For Julia -- at an important moment

Dear Julia,

Reading some of the recent exchanges, I am very concerned to
communicate my encouragement and to say how much you have already
added to this forum, and how much I hope that you will stay.

One reason I've been mostly a spectator in these exchanges over the
last few days is that I posted a long reply about a week ago, maybe
overly long, and read your article explaining that you are just
catching up with e-mail during your travels away from home. Thus I
guessed that it might be best to give you some time to respond to my
earlier message -- happily noting your mention of the theme of "found
objects" -- before offering more new comments.

However, events can take on their own momentum, and I would like first
to respond to few points of discussion, and then to express more about
how reading your article has enriched my own approach to music.

First of all, the "relevant properties" of a given tuning can very
much depend on style and context. This is an art, not an exact
science. The best approach, it seems to me, is to compare notes in a
framework of mutual appreciation and discovery, celebrating the ways
in which the same intervals or "grid" patterns can inspire very
different styles and interpretations.

For example, to learn the "relevant properties" of a 433-cent third in
your music, I must enter your world, and seek to understand its
sonorous beauty, with your theoretical concepts as a helpful map.

As it happens, a third around 433 cents is also one of my favorite
intervals, but the context and thus the "relevant properties" are a
bit different. Each style and perspective has its own value, its own
world of possibilities.

At its best, comparing notes can not only give us a better
understanding of each other's music and conceptual maps, but can lead
to a bit of creative borrowing where a "loan element" from one style
or tradition enriches another, rather like a linguistic loan word.
Sometimes, this may mean "discovering" intervals that were already
there in one's own intonational backyard, but had been neglected until
a helpful visitor called our attention to them.

For example, I have a tuning based on two 12-note Pythagorean chains
with some very small minor sixths at around 750.145 cents -- or, more
precisely, a ratio of 57344:37179. Reading the remarks about 750-cent
intervals in your paper, I have resolved to be sure that this
beautiful interval gets used, as well as some related 42-cent and
48-cent melodic microintervals.

Also, just yesterday, I was looking into some scales within a tuning
system that has me really excited, and found myself looking at a
progression where the scale seemed to shape the resolution as much as
vice versa.

Then I said to myself, "Ah, a `found object' reminding me a bit of
Julia: taking the scale as a given, and going from there. It's OK to
be curious about the possible theoretical implications, but at this
point don't be too concerned -- just enjoy it, and see where it leads
musically."

There's lots I could say about consonance/dissonance and related
theories, but at the moment a bit of harmonic and melodic empathy
could be more important than such an analysis, which I'd be glad to
discuss further at some point. For now, I'll just say that the
questions you raise about the 4:3 fourth, and the minor sixth or
related intervals at just about any ratio, are valid and important,
and that the "question of the fourth" has a fascinating history in
14th-17th century European theory which I find of great interest.

One thing I would like to acknowledge as someone who does often "tune
by ratios" both large and small, or to tempered approximations of
these ratios.

Somehow tuning "pure" or "near-pure" ratios can sometimes lead to a
certain "horse pride," to borrow a sobering metaphor. It was said in
Classic times by one writer than the power and speed of riding a horse
could result in an intoxicating sense of personal power and pride --
possibly reflected in some of the wars and conquests of the era.

More generally, this might be temptation of any artist struggling and
rejoicing to develop a new style, and facing allegations that this
style is "unnatural" if not "musically impossible." An unfortunate, if
not so surprising, reaction is to reply that the "common practice" is
in fact better described by such pejoratives.

Reflecting on the exchanges here, I suspect that one might catch a bit
of this "horse pride" even in a musician and theorist such as Kathleen
Schlesinger, who in her study _The Greek Aulos_ (1939) champions
complex ratios with fascinating precedents in ancient Greek theory.
She defines "modal" octaves based on sets of ratios like the following
12-note piano tuning, for which I'll also give cents and 72-tET
approximations:

22/22 22/21 22/20 22/19 22/18 22/17 22/16 22/15 22/14 22/13 22/12 22/11
0 81 165 254 347 446 551 663 782 911 1049 1200
0 83 167 250 350 450 550 667 783 913 1050 1200

Having presented this tuning, she remarks:

"Many musicians demur when introduced to the ratios
of this modally tuned piano, for they consider that
a scale containing intervals such as 12/11, 11/10,
15/13, forms a proposition impossible to bring into
operation in practical music. That is an objection
which comes naturally enough from modern musicians
born and brought up in an atmosphere of our major
and minor scales, with their more or less false
relations, but this is an entirely individual
matter, for many there are who react immediately
in delight on hearing this new language of music."
[Kathleen Schlesinger, _The Greek Aulos_ (Bouma's
Boekhuis, Groningen, 1970; Reprint of edition by
Methuen, London, 1939), p. 541.

Here one might ask, why "more or less false relations" instead of
simply "different relations"? Please let me admit that I am hardly
immune to this "horse pride" either. The antidote is to celebrate and
assert the integrity both of our own traditions or styles and those of
others, a balance sometimes more easily sought that maintained.

In fairness to Schlesinger, I should add that only a couple of pages
later she quotes the composer Elsie Hamilton, an exponent of this
integer-based music who explains that

"the two systems... represent two distinct
musical worlds, each quite complete in itself"

and urges an approach of "allowing each to work upon one through its
own inner logicality." (Ibid. p. 543.)

If we can join in affirming and celebrating this kind of pluralism and
tolerance, then the theoretical dialogues can follow in mutual respect
as one side of a joyous comparing of notes.

Most appreciatively,

Margo Schulter
mschulter@value.net