Re: An experiment -- for John deLaubenfels and Jacky Ligon

Hello, there, everyone, and I'd like to express my special thanks to
John deLaubenfelts and Jacky Ligon for their inspiration and
assistance in my exploration of neo-Gothic just intonation (JI) based
on pure ratios of 2, 3, and 7 -- including a maybe quite revealing
experiment.

First, John, in response to your welcome invitation, I should express
both my desire to make this music available (via the Web, CD's, or
otherwise) and my technical frustrations at not having some convenient
recording device available. Of course I invite any assistance, and
hope in the next months to produce a tentative cassette version of
some performances and improvisations on a Yamaha TX-802 in various
neo-Gothic tunings which possibly might be used to generate some
appropriate Web versions. Maybe we could call it "Music from the
pre-General-MIDI Era."

Recently Joseph Pehrson and Dan Wolf (happily returned to this List
despite some significant financial barriers affecting users in various
parts of our "global village") were discussing the theme of "rewrites
of history," and I wonder if that phrase doesn't sum up about 90% of
what music means to me. While the experiment I'm about to describe may
reflect one very aurally concrete side of that phrase, a recent
discussion of 46-tone equal temperament (46-tET) may reveal another.

One reason "rewrites of history" can encompass an immense scope of
musical variety and what we might term "innovation" (paradoxically or
otherwise) is that history, to borrow from Admiral Grace Hopper,
offers so many standards to choose from.

For some people, 46-tET represents a not-so-close approximation of
ratios of 3, 5, and 7, after the manner of the 22 srutis. This
discussion seemed oriented especially to fretted instruments, long
associated with equal temperaments, so there may be reasons to prefer
46-tET which might not be so obvious to me as a keyboard player
uninitiated in such fretted instruments.

However, for me, 46-tET means above all "virtually pure 14:11 major
thirds." I consider it a kind of neo-Gothic equivalent of 31-tET with
its near-pure 5:4 major thirds, and in fact 46-tET comes even closer,
something like 417.39 cents in contrast to a true 14:11 at ~417.51
cents. Of course, there's also the diminished fourth and augmented
second at not too far from 21:17 and 17:14; I consider these also
principal intervals which give 46-tET its musical identity.

Yes, we can also get rough approximations of 7-based ratios, which I
tend to describe in keyboard terms: a "large major second" for a
near-7:6, or a "large major sixth" for a near-7:4. This means that
with two keyboards tuned a 46-tET diesis (~52.17 cents) apart, playing
D-E* or D-B* (an asterisk showing a note on the upper keyboard) will
produce these rather 7-ish ratios.

Here I'm tempted to add that if I really wanted to optimize those
"7-flavor ratios," however, I would temper the fifths a tad more and
use an "e-based" temperament where they are about 2.65 cents wide
(~704.61 cents). This gives a virtually pure 7:4, and a closer 7:6
and 9:7 than in 46-tET -- but an augmented second, for example, further
from a "supraminor" ratio of 17:14, which 46-tET better approximates.

However, our "real life alternative history novel" gets stranger at
this point, because I need to remember that probably most people
reading this normally assume that thirds are stable intervals, whereas
in neo-Gothic music they are just as routinely unstable. Similarly a
"7:4" might mean something quite different in a neo-Gothic 12:14:18:21
contracting to a fifth than in a 19th-century 4:5:6:7. Isn't it fun
how something like "46-tET" can set off such different views, serving
as a kind of musical portal into alternative realities?

Enough of theory; now to that concrete experiment.

When I made an inquiry late last week about TX-802 timbres for
"locking-in" JI partials a la Dave Keenan, to whom I am immensely
indebted for the experiment which follows, Jacky Ligon responded via
e-mail most obligingly and in step-by-step detail as to how to create
such a harmonic timbre for this synthesizer from the front panel.

Jacky, your steps guided me with a true user-friendly aplomb through
the process of setting up a harmonic texture with some qualities of a
reed organ, or maybe a harmonium, featuring both even and odd
partials.

Using some familiar built-in timbres, which I favor for emulating such
medieval and Renaissance instruments as harpsichords, organs, and
crumhorns, I had already noticed that the pure 7-based versions of
unstable sonorities in my 2-3-7 neo-Gothic JI scheme did have a
certain "smoothness" distinguishing them from the usual complex
Pythagorean 3-based ones -- but that both versions could sound "in
tune."

However, I wondered, what difference might a dedicated harmonic timbre
make? Would the 7-based intervals stand out in a special way as more
"concordant," or the complex 3-based intervals become especially
strident or tense?

Having set up the timbre, I was ready to learn through experience,
just as Roger Bacon advocated about 750 years ago.

What I found, maybe with a mild feeling of surprise, was that the
usual complex Pythagorean intervals sounded quite normal and "in
tune," and the 7-based intervals indeed audibly "smooth," and at the
same time somewhat "strange" -- maybe more so that using a "puff pipe"
organ or harpsichord emulation.

The beating on a usual Pythagorean sonority such as g-b-e' or G3-B3-E4
(64:81:108) sounded "warm," "familiar," "at-home," while the same
sonority as a pure 7:9:12 sounded a bit "strange" as well as smooth --
as if the beatlessness placed it in a certain bold, almost stark,
relief. The latter effect, of course, has its own fascination, and
lends a special kind of emphasis to a cadence.

However, it wasn't a simple dichotomy of simpler means necessarily
more "concordant" or "in tune." I'm almost tempted to propose a
bumpersticker, although without an automobile on which to display it:
"27:16 gives me a warm fuzzy."

This experiment also let me experience the kaleidoscopic nature of my
own musical perception: 14:18:21 (e.g. f-a-c' or F3-A3-C4 in a 7-based
version) might sound either very strident or alluringly smooth in a
different way.

Anyway, my experiment with the Dave Keenan "locking-in partials"
timbre, courtesy of Jacky Ligon as TX-802 and documentation maven,
showed me that I hear complex Pythagorean intervals as "in tune" in
this acoustical setting, and 7-based intervals as different, often
strange and often alluring, supplementing but not supplanting those
complex 3-based ratios.

Here I can picture someone adding, as I'll do myself: "Of course you
like the `warm fuzziness' of the beating in a 27:16, because it whets
your appetite for the stable octave you've been conditioned by some 30
years of musical experience and practice to expect will follow; keep
in mind just how culturally specific the results of this experiment
are, whatever universals of 'harmonic entropy' might obtain."

Where to go from here? One possibility occurring to me a few days
before this experiment is a kind of fusion between Easley Blackwood's
remarks on JI and the textural contrasts of the late 16th-century
madrigal exemplified by Gesualdo around 1600.

How about a neo-Gothic 2-3-5-7 JI style with slow passages featuring
mostly note-against-note motion with pure low-integer sonorities
(slowing down permits an easier time at the keyboard as well as more
appreciation of the pure sonorities), and faster passages with more
complex Pythagorean intervals? One thing the experiment confirms: I
want to keep those pleasantly fuzzy and beatful Pythagorean intervals
available for those slower passages also -- why not enjoy the full
variety?

Anyway, John and Jacky, I'm posting an article on defining JI from a
"three-dimensional" viewpoint which will consider both complex
integer-ratio systems and adaptive JI tunings; thank you both for
providing much of the substance for this article in practice and
theory.

Most appreciatively,

Margo Schulter
mschulter@value.net