Re: What is JI?: Reply to Daniel Wolf and John deLaubenfels

Hello, there, and I'd like to reply to some helpful suggestions from
Daniel Wolf with which I warmly agree, and to a very courteous and
compelling response from John deLaubenfels on the issue of new
adaptive tunings for historical pieces. Both of your responses show
how dialogue of this kind, made possible by the Tuning List, can
indeed cause an author such as myself to change her views, or at least
to "refine" their expression in a way which may amount to the same
thing.

Before responding to these two replies, I would like briefly to
acknowledge other replies centering around the music of Charles Ives,
a topic I was incautious enough to write about without actually
knowing the music. Of course, it might be argued that my indiscretion
at least had the effect of prompting thoughtful and often poetic
responses from Johnny Reinhard and Dan Stearns alike. In another
article, I may venture a few comments.

Having taken up some considerable length in my original post, I shall
attempt to define here more concisely, with the benefit of much help
from Daniel Wolf and John deLaubenfels, two new and hopefully better
concepts: "just realization," and "Xeno-Just realization."

------------------
1. For Daniel Wolf
------------------

Turning first to Daniel Wolf's reply, I would like warmly to agree
with what I realize are words of good counsel:

> Isn't it more useful to define the tuning independently of the
> compositional technique and then to analyse the way in which
> individual repertoires, composers or compositions project (or fail
> to project) aspects of that tuning?

Upon reading these words, I realized that in my article I was mixing
two issues which in fact it should have been my goal to differentiate:
whether a tuning is "JI," and whether it has enough pure ratios
"justly" to represent the intervals called for by a given music.

Very specifically, what I was seeking to address in my definition is
the kind of viewpoint which assumes that a "true JI" system must have
certain specific ratios available such as a 5:4 major third (excluding
a 3-limit system), or a 7:4 minor seventh (excluding also a 5-limit
system). My solution at first blush was to propose that these
lower-prime-limit systems are "JI" if and only if they are used for
music which can be "justly" realized within their limits.

However, I now realize in a way that my definition does deliberately
the same questionable thing that others may be doing unintentionally:
mixing the issue of whether a system is JI, and whether or in what
manner it fits a given compositional or improvisational style.

Therefore I would like to propose _two_ definitions, one of a "just
intonation system," and the other of the "just realization" of a given
composition or style.

First, here is my new definition of a "classic JI system," with much
indebtedness to your point about not necessarily requiring a
"complete" set of ratios up to some odd limit:

A tuning system is a classic just intonation system
if:

(1) All intervals in the system are defined as
integer ratios;

(2) The system provides some set of intervals
other than the unison and octave based on
low-integer ratios.

As you point out, a definition of JI should not exclude a system such
as that of La Monte Young because it may have 7-based but not 5-based
ratios, for example.

Letting these two objective criteria suffice to define a system as
"JI," I would propose a concept of "just realization" (JR):

A JI system provides just realization for
a given musical composition or style if:

(1) For music based on a contrast between
stable and unstable intervals, as in
historical modal or tonal Western
European polyphony, the system provides
pure ratios for all stable concords; or

(2) For other musics, it provides a set of
pure ratios sufficient to represent the
intended interval structure of the
composition or style.

This may, as you point out, allow for musics where concepts such as
"stable concords" (implying a contrast with unstable sonorities) may
not apply. If Harry Partch's JI system provides the set of pure
intervals called for by his music, we have JR, regardless of whether
such concepts as "concord/discord" apply.

To sum up: I would say that a 3-limit tuning is always JI, and is JR
for Perotin or Machaut, but not for Palestrina or Bach. The systems of
La Monte Young and Harry Partch are likewise always JI, and are JR for
their respective musics, or for other similar styles.

------------------------
2. For John deLaubenfels
------------------------

Please let me quote some of the most gracious words I have seen on
this Tuning List:

> Margo, you may be the least combative member on this list (not
> counting, I suppose, those who don't post at all!), but I feel
> compelled to respond.

Here, as a pioneer in the area of adaptive tuning, you were replying
to my comment that

>> [...] JI musicians and advocates may differ not only in their
>> choice of odd-limits and musical styles, but in their preferences
>> regarding levels of contrast between concords, dual-purpose
>> sonorities, and discords. Such varying tastes lend emphasis to
>> the point that an ideal JI system for one kind of music may do
>> great intonational injustice to another.

While this statement _could_ be read narrowly to address only what I
would call the issue of "underrealization," for example using a
3-limit JI tuning for 5-limit music, it could equally well be read to
describe using 7-limit JI for historical music generally associated
with a 5-limit outlook as a "great intonational injustice." The fact
that I chose to leave the second reading open reflected my real
ambivalence at the time about such adaptive tunings, not an
unintentional slip or a misunderstanding.

For this I take full responsibility, but am pleased to say that your
gentle and friendly response -- under the circumstances, showing more
restraint than I've ever had cause to exercise here myself -- has
caused me to reconsider my own feelings and remember the experimental
side of my own musical roots. As a result, I am pleased both to defend
adaptive tuning and to suggest a new term for it: Xeno-JI (XJI), or
more maybe more formally, "superjust representation" (SJR).

At the start, I should emphasize the importance of affirming the value
of historical and "period-appropriate" tunings in an _inclusive_ way.
To say that "the 81:64 major third of 3-limit in Machaut and the 9:5
minor seventh in Monteverdi are musically to be valued" need not and
_should not_ be taken to imply, "any other tuning of these intervals
in a performance is an act or artistic injustice."

Rather, as you say, to "distort" a piece in a pleasing manner is not
artistic injustice, but artistic variety. Of course, I would urge that
we _also_ cherish and relish more likely historical intonations for
the piece, thus more deeply appreciating both types of interpretations.

Maybe I have a special responsibility to point out that my own
approaches are hardly pure and always "historically authentic."

First, someone could ask, "Is a Yamaha TX-802 really an authentic
medieval or Renaissance instrument?" This is indeed the instrument I
use for my explorations of the tunings I discuss here.

Even some of my "period tuning" experiments involve an artistic guess:
for example, my approach to early 15th-century music of using
Pythagorean thirds and sixths as cadential intervals resolving for
example to fifths and octaves, but schisma thirds and sixths for
prolonged noncadential sonorities involving sharps. This is a "guess,"
maybe a kind of historical novel with some footnotes. I further
confess to trying (and liking) an interpretation with a comma
inflection

E4 F#4 G4
Db4 C#4 D4
A3 G3

to have it both ways, a beguilingly smooth diminished fourth between
the lower voices for the opening sonority and then an active major
third (along with the major sixth) for a classic Gothic cadence with
the usual verve and energy. This is a "distortion" -- however artful
or otherwise -- at least as far from likely period practice as doing
Bach in 7-limit.

Further, while more than ready to defend 16:9 and 9:5 as realizations
of the minor seventh, I must admit to devising a "Xeno-Gothic" tuning
(24-note Pythagorean or 3-limit JI) using minor sevenths a Pythagorean
comma smaller than 16:9 -- about 3.8 cents from 7:4 -- for sonorities
resolving to fifths. Yes, I can quote Marchettus of Padua to provide a
_possible_ basis for this experiment -- but then again, you might
quote certain 18th-century theorists on the "harmonic seventh" to
justify the use of 7:4 in music of that era.

Then, again, I confess to trying a Monteverdian sonority of minor
seventh and fifth above the bass, but using an augmented sixth -- and
finding the standard resolution intriguing in this tuning. Yes, I did
it using a near-7:4 interval in 1/4-comma meantone (a la Dave Hill) --
but I enjoyed it while knowing very well that a regular minor seventh
would be the expected choice.

Having made my due confessions for the moment, I would propose that we
define "superjust realization" (SJR) as the application of a JI system
to a piece so as to use simpler or more pure ratios for some intervals
than a likely period-specific tuning would involve. Your 7-limit
interpretations of 18th-19th century music may fit this category, and
I also like the term "Xeno-Just realization" (or XJR).

Your reply raises some fascinating issues about technical and musical
factors shaping intonational choices, historical or otherwise, but for
now I would like warmly to thank you for the reply you felt compelled
to write, and wrote so compellingly as well as graciously.

Most appreciatively,

Margo Schulter
mschulter@value.net