More on Bill Sethares's _Xentonality_

Hello, everyone, and may I express my special appreciation to Bill
Sethares and Aaron Johnson alike for helping to provide me with an apt
occasion to offer some comments to a discussion of a classic for our
community: Bill Sethares's _Xentonality_.

For Aaron's review and addendum that started this discussion rolling,
by the way, please see

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While Bill has done very sophisticated mathematical investigations of
tuning, timbre, and sensory consonance or dissonance as it is
sometimes called, I would like here above all to emphasize his
contributions as a practical musician, in keeping with the focus of
this forum. What _Xentonality_ demonstrates in most creative ways is
that tuning/timbre matching can not only generate some interestingly
consonant intervals; it can serve as a basic for beautiful music.

Of course, as Bill himself would emphasize, this isn't the first such
demonstration, and the principle manifests itself in various world
musics: but as Aaron Johnson has aptly written, _Xentonality_ is
indeed a collection of "etudes" in the science and art of harmonizing
tuning and timbre (or vice versa).

Indeed, in my own idiomatic vocabulary, _Sethareanize_ has become a
very useful verb, meaning basically "to experiment with timbre and
tuning, or to make music based on such experimenting." Likewise,
_Sethareanization_ means the process of "well-timbrement," or
according tuning and timbre. Of course, one might also name such a
practice after the masterful builders of African xylophones, or
Javanese or Balinese gamelan instruments, or such xenharmonicists as
Ivor Darreg, John Chowning, and Wendy Carlos; but my usage might
reflect Bill's role as an explicator and exemplar of this process.

What I can definitely say is that "Sethareanization" is a contagious
exercise: I'm writing this after having devised a tuning/timbre
combination for a new (to me) temperament, and am writing in the
afterglow of an exhilarating process. Part of the fun of listening to
_Xentonality_ is the element of empathy: "How might I, or have I,
approached this same tuning?"

Here I'll seek to complement Aaron's fine review by addressing a few
tracks of special interest to me in a CD album where every piece
offers inspiration to listeners and musicmakers alike.

How could I resist a gorgeous piece like _Seventeen Strings_, given my
love for quintal/quartal harmony (chords built with fifths or
fourths)? Here Bill has taken a beautiful harp texture and customized
the timbre to 17-tET. While I might guess that the timbral adjustment
was done in part to get "smoother" or less tense thirds, I might ask
whether the fifths and fourths (about 3.93 cents respectively wide and
narrow of a pure 3:2 or 4:3) were also made to seem closer to just, as
for example in a Pythagorean tuning.

Whatever Bill has done in technical terms, those arpeggiated
sonorities in fifth and fourths are really beautiful, and the portions
with more emphasis on thirds indeed have a "smooth and pleasant"
quality, a judgment which I might guess a listener less accustomed to
the rather active or "beatful" thirds and sixths in this portion of
the spectrum -- when played in typical harmonic timbres -- might
share.

By the way, a tuning like 17-tET can also illustrate how the nuances
of "Sethareanization" may vary according to style. The major third in
this temperament, at about 423.53 cents, seems near the point of
maximum complexity or tension between the simple ratios of 5:4
(~386.31 cents) and 9:7 (~435.08 cents), so that in many timbres the
effect can sound decidedly "dissonant." In a medieval or neo-medieval
European style where thirds and sixths are active and unstable, a bit
of discretion in choosing a timbre can help to achieve the desired
effect of "imperfect" or _partial_ concord.

However, as _Xentonality_ shows, it's also possible to adapt 17-tET to
styles where thirds and sixths are fully concordant, and moreover to
do so in a delightfully rich texture based on an artfully modified
Celtic harp sample.

A characteristically urbane side of Bill's music comes out in _Unlucky
Flutes_, which I might describe as a kind of jazz ensemble piece in
13-tET -- or, at least, I find the style somehow "jazzy," an adjective
I also apply to some of my favorite 14th-century music. Here, as in
much jazz, the melody is a big attraction, and the "bass" line adds to
the charm.

As stated in the notes: "All instruments clearly retain their tonal
identity, yet sound harmonious even on sustained passages." As someone
who has borrowed and designed some timbres for 13-tET on the Yahama
TX-802 FM synthesizer, I can say that meeting both parts of that
statement at the same time -- getting a "harmonious" sound with a
mixed ensemble of "flutes, guitars, bass, and keyboard" -- is indeed
impressive. My own more technically modest approach has been simply to
borrow or concoct a texture or two that to my ears make the interval
of 8/13 octave (about 738.46 cents) sound like a reasonably persuasive
and concordant "fifth," and go from there.

The result of Bill's technical achievement is something that reminds
me of a jazz ensemble from around the 1960's: witty, cultured, and
musically most engaging.

As it happens, two pieces on this CD tie in with one of my first
introductions to Bill Sethares and his timbre/tuning creations:
hearing some of the customized electronic "instruments" he designed
for Gary Morrison's 88-cET or "88-cent equal temperament" on a
cassette which Morrison kindly sent me offering a kind of guided tour
of this tuning. I recall that Bill designed a "bagpipes" timbre, for
example, fit to one of the possible quasi-octave intervals of this
tuning, either 1144 cents or 1232 cents.

_Haroun in 88_ has a flavor I again find "jazzy," and I might say
"upbeat," with nice counterpoint. There's a richness to the harmony
and texture which _might_ reflect the stretched-octave tuning, but
also more generally the thematic interchange and interplay between the
voices, something effective in lots of tuning systems and styles. If
asked to propose an ostentatiously "88-cET" scenario, I might suggest
some gamelan-like texture with an accent on shimmering 1232-cent
quasi-octaves. This seems to me rather more subtle, with an affability
and refinement that might suggest jazz or Blues.

Also in 88-cET, the companion piece _88 Vibes_ has indeed what I might
call a "vibrant" quality, using a spectrally mapped "vibraphone"
timbre. As I wrote in my notes, this piece has a "brightness and
mystery" about it; there are some effects like glissando sweeps to
catch the ear, and a lyrical theme with a chord progression I'm almost
tempted to compare to a hypothetical version in minor of the Beatles'
_Let it Be_. Possibly this last comparison might give caution about my
opinions concerning a wide range of post-1400 music, but the
impression of something "different, and yet not that unfamiliar" is
worth noting.

Now we come to the other piece I'm reviewing here, and which has given
me cause for a bit of cursory Web research on the sociocultural
background: _The Turquoise Dabo Girl_ in 11-tET. My first association
on seeing this title around the time I was first getting in touch with
Bill Sethares on the Internet was with the Latin phrase _Ibi dabo
tibi_ ("There I will give you...") from the motet _Quam pulchra es_ by
the English composer John Dunstable (c. 1370?-1453).

A Dabo girl, as it turns out, is a woman in the science fiction series
_Deep Space Nine_ who operates the wheel for a game of chance called
Dabo, apparently some futuristic variant of roulette.[1] It's not an
especially high-status position to occupy, and the main role
expectation is to attract and hold the interest of as many gambling
customers as possible, using just about any alluring means to do so.

However, the role of Dabo girl does not necessarily define the woman
(from whatever solar system) playing it: "today a Dabo girl, tomorrow
the leader of an interplanetary liberation movement."

Approaching the piece from this perspective, I might hear in _The
Turquoise Dabo Girl_ both the exotic and alluring atmosphere of a
_Deep Space Nine_ casino, and the inner character and strength of a
person who finds herself in the role of a Dabo girl, but has lots of
things to express beyond that role.

The opening portion might accentuate more the "exotic" theme: I found
it "a bit `brooding,' but not necessarily unfriendly." One comparison
evoked my childhood: how about using this as a neat theme in the late
1950's or early 1960's for a mystery series on television, or a movie,
about some sophisticated investigators, like _The Thin Man_ or _The
Pink Panther_?

Then things get more lyrically, I might say yearningly, concordant --
not that the previous effect was "dissonant." Paul Erlich once
concluded, if I recall correctly, and my own experiments with 11-tET
seem to confirm, that this harmonic sweetness results in part from the
use of a sonority like 0-6-9-13 steps or about 0-655-983-1418 cents.
The effect, like that of a just 4:6:7:9 (~0-702-969-1404 cents) or
some closer tempered approximation, is a resonant and intriguingly
complex concord. As Paul Erlich has noted, having a multi-voice chord
fitting this kind of pattern can compensate for inaccuracies in the
tuning of individual intervals, like the 11-tET fifth -- at around 655
cents, some 47 cents narrow of a just 3:2, and inviting the more
likely description of a large tritone (e.g. 16:11, around 649 cents).

In more conventional terms, 0-6-9-13 steps could be described as a
very narrow fifth, small minor seventh, and rather wide major ninth;
in Bill's spectrally mapped "instrumentation," this can convey a
"minor seventh" flavor fitting with an aura of "cool" and
sophisticated harmony a la the 1950's or 1960's.

One question which Bill himself asks in his notes about a "pan flute"
melody harmonized in the "chorus" of the piece: "Does this have the
feeling of some kind of (perhaps unfamiliar) `cadence' as the melody
resolves back to its `tonic'?"

My own answer would be "Yes, and rather like a remissive or Phrygian
cadence; at least, I pick up the ascending `whole-tone' motion in one
or some of the upper voices (by a 2-step interval of around 218 cents,
I'd guess), and this suggests to me an effect like descending motion
in some other voice by a `semitone' of one step, or around 109 cents."

As I might cheerfully conclude by cautioning again, Sethareanizing can
be a highly contagious participant sport, and these consummate etudes,
as Aaron has well described them, provide an incentive and inspiration
for others of us who seek to emulate his most subtle art.

----
Note
----

1. While I tend to regard my free association of "Dabo girl" with
Dunstable's setting of the words _Ibi dabo tibi_ as fortuitous, one
unofficial explanation of the name "Dabo" indeed derives it from the Latin
_dabo_, "I shall give" -- as in an advertisement of sorts: "Look at the
prizes we're giving out if you pick the right number!" Another unofficial
derivation is from a proper name. I'm not sure if the creators of _Deep
Space Nine_ have spoken to this question.

Most appreciatively,

Margo Schulter
mschulter@...

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@c...>
wrote:

> Indeed, in my own idiomatic vocabulary, _Sethareanize_ has become a
> very useful verb, meaning basically "to experiment with timbre and
> tuning, or to make music based on such experimenting."

I've used it as a verb also, but I meant "shifting the partial tones
of a timbre to correspond with the tuning of a temperament" or what
you call "well-timbrement" below.