." Is it possible that that excellent
923-cent sixth expanding to an octave guides my appreciation of the
rest of the progression?

Brian, I apologize if some of these details aren't so clear; some
recent 13-tET improvisations I've done and Jacky Ligon has most kindly
converted to .mp3 format and posted here may say more than words to
explain my approach.

Mainly, my message would be: "Experiment, experiment, experiment."

If you're familiar with a given style, take that as your base -- and
explore from there.

Without getting too much into historical questions, I would make one
very important point: 12-tET is a relatively recent standard for
keyboard instruments, and many historical forms of European
counterpoint and part-writing are premised on other types of
historical tunings: medieval Pythagorean, Renaissance meantone, and
Baroque-Romantic _unequal_ well-temperaments.

For example, playing conventional 16th-century counterpoint in a usual
meantone, you are "in the music's natural element" -- this is a
standard period keyboard tuning. Carry the tuning beyond 12 notes, and
you have not only more transpositions (used in some adventurous pieces
of the era), but new types of intervals -- the exciting things that
Vicentino explored in practice and theory.

My own journey has branched out from medieval Pythaagorean and
Renaissance meantone. Like Vicentino in the mid-16th century, or Fabio
Colonna in the early 17th century, I've discovered (or rediscovered)
some new progressions to go with the old; also, it can be fun in
larger tuning systems especially to experiment with different sizes or
"flavors" of the same (more or less) "type" of interval or
progression, for example major sixth expanding to octave.

There are many sides to this: getting a new flavor of a familiar
progression, or hitting on a new kind of progression and then trying
to "explain" it in terms of familiar patterns -- a fun exercise, as
long as the explanation doesn't get in the way of the doing and
enjoying.

One thing I relish is the moment in exploring a new tuning of: "I'm
don't quite know yet what to call this, but I hear it and I like it!"

While I've discussed medieval and Renaissance European counterpoint,
what I say might apply to the many forms of counterpoint in African
musics, for example, or in Javanese or Balinese gamelan. There are
"traditional" tunings, with some regional affinities as well as
variations for gamelan pelog and slendro scales, for example, as well
as a range of possible "different" realizations in equal or unequal
tuning systems.

Please experiment -- and enjoy!

Peace, love, and happy holidays to all,

Margo

🔗M. Schulter <MSCHULTER@...>

Hello, there, everyone, and maybe I could comment on counterpoint and
microtonality and counterpoint from a first-person view, while also
celebrating something of an anniversary.

In late 1966, taking a "music appreciation" course in high school
which turned out to be a survey of music history, I fell in love with
Renaissance European music, and then found out how much I adored
parallel fifths and fourths, rapidly leading me to embrace medieval
styles also.

By early 1967, 35 years ago, I was exploring this music both in
recordings and in a kind of independent study that my music teacher
arranged after determining through experience that I did not have the
pitch accuracy needed to carry my part in the school choir. Instead, I
spent that hour reading medieval and Renaissance music history, a
process that got me very excited about the Notre Dame School around
1200, and also some subtleties of the 14th century.

For the next 30 years, making music would mean mostly playing any
available organ, harpsichord, synthesizer -- or, in a pinch, a piano
-- mostly tuned, I would guess, in the default 12-tET. Improvising in
13th-16th century styles was my everyday language, meaning much
counterpoint but little "microtonality."

In the late 1970's I read about Nicola Vicentino, and was fascinated
by the new intervals he described; also, having read some discussions
of Pythagorean tuning, I persuaded a friend to tune a harp in pure
fifths, and found it quite delightful -- but wasn't sure how to go
about finding or placing a keyboard in this temperament.

Then, in 1998, I started playing a TX-802 in the historically
appropriate medieval Pythagorean and Renaissance meantone tunings --
and found myself also trying out things like 24-note Pythagorean and
17-tET. People like John Chalmers played a central role in getting me
involved in the scene, and giving me much invaluable advice.

Coming as I was from a medieval and Renaissance background, where
music generally assumes unequal semitones and does _not_ assume the
specific features of 12-tET, the main difference in approaching
familiar counterpoint or polyphony in these tunings is that the
intervals were more "colorful" or idiomatic. It was mostly a matter of
playing the same notes, and getting a more interesting result.

However, with 17-tET or 24-note Pythagorean, I was venturing into some
new interval types, as also happened when I had the thrill in August
of 1999 of first playing a 24-note meantone tuning likely close to a
subset of what Vicentino may have used in 1555 for a 31-note cycle on
his _archicembalo_ or "superharpsichord."

It's one thing to read about Vicentino, or even to read his treatise
itself (available now in a fine English translation by Maria Rika
Maniates and Claude Palisca), and another actually to try out some of
his fifthtone progressions and cadences at the keyboard. I found
myself exploring these progressions and coming up with some variants
of my own.

Then, in June of 2000, I started looking at some regular temperaments
of a "neo-Gothic" kind with fifths wider than pure -- often tempered
about the same amount as in 12-tET, but in the opposite (and I might
say more interesting) direction.

Here I would say that tradition, innovation, insight, and sheer
inspiration mix with a lot of keyboard experience and practice to
shape my outlook on "counterpoint and microtonality" in a given
tuning.

For example, when I first tried a temperament of around 704.61 cents,
I hadn't considered the idea of "supraminor/submajor" thirds -- but
that's what I encountered, some thirds maybe a bit more "polarized"
than usual neutral ones around 11:9, say something like 14:17:21. My
traditional patterns of 14th-century counterpoint and three-voice
cadences suggested to me a resolution which I liked very much. From
there I could explore similar intervals in a system I had already
tuned like 29-tET -- really beautiful -- and also look for new systems
in this general region.

Then came a process of seeing what happens with 24-note tunings in the
"704-cent neighbhorhood" -- I knew some of the attractions of 29-tET
because of a connection with 14th-century theory (however uncertain),
but by October of 2000 was looking into this for some other
temperaments. This was a time of more delightful surprises.

Maybe others can be the best judges of the outlook of my music -- and
my special thanks to Jacky for making some pieces from a recent
cassette available on the Web, with very sophisticated noise reduction
and other touches of artistry as well as technical finesse.

However, I do see musicmaking, at least for me, as in interactive
process in which I approach a new tuning from a perspective of certain
familiar patterns -- which can be modified, or added to, in ways that
I need to play in order to find.

There's excitement in both the practice and theory: I can find delight
either in finding some new progression at the keyboard, often by
accident, or in coming up with some of kind of "new tuning" and
finding out that it's identical to something documented centuries ago
in some world music tradition.

Of course, simply playing a synthesizer seems something quite modest
compared to designing and building instruments -- whether in a
traditional gamelan ensemble, or in the manner of Nicola Vicentino,
Harry Partch, or Ivor Darreg.

Getting the right balance of practice and theory can be a delicate
process, but I'd emphasize that theory is mostly for me practice
distilled, or sometimes practice anticipated, although I also
celebrate the more general and philosophical side.

A final remark on counterpoint: often music is rather like an
alternate history novel for me, with lots of familiar patterns but
with "one important detail changed" -- or maybe several <grin>.

In peace and love,

Margo

counterpoint and microtonality

🔗xbrianskix@...

🔗graham@...

🔗paulerlich <paul@...>

🔗M. Schulter <MSCHULTER@...>

🔗M. Schulter <MSCHULTER@...>