Yahoo Tuning Groups Ultimate Backup makemicromusic Theory and Tonality in JI

>
>Hi.
>I've read 'Genesis of a Music', Fokker's 'Just Intonation',
>Chalmers' 'Divisions', and a few internet and journal resources, and
>I have a decent set-up. I'm rearing to go with the JI; but I
>haven't seen much discussion of extended tonality, modulations,
>etc. I guess I'm interested in building tonalities that have some
>symmetry and good pacing to them, that is, not just throwing
>everything in at once. It seems, when I've done JI stuff, I want to
>keep taking it further and further, and it gets jumbled. I have a
>few ideas on this that I have yet to work out, but I'm wondering,
>are there texts or established systems that incorporate these kinds
>of limitations that I can check out?
>

Maybe one thing to try is to, rather than starting by trying to come up
with a theoretical underpinning for a JI scale set, rather than figuring
out what scale you need to be able to modulate from X to Y to Z,
just tune up an arbitrary scale on a keyboard, play around with it a
lot, discover different tonal "areas" that you can move through, to and
between. By "tonal" I don't mean traditionally tonal necessarily, just
a harmonic "area" that sounds like you are in a certain "place" . . . .
modulating doesn't have to be "I V V/V V etc." It can be a movement
between areas that one can't really describe. . .

I would say that "good pacing" is not something you can build into a
scale. I suppose you could try to build in the possibility for good
pacing . . .but I think it would be more fun to just make an arbitrary
scale and then figure out how to pace well a composition or
improvisation in that scale.

🔗Margo Schulter <mschulter@...>

> Message: 4
> Date: Thu, 09 Dec 2004 19:59:22 -0000
> From: "Chuckk Hubbard" <BadMuthaHubbard@...>
> Subject: Theory and Tonality in JI
>
>
> Hi.
> I've read 'Genesis of a Music', Fokker's 'Just Intonation',
> Chalmers' 'Divisions', and a few internet and journal resources, and
> I have a decent set-up. I'm rearing to go with the JI; but I
> haven't seen much discussion of extended tonality, modulations,
> etc. I guess I'm interested in building tonalities that have some
> symmetry and good pacing to them, that is, not just throwing
> everything in at once. It seems, when I've done JI stuff, I want to
> keep taking it further and further, and it gets jumbled. I have a
> few ideas on this that I have yet to work out, but I'm wondering,
> are there texts or established systems that incorporate these kinds
> of limitations that I can check out?

Dear Chuck,

Please let me suggest that while a lot of the theoretical issues you raise
might be discussed elsewhere, for example non12comp (Aaron Johnson's group
on Google Groups), or e-mail (as a JI enthuasiast I enjoy these
discussions), I might offer some general encouragement at least here.

One point is that "JI" can have lots of directions. For example, my
approach has been mostly to start with historical JI-based practices of
13th-14th century Europe (mostly Pythagorean) and the medieval Near East
(lots of emphasis on superparticular ratios, e.g. 12:13:14, with influence
from classic Greek theory).

People like David Doty have produced some very interesting music based on
"What if...?" questions, like "What if conventional European theory had
evolved so as to recognize ratios of 7 as concordant?"

Sometimes there's the question of "a specifically JI music" versus "a
music that happens to use integer-based intervals, including some simpler
ones." For example, the division of some kind of minor third into two
neutral seconds is common in medieval and modern Near Easter music; but
this might be expressed as "64:59:54" (Safi al-Din) or as "14:13:12" (Ibn
Sina) or as "13:12:11" (one of my own realizations of this basic idea),
or just "a minor third divided into two neutral seconds, but with the
lower one a bit smaller." The last concept is not necessarily "just," but
can be implemented with various just ratios, as in some of the medieval
Near Eastern tunings.

Composers like Jacky Ligon are taking the approach of aiming not
necessarily for "simple" ratios, but for relationships between often
complex ones, for example the subtly graduated sizes of melodic steps.
While small steps (like the well-known commas) are often seen as a kind of
"bug" or navigational hazard of JI, they can be used to excellent effect,
and I'm trying to get into this more.

LaMonte Young has done fascinating things with very high ratios, as well
as with comparatively simpler ones like 16:21:24:28. Alison Monteith has a
very interesting article in the latest issue of _1/1_ on some just gamelan
tunings of Lou Harrison and her process of building custom instruments,
composing, and performing in these tunings as music for dramatic
productions. Also, _1/1_ has had recent articles, for example, on the use
of complex ratios as dissonances by Kyle Gann (curiously, I use at least
one of these same ratios as a kind of "imperfect concord," which shows how
styles can vary)!

Over in non12comp, there have been some musical examples and articles
about JI with ratios of 2-3-7, including some discussion by Aaron Johnson
about some music he composed for a production of _Peer Gynt_ (well
received).

Most appreciatively,

Margo Schulter
mschulter@...

🔗hstraub64 <hstraub64@...>

--- In MakeMicroMusic@yahoogroups.com, "Chuckk Hubbard"
<BadMuthaHubbard@h...> wrote:
>
> Hi.
> I've read 'Genesis of a Music', Fokker's 'Just Intonation',
> Chalmers' 'Divisions', and a few internet and journal resources, and
> I have a decent set-up. I'm rearing to go with the JI; but I
> haven't seen much discussion of extended tonality, modulations,
> etc. I guess I'm interested in building tonalities that have some
> symmetry and good pacing to them, that is, not just throwing
> everything in at once. It seems, when I've done JI stuff, I want to
> keep taking it further and further, and it gets jumbled. I have a
> few ideas on this that I have yet to work out, but I'm wondering,
> are there texts or established systems that incorporate these kinds
> of limitations that I can check out?
>

I think a good start is Schönberg's modulation pattern. It sees a
modulation as a tripartite process consisting of:

1. A NEUTRAL PHASE where the old key is weakened, e.g. by using
ambiguous chords (chords that are common in both keys), or by entering
quickly into the new key and coming back at once.

2. A FUNDAMENTAL to mark the turning point where the old key is left.
This is typically done by using chords from the new key that do not
belong to the old key.

3. A CADENCE to establish the new key.

With this pattern at hand, you can, once you have defined the scales
and chords of a new system, determine which chord is to use in which
phase. As an example from traditional 12tet: if you want to modulate
from C major to G major, ambiguous triads are C, Em, G and Am while
all triads containing the f# are candidates to mark the fundamental
step. As for the cadence, one of its purposes is to uniquely establish
the new key. This led to the idea of the "cadencial set" (Mazzola),
which is defined as a set of chords that determine a key completely.
Using again an example from 12tet: The chords IV and V uniquely fix a
certain major key, as well as the chords V7 and I - which may be one
of the reasons that these became popular as parts of classical cadences.

I have used this pattern for a composition of mine - not microtonal
(yet...), but based on non-classical scale. I am currently working on
microtonal music, for which the same methodology works fine. If you
want more details, you can have a look at

http://home.datacomm.ch/straub/mamuth/modul/ontosu_e.html

Good luck,

Hans Straub

🔗Kraig Grady <kraiggrady@...>

The example here of 64:59:64 shows how , like the ancient greeks often where often more interested in Medients more that simple ratios. By medients ratio which are midway between two others. Ptolemy mention also the division of three also besides two. Which is the basis for his own enharmonic scale.

Each persons stretch of tonality is different and seem up to each one how far one ca go. One can take the resources of 20th century music and interpret the harmonic language of the variety of pieces in term of JI ( correctly or incorrectly, the idea is to examine approaches) to se what appeals to ones palette.

Margo Schulter wrote:

> Sometimes there's the question of "a specifically JI music" versus "a
>
>music that happens to use integer-based intervals, including some simpler
>ones." For example, the division of some kind of minor third into two
>neutral seconds is common in medieval and modern Near Easter music; but
>this might be expressed as "64:59:54" (Safi al-Din) or as "14:13:12" (Ibn
>Sina) or as "13:12:11" (one of my own realizations of this basic idea),
>or just "a minor third divided into two neutral seconds, but with the
>lower one a bit smaller." The last concept is not necessarily "just," but
>can be implemented with various just ratios, as in some of the medieval
>Near Eastern tunings.
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Chuckk Hubbard <BadMuthaHubbard@...>

--- In MakeMicroMusic@yahoogroups.com, "hstraub64" <hstraub64@t...>
wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Chuckk Hubbard"
> <BadMuthaHubbard@h...> wrote:
> >
> > Hi.
> > I've read 'Genesis of a Music', Fokker's 'Just Intonation',
> > Chalmers' 'Divisions', and a few internet and journal resources,
and
> > I have a decent set-up. I'm rearing to go with the JI; but I
> > haven't seen much discussion of extended tonality, modulations,
> > etc. I guess I'm interested in building tonalities that have
some
> > symmetry and good pacing to them, that is, not just throwing
> > everything in at once. It seems, when I've done JI stuff, I
want to
> > keep taking it further and further, and it gets jumbled. I have
a
> > few ideas on this that I have yet to work out, but I'm
wondering,
> > are there texts or established systems that incorporate these
kinds
> > of limitations that I can check out?
> >
>
> I think a good start is Schönberg's modulation pattern. It sees a
> modulation as a tripartite process consisting of:
>
> 1. A NEUTRAL PHASE where the old key is weakened, e.g. by using
> ambiguous chords (chords that are common in both keys), or by
entering
> quickly into the new key and coming back at once.
>
> 2. A FUNDAMENTAL to mark the turning point where the old key is
left.
> This is typically done by using chords from the new key that do not
> belong to the old key.
>
> 3. A CADENCE to establish the new key.

I remember that now. Schoenberg's Theory was my first book, that I
used to compose my audition pieces, though I used his ideas
loosely. Very, very stimulating.
I think, though, that even using a dominant as an identifying factor
can become just one more part of a broader vocabulary. To say
tonality is dependent on certain cadences seems like getting hung up
on convention. I'm learning about jazz in school, and am kind of
disappointed. This ii-V-I/i stuff is overrated. Once the brain
notices such a progression in several places in a short time,
the "simplest possible figure" is updated to allow for it as a
device, a gesture, rather than a defining element. My teachers are
trapped in it, arguing whether you're "really in" whichever key
without any acoustic or cognitive background as to where that comes
from.
Most teachers either just say "we're used to hearing it so we expect
it" and leave it at that, or say "it's based on natural harmonics
and is universal" and leave it at that. No doubt both things are
factors, but should be the start, not the end, of inquiry.

http://homepages.ius.edu/RALLMAN/gestalt.html
Wonderful illustrations:
http://www.labyrinth.net.au/~saul/essays/05lawsPercept.html

The fundamental answer, to me, is the Law of Pragnanz. A piece is
defined by the simplest way of explaining its structure. Whenever a
new element defies that structure, its consonance/dissonance depends
on to what level the whole must be redefined (in the listener's
mind) to incorporate the change.

In regards to "We're just used to hearing it", it is true that
humans will accept just about any stimulus through familiarity,
whether it is "understood" or not. Like a microwave oven: people
don't know how it works, but have accepted that it does and that it
belongs there, and they know its purpose. They have some
association for it, so they "know what it is". But a progression
descending by 5ths, more than once, already has an inherent
structure that is not dependent on having "gotten used to it".
Meyer points out, in the part of "Emotion and Meaning In Music" that
I've just gotten to, that the wilder and more chaotic music is, the
less surprise is possible in it. Once the listener doesn't know
what to expect, they can't be surprised.

Also interesting is "The Magical Number Seven Plus or Minus Two"
http://www.well.com/user/smalin/miller.html

He says we respond to an overload of info by making *simultaneous*
judgments of several factors, increasing the possible categories for
discernment. Also, "chunking", whereby we can log the details and
the broader things separately but with similar definitions......

I think all these things are compelling for the microtonalist,
implying principles by which our explorations will be accepted or
rejected by other musicians, which in turn determines the quality of
the works of future generations of microtonalists.

Your ideas sound interesting and exploratory, it sounds like you're
applying this sort of stuff (lately I'm only talking about it).

See you.
Chuckk

>
> With this pattern at hand, you can, once you have defined the
scales
> and chords of a new system, determine which chord is to use in
which
> phase. As an example from traditional 12tet: if you want to
modulate
> from C major to G major, ambiguous triads are C, Em, G and Am while
> all triads containing the f# are candidates to mark the fundamental
> step. As for the cadence, one of its purposes is to uniquely
establish
> the new key. This led to the idea of the "cadencial set" (Mazzola),
> which is defined as a set of chords that determine a key
completely.
> Using again an example from 12tet: The chords IV and V uniquely
fix a
> certain major key, as well as the chords V7 and I - which may be
one
> of the reasons that these became popular as parts of classical
cadences.
>
> I have used this pattern for a composition of mine - not microtonal
> (yet...), but based on non-classical scale. I am currently working
on
> microtonal music, for which the same methodology works fine. If you
> want more details, you can have a look at
>
> http://home.datacomm.ch/straub/mamuth/modul/ontosu_e.html
>
> Good luck,
>
> Hans Straub

Theory and Tonality in JI

🔗Chuckk Hubbard <BadMuthaHubbard@...>

🔗Christopher Bailey <chris@...>

🔗Margo Schulter <mschulter@...>

🔗hstraub64 <hstraub64@...>

🔗Kraig Grady <kraiggrady@...>

🔗Chuckk Hubbard <BadMuthaHubbard@...>

🔗Kraig Grady <kraiggrady@...>