First recording in 13-tET -- response to Paul Erlich

[Dear Paul, and everyone: Since writing this, I taped some first
examples in 13-tET, and hope to be taping more over the next week so
as to have something that I can mail to people, and at some point with
some very generous help offered by participants in this and related
tuning forums, make available on the World Wide Web. Please let me
note Jacky Ligon's very skilled and patient role in making my
timbre-specific examples available in the last issue of TMA as one
example of such help.]

Hello, there, Paul, and thanks for your enthusiasm about my 13-tET
article. I'm pleased to say that I now have a set of timbres, and am
about ready to start taping some music.

It's a fascinating tuning, and I find that some standard 13th-14th
century progressions, including a couple of favorite chromatic ones
described and advocated by Marchettus of Padua (1318), map directly
and very pleasantly to my keyboard.

Other progressions, especially when I try them on different steps in
my keyboard arrangement, remind me that 13-tET is not a regular
diatonic tuning -- part of the fun.

Once the 8-step interval around 738 cents is "smoothed" enough to have
a "3:2-like" quality, 13-tET is a delightful neo-Gothic scale. I'm not
saying that 0-738-1200 rounded cents as a stable trine is identical to
a just 0-702-1200 -- only that it can have the same musical meaning,
more or less, as happens less dramatically in various temperaments.

One very appropriate term for the tuning/timbre adjustments would be
Chowningization, in honor of John Chowning both as the inventor of the
FM synthesizer and its algorithms, and as the composer of _Stria_
(1981) based on a division of Phi into nine equal parts almost
identical to 13-tET.

At some point, maybe, we might have an amusing discussion about what I
might term "categorical entropy" -- a tendency maybe to interpret
sonorities not only based on simple ratios, but on familiar interval
categories in a given style (like the often complex thirds and sixths
of Gothic or neo-Gothic music).

For example, the 10-step or 923-cent interval in 0-461-738-923 (or
0-5-8-10 steps) seems to me have a certain consolidating power: it
signals, in Gothic/neo-Gothic terms, "major sixth sonority seeking
expansion to trine," with the major sixth resolving to an octave.
To me, it's a kind of musical synonym for 0-408-702-906 or maybe
0-435-702-933 -- there's a kind of "pattern recognition."

Please note here that I'm using the neo-Gothic category of "major
sixth" to explain my expectation, with 923 cents neatly fitting it,
but would caution that the term "10-step" is generally better. Usual
interval addition based on Pythagorean or meantone, etc., doesn't
generally apply in 13-tET, so counting steps or cents is usually best.

Curiously, 461 cents can represent for me a stable "4:3-like" interval
in 0-738-1200 (or also 0-461-1200), but can seem to take on the role
of a large and active cadential interval expanding to an 8-step
consonance -- in usual neo-Gothic terms, a "large major third."
Sometimes it seems to have something of this latter effect even as a
simple interval or dyad, but in 0-5-10 (0-461-923) or 0-5-8-10 that
10-step interval may favor such an interpretation of the 5-step as
part of the overall pattern.

Anyway, 13-tET seems to me very special and charming, sometimes almost
like Pythagorean and sometimes charmingly unpredictable in presenting
new patterns and possibilities that I should learn more about as I
become more experienced.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:

> At some point, maybe, we might have an amusing discussion about
what I
> might term "categorical entropy" -- a tendency maybe to interpret
> sonorities not only based on simple ratios, but on familiar interval
> categories in a given style (like the often complex thirds and
sixths
> of Gothic or neo-Gothic music).

I've brought up categorical perception many times before, even
recently, since it's a very important effect. For most people, at
least in Western culture, categorical perception operates within the
12 categories of 12-tET. The boundaries are roughly at
the "quartertones"; except for the unison and octave, which have
narrower boundaries; and the intervals adjacent to them, which have
correspondingly wider ones on that side.
>
> For example, the 10-step or 923-cent interval in 0-461-738-923 (or
> 0-5-8-10 steps) seems to me have a certain consolidating power: it
> signals, in Gothic/neo-Gothic terms, "major sixth sonority seeking
> expansion to trine," with the major sixth resolving to an octave.
> To me, it's a kind of musical synonym for 0-408-702-906 or maybe
> 0-435-702-933 -- there's a kind of "pattern recognition."

There may also be various difference tones effecting the "solidity"
of this chord.