Re: World musics and intonations -- some questions

Hello, there, everyone, and I'd like to address a point about which
Paul Erlich inquired in a very friendly and engaging dialogue about
his paper in _Xenharmonikon 17_ (1998), but may be of such general
interest that it may invite a thread of its own.

In the earlier dialogue, I remarked that it might be viewed as
fortunate that the 20th-century theory of Western European and related
compositional traditions didn't develop any consensus approach
"unifying" the different eras of this practice.

The reason for this conclusion was my concern that such a paradigm
might appear to account too "neatly" for the diversity of Western
European compositional styles -- thus making the ethnocentric equation
of "our music" or "our theory" generally with European compositional
theory all the more easy.

Another way of putting this is that other world musical traditions
might have even more difficulty in gaining recognition as equally
basic to any "universal" model of musical style, or more specifically,
for this forum, of intonational style.

Of course, this is not to say that such styles are unrepresented here
-- consider, as one outstanding example, the participation of Haresh
Bakshi who has shared his insights as a musician trained in the
traditional music of India. Also, contributors such as Kraig Grady,
Paul Erlich, and Daniel Wolf have focuses on such musics.

However, often the term "we" can point to what might be a less than
universal consensus -- no problem, as long as the implicit limits of
consensus are recognized.

This is why I find that the absence of a musical "consensus" even
among those of us approaching music mainly from _some_ kind of Western
European compositional perspective could serve a helpful purpose, by
reminding us that yet greater variety is to be found outside of what
is actually a rather narrow subset of world musics.

On the basis of some questions asked by others on this list, and some
random reflections, I might raise a few issues for relaxed
consideration, issues inviting receptiveness both to new viewpoints
and to new musical possibilities:

(1) If a sizable portion of the people discussing gamelan
intonation here were Balinese or Javanese gamelan
musicians, how might the discussion be different?

(2) If a sizable portion our our participants came from
a range of world polyphonic traditions featuring, to
use the interval categories of the European compositional
tradition, a variety of preferences such as parallel
fifths, fourths, thirds, or seconds, how might "n-limit"
concepts vary in formulation or musical significance?

(3) If the numeration systems connected with these musics --
not always necessarily formalized for all aspects of
a musical piece or performance -- were part of our
common vocabulary, how might dialogues on "music and
math" take on a new direction, or many new directions?

Please let me conclude by saying that I feel a special responsibility
to raise these questions as someone who may be in a _relative_
minority on certain stylistic questions, but on the other hand is for
the most part discussing things in a Western European framework, only
based on different eras than those best known.

Sadly, despite the powerful metaphor of the "global village," the
Internet and at least many of its music forums still seek truly global
representativeness as a goal rather than an accomplished or even
approximate reality.

Conceptual and artistic issues aside -- and there are some potentially
enriching as well as troubling ones -- I hope that this kind of
reflection on the range of world musics, intonations, and numerations
may exert a certain "tempering" effect on what might seem heated
controversies, putting things in a larger perspective.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:
> Hello, there, everyone, and I'd like to address a point about which
> Paul Erlich inquired in a very friendly and engaging dialogue about
> his paper in _Xenharmonikon 17_ (1998), but may be of such general
> interest that it may invite a thread of its own.
>
> In the earlier dialogue, I remarked that it might be viewed as
> fortunate that the 20th-century theory of Western European and related
> compositional traditions didn't develop any consensus approach
> "unifying" the different eras of this practice.

I wholeheartedly agreed with this point, but inquired about a different one. Nevertheless, we can
drop this discussion, as it appears there's very little we disagree on. Not sure about you being
in the "minority" position on much of anything, particularly if I am not also counted as part of that
minority.

on 7/1/01 3:54 AM, tuning@yahoogroups.com at tuning@yahoogroups.com wrote:

> From: mschulter <MSCHULTER@VALUE.NET>
> Subject: Re: World musics and intonations -- some questions

> (1) If a sizable portion of the people discussing gamelan
> intonation here were Balinese or Javanese gamelan
> musicians, how might the discussion be different?

Margo,

Many thanks for asking this great question. I am not an expert in gamelan,
although I greatly enjoy the music, but this question can and perhaps should
be asked by anyone involved in study and practice of world music. Substitute
any other musical genre in place of the word gamelan, ask the same question,
I think the answers would be enlightening.

My specialties are with traditional folk music, mostly of American and/or
European origin, particularly Celtic, Appalachian, delta blues, and eastern
European klezmer, among others. In all of these musics, non 12-ET pitches
are used widely, and with specific intent, but not generally discussed by
the players in terms used by people on this type of forum. If we look at
these musics from a perspective gained from study of JI and microtonality,
we will often see use of natural scales and harmonies.

At the same time, I find that, although I've been intensely studying JI with
the goals of achieving the ability to accurately and consistently play just
intervals for my own composition, I have no desire to impose too much
precision of analysis of intonation on my folk music playing. For example,
rather than over-analyzing a folk tune to see exactly which third or seventh
is being used, whether a 3, 5, 7 or other limit, seems counter-intuitive to
just listening to the old and young masters live and on 78s, and playing the
tune by ear with these microtonal shadings. After all, folk music is an oral
tradition.

It is unfortunately all too easy for the perspective of the folk
practitioner to be dismissed or ignored in a forum where everything is
discussed from a more mathematic approach, simply because that person isn't
speaking the academic language "properly". And so it is important for us on
this list to learn to truly listen to other voices and other ways of using
microtonality. Otherwise we greatly run the risk of an elitist discourse.
For that matter, the very fact that we are having this discussion in English
on the internet is excluding people who either might wish to be part of this
dialog, but don't have access to the computer technology that all of us on
this list enjoy, and/or they don't speak English.

Thanks again for bringing up this question, I look forward to hearing other
peoples' thoughts on this subject.

Seth

--
Seth Austen

http://www.sethausten.com
emails: seth@sethausten.com
klezmusic@earthlink.net

Margo,

You've brought up some points that have been the focus of much
of my work---obviously, fascinating points, in my opinion!
As you know, my work involves the representation of music
theories as pieces of software. I strove, from the beginning
of my project, to be as general as possible; it's one of my
design tennants that any existing musical object (a scale, say)
should be representable by my system and, furthermore, that
anything we might call a scale (whether it already exists or
not) should be representable as a Rusty scale.

This wasn't the result of any sort of politically correct impulse,
but came out of practical experience (I don't think every musical
idea is equal, but I think they're all useful to some degree).
I found ideas from other music theories fascinating and useful
in composition, but I also found, when trying to learn about them,
that _writing_ about music theories was uniformly confused and
insular throughout the world. So, I set out, for each sort of
musical object, to find the format for representing its various
manifestations most naturally. Of course, world music theories
informed this to a great degree, but I also found useful a sort
of "first principles" approach to the business of seeking these
"forms of forms" of music theories. At the end, I think I've
got a universal, tradition-independent (or nearly so) language
for talking about music theories and, since it's in the form of
software, for animating them in practice.

Underlying all this, there's an interesting assumption---I think
there is a one-to-one correspondence between musical traditions
or generes and the music theories that generate them. I also
think that the relationship between different genres/theories is
probably a lot like that between different languages---if we
mapped them we would find trees with branches, borrowed elements,
etc. In looking for a universal language for music theory/style,
I didn't look exclusively to the tree of Western music and its many
branches, but to the whole forest and, more than that, to the
nature of the objects themselves.

For a tuning example, I think that representing tunings as
networks of fuzzily-defined intervals reflects in a general
way (the fuzzy intervals could be effectively crisp) the way
everyone thinks of tunings, consciously or not. Of course,
there's a lot more to it than that---there are many refinements,
modifiers, parameters and so on---to use a gamelen example, I
allow the possiblity of mis-tuned unisons with a unison offset
parameter---a subtlety informed by Balinese practices.

So, is my system complete, correct and useful (Aquinas would ask
if it had wholeness, harmony and radiance)? I think so, but I
invite everybody to give me their opinions (especially you, Margo!).
If there are any specific points that I've fallen short on, I'd
love to hear about them!

You also asked some interesting, more specific questions:

> (1) If a sizable portion of the people discussing gamelan
> intonation here were Balinese or Javanese gamelan
> musicians, how might the discussion be different?

In that case, I think that a lot of the discussion would revolve
around the nature and practice of _embat_---the subtle differences
between different realizations of the same tuning system. It's
a fascinating subject---the different flavors that can be gained
by small variations on intonation. I think it's similar to the
differences between well-temperaments and their keys (and that it
has a similar underlying representation)---to use an example from
"our" music. I always wondered why this was so seldom discussed
on the list.

> (2) If a sizable portion our our participants came from
> a range of world polyphonic traditions featuring, to
> use the interval categories of the European compositional
> tradition, a variety of preferences such as parallel
> fifths, fourths, thirds, or seconds, how might "n-limit"
> concepts vary in formulation or musical significance?

I'm not so sure about how this would affect notions of n-limit
(except that it might be more important in traditions where seconds
were prominent) but, it would be nice to see more discussion
about voice leading (and harmonic function, come to think of it)
with different tunings. Your posts are refreshing for that reason!
Unfortunately, I'm afraid most people just doodle around with
a new scale rather than thinking about it. I love it when people
think.

> (3) If the numeration systems connected with these musics --
> not always necessarily formalized for all aspects of
> a musical piece or performance -- were part of our
> common vocabulary, how might dialogues on "music and
> math" take on a new direction, or many new directions?

Here, I have to ask you to clarify what you mean by "numeration".
Do you mean the format for expressing intervals (JI, ET, fuzzy,
etc.) or the vocabulary of interval classes (seconds, thirds, etc.)
or the morphology of scales (e.g. tetrachords)?

>Sadly, despite the powerful metaphor of the "global village," the
>Internet and at least many of its music forums still seek truly global
>representativeness as a goal rather than an accomplished or even
>approximate reality.

I agree. I had hoped my work would make "foreign" ideas common
property---no luck yet, but I keep on.

-m
_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com

In a most gracious reply, Michael Saunders wrote:

> Margo,

> You've brought up some points that have been the focus of much of my
> work---obviously, fascinating points, in my opinion! As you know,
> my work involves the representation of music theories as pieces of
> software. I strove, from the beginning of my project, to be as
> general as possible; it's one of my design tennants that any
> existing musical object (a scale, say) should be representable by my
> system and, furthermore, that anything we might call a scale
> (whether it already exists or not) should be representable as a
> Rusty scale.

Hello, there, and please let me thank you for a most thoughtful
response to my post, and also for pointing out the flexibility of your
Rusty approach, something I admire when I read your _Xenharmonikon_ 17
article and other documentation. Here I'm quoting some excerpts that
especially move me to respond, but your entire message is well worth
reading, carefully and with pleasure.

/tuning/topicId_25891.html#25946

> Of course, world music theories informed this to a great degree, but
> I also found useful a sort of "first principles" approach to the
> business of seeking these "forms of forms" of music theories. At
> the end, I think I've got a universal, tradition-independent (or
> nearly so) language for talking about music theories and, since it's
> in the form of software, for animating them in practice.

While this may be an ideal more to be approached than perfectly
realized, I deeply appreciate your commitment to make those "first
principles" as encompassing as possible. This is a virtue,
unfortunately, overlooked in lots of conceptions of "music theory."
Of course, the problem of a software program may make the definitions
both flexible ("fuzzy") and operational at the same time, an
interesting mix.

> Underlying all this, there's an interesting assumption---I think
> there is a one-to-one correspondence between musical traditions or
> generes and the music theories that generate them.

Here I would agree, and also with your suggestion of deeper branchings
as well as borrowings.

Of course, there is also the important insight, to continue your
language metaphor, that "language is system." If in much of my music I
take a "regular major third" as "an interval formed from four fifths
up, typically somewhere between around 81:64 (~407.82 cents) and 9:7
(~435.08 cents)," then my viewpoint may be quite _systemically_
different from a style where the ideal is around 5:4 (~386.31 cents).

Your algorithms seem very much to allow for such choices.

> For a tuning example, I think that representing tunings as networks
> of fuzzily-defined intervals reflects in a general way (the fuzzy
> intervals could be effectively crisp) the way everyone thinks of
> tunings, consciously or not.

While "everyone" may be a rather universal generalization, I would
certainly recognize that various people _can_ think of tunings with
assorted degrees of "fuzziness," and that your model seeks to
accommodate this spectrum of views through an impressive range of
options.

For example, what I'd call a choice between "fixed" and "variable"
intonations for a given scale (your "stable"/"unstable" options) is a
very valuable feature, which raises possibilities for the kind of
adaptive tuning with which John deLaubenfels is so successfully
experimenting.

> Of course, there's a lot more to it than that---there are many
> refinements, modifiers, parameters and so on---to use a gamelen
> example, I allow the possiblity of mis-tuned unisons with a unison
> offset modifiers, parameters and so on---to use a gamelen example, I
> allow the possiblity of mis-tuned unisons with a unison offset
> parameter---a subtlety informed by Balinese practices.

This is a really nice feature, maybe parallel to the "detuning"
supported by some synthesizers.

> So, is my system complete, correct and useful (Aquinas would ask if
> it had wholeness, harmony and radiance)? I think so, but I invite
> everybody to give me their opinions (especially you, Margo!). If
> there are any specific points that I've fallen short on, I'd love to
> hear about them!

Based on my first reading, I'd say that you've covered a very large
range of possibilities; of course, with software, actual users might
best test the implementation. However, really, the design is a very
moving musical statement as well as effort to implement it; that's why
I have enjoyed your writings so much.

[On Balinese and Javanese viewpoints]

> In that case, I think that a lot of the discussion would revolve
> around the nature and practice of _embat_---the subtle differences
> between different realizations of the same tuning system. It's a
> fascinating subject---the different flavors that can be gained by
> small variations on intonation. I think it's similar to the
> differences between well-temperaments and their keys (and that it
> has a similar underlying representation)---to use an example from
> "our" music. I always wondered why this was so seldom discussed on
> the list.

Could _embat_ also be a bit like the neo-Gothic concept of
intonational "flavors" -- a word you use here?

These flavors and their musical context get discussed in my series "A
Gentle Introduction to neo-Gothic progressions," with some tables of
flavors in Parts 2A and 2C:

/tuning/topicId_15038.html#15038 (1/Pt 1)
/tuning/topicId_15630.html#15630 (1/Pt 2A)
/tuning/topicId_15685.html#15685 (1/Pt 2B)
/tuning/topicId_16134.html#16134 (1/Pt 2C)

One feature of these "flavors" for intervals such as thirds is their
"fuzziness," a pleasant word to use in this dialogue given our common
affection for it.

For example, there's a fuzzy overlapping between the "ratio zones" of
"17-flavor" (~21:17, ~17:14, "submajor/supraminor" thirds centering
around 366 cents and 336 cents) and "49-flavor" ("neutral" thirds
centering around 49:40, or 351 cents).

One of my favorite tunings has alternative thirds (augmented seconds
and diminished fourths) at around 341 cents and 363 cents. I tend to
regard this as a "strong 17-flavor," but not too far from a more
"neutralish" territory.

[On how viewpoints from various world musics might affect "n-limit"
concepts]

> I'm not so sure about how this would affect notions of n-limit
> (except that it might be more important in traditions where seconds
> were prominent) but, it would be nice to see more discussion about
> voice leading (and harmonic function, come to think of it) with
> different tunings.

Yes, the interaction between tunings and progressions is an
interesting one, and one step I'm trying to take now is to record some
complete pieces in a range of tunings and timbres.

To borrow your language metaphor, phonology (intonation) can take on
more meaning with a bit of syntax (basic progressions), but a corpus
of complete conversations or narratives is all the better.

[On "numeration" in various world musical traditions]

> Here, I have to ask you to clarify what you mean by "numeration".
> Do you mean the format for expressing intervals (JI, ET, fuzzy,
> etc.) or the vocabulary of interval classes (seconds, thirds, etc.)
> or the morphology of scales (e.g. tetrachords)?

That is a very fair and helpful question, and my reply would be,
"indeed all of the things you have so helpfully listed."

By the way, may I confirm that in my compositional or improvisational
outlook, there are indeed various degrees of "fuzziness."

Comparing notes of this might make for an interesting dialogue; it
also gives me an opportunity to consider some of my own assumptions
(tacit or otherwise).

Please let me conclude by expressing great admiration for your effort
to keep "first principles" flexible and inclusive, a very valuable
ideal to seek, even if the process of communication is a gradual one.

Again, however incomplete a response this may be -- and may the
incompleteness at least leave room for much further dialogue -- thank
you for such a generous response, and a welcome occasion to share my
esteem for your contributions.

Most appreciatively,

Margo Schulter
mschulter@value.net