Re: TD 945 -- On JI (for Jacky Ligon)

Hello, there, everyone, and a special welcome back to Jacky Ligon.

Please let me begin by saying that I consider just intonation (JI) in
the most comprehensive classic sense to mean exactly what David
Beardsley has said: tuning by integer ratios.

Of course, I also agree with Dave Keenan that there are different
_kinds_ of JI intervals and styles, and that a ratio such as 3:2, for
example, has a different kind of "justness" from a ratio of
intermediate complexity such as 21:17, or one of impressive complexity
such as 12544:9801 (81:64 plus two 896:891 commas).

As someone who delights to have integer ratios of all three kinds in
my JI tunings, I would say that they are all part of the picture,
which is not to say that they are equally everyone's cup of tea in the
"JI community."

Attempts to set some limit on the size of integer ratios used in JI
seem to me both needlessly restrictive and futile, but certainly we
can recognize the fact that more complex JI intervals have a quality
much like those of tempered (irrational) ratios surrounding them; and
similarly that some tempered intervals are "virtually just."

For example, when I tune 24-note Pythagorean or "Xeno-Gothic" (the
latter term implying a neo-Gothic stylistic context), I certainly
consider this a "JI tuning," a description including all the ratios
and intervals of the tuning, however simple (2:1, 3:2, 4:3, 9:8) or
complex.

At the same time, I recognize that the interval of 16 fifths up, for
example, 43046721:33554432 (~431.28 cents), is "just" in the sense
that it is an integer ratio derived from pure fifths, but from another
point of view a "virtually tempered" approximation of 9:7, being
around 3.80 cents narrow of this simple ratio.

Tempered intervals, conversely, may approach simple (or complex)
integer ratios as closely as one desires: thus 10/31 octave is very
close to 5:4; 8/22 octave to 9:7; 16/46 octave to 14:11, etc.

Jacky, a ratio from one of your JI tunings sticks with me: 29:23
(~401.30 cents), quite close to 4/12 octave. It seems to me that JI
and the various forms of temperament (regular and irregular) are and
should be free to take in the valleys, plateaus, and summits of the
intonational landscape -- from the most simple to the most complex.

The idea of "tuning by integer ratios," of course, may carry various
implications for various people and styles of music, for example:

(1) Using the simplest and purest possible ratios for stable
concords in a given style;

(2) Preferring epimores or superparticular ratios for intervals
making up a tetrachord, for example (e.g. 9:8-8:7-28:27);

(3) Seeking to maximize the simplicity or "suavity" of certain
unstable intervals and combinations as well as stable ones,
e.g. 4:5:6:7 in an 18th-century setting (Euler), or 7:9:12
in a neo-14th-century setting.

Possibly one might use capitalization to suggest a difference in
nuance between a "just" interval (any integer ratio) and a Just
interval (an interval with a _small_ integer ratio readily tuneable by
ear by a locking in of partials).

Also, JI systems feature what we might regard as three types of
intervals:

(1) "Simple" JI intervals a la Dave Keenan, or the "valleys"
of Paul Erlich's harmonic entropy, where locking in of
partials occurs, with Paul's suggested upper limit of
complexity by the point for a ratio a:b where a*b=105.

(2) "Intermediate" JI intervals such as 14:11 or 13:11 where
combination tones may give ratios something of a
"quasi-Just" quality (I leave this as an open question).

(3) "Complex" JI intervals such as the regular Pythagorean
major and minor thirds at 81:64 and 32:27, as well as
a variety of large-integer ratios in more recent JI
systems (e.g. LaMonte Young).

A typical JI system may have some intervals from each of these three
categories, which is to say that _some_ just intervals are also Just
or "pure."

In a JI array I posted here some weeks back, for example, and for
which the Monz designed a beautiful lattice, I find it natural to
speak of "a pure 3:2"; somewhat more of a poetic trope or liberty to
speak of "a pure 14:11"; and quite unlikely to speak of "a pure
12544:9801." Yet all three intervals are part of the total musical
reality, the first two by design and the last as a kind of
serendipitous gift, each with its own musical beauty.

As Leonhard Euler approached the problem of consonance/dissonance, so
would I approach the diverse intervals of JI: there is a continuum of
the simple and the complex.

Most respectfully,

Margo Schulter
mschulter@value.net

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and a special welcome back to Jacky Ligon.

The pleasure is mine.

>
> Jacky, a ratio from one of your JI tunings sticks with me: 29:23
> (~401.30 cents), quite close to 4/12 octave. It seems to me that JI
> and the various forms of temperament (regular and irregular) are and
> should be free to take in the valleys, plateaus, and summits of the
> intonational landscape -- from the most simple to the most complex.

Yes, and in the context of composing with tunings that are derived
from the non-linear spectra of instruments made from metal, tuned
membranophone percussion and synthesis techniques; the complex ratios
that are found in the overtone structures of these kinds of timbres,
(to my ears) become the most correct intervals to use. An observation
that I have made during my exploration of the spectrum scales, is
that inharmonic instruments do indeed sound more consonant when tuned
to intervals derived from the timbre itself. Some of the electronic
timbres I analyzed were inharmonic FM sounds which I had been
familiar with using and hearing in 31 Prime Limit JI for years (e.g.
some bell-like pads with no attack transients). When I tuned them to
their own spectrum scales - which had wildly high number ratios (!) -
they all sounded much more appropriately tuned than I had ever heard
before. It's hard to explain what an epiphany this was to hear this
same kind of effect - this beautifully sweet and sometimes eerie
harmony and melody - on many different timbres and tunings. I would
test them in 12tEt, and JI, but none sounded as good. Now I'm seeing
all this as two distinct philosophical approaches to tuning - (1.)
Temperaments, JI etc.., where one is primarily concerned with the
fundamental pitch relationships alone (overtones fall where they will
relative to the chosen tuning system), and (2.) Spectrum Scales,
where the timbres dictate the appropriate tuning (where imposing an n-
tET or JI tuning isn't appropriate). Inharmonic timbres take on a
whole new life with the latter - hearing is believing.

>
> The idea of "tuning by integer ratios," of course, may carry various
> implications for various people and styles of music, for example:
>
> (1) Using the simplest and purest possible ratios for stable
> concords in a given style;
>
> (2) Preferring epimores or superparticular ratios for intervals
> making up a tetrachord, for example (e.g. 9:8-8:7-28:27);
>
> (3) Seeking to maximize the simplicity or "suavity" of certain
> unstable intervals and combinations as well as stable ones,
> e.g. 4:5:6:7 in an 18th-century setting (Euler), or 7:9:12
> in a neo-14th-century setting.

And I humbly add a possible 4th implication: Choosing the intervals
in a tuning for their unique melodic properties (a primary focus
here). Many times I find that what might not work well in "full
fisted harmony" (a humorous term I use for the 12tET compositional
style of a "child piano prodigy" friend of mine), is wondrous when
played melodically.

>
> As Leonhard Euler approached the problem of consonance/dissonance,
so
> would I approach the diverse intervals of JI: there is a continuum
of
> the simple and the complex.
>

It's like an infinite color palette to chose from. As always, context
dictates correct choices.

Best Regards,

Jacky Ligon

--- In tuning@egroups.com, ligonj@n... wrote:
> --- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:

http://www.egroups.com/message/tuning/15664

Welcome back, Jacky... (although we have continued to correspond
off-line...)

It sounds as though you have been studying Sethares, correct?? I
would be interested in hearing some music that you derive from such
studies... since I am a "fan" of your work.

Please let me know if you post anything!

________ ___ __ __
Joseph Pehrson

--- In tuning@egroups.com, ligonj@n... wrote:

> Now I'm seeing
> all this as two distinct philosophical approaches to tuning - (1.)
> Temperaments, JI etc.., where one is primarily concerned with the
> fundamental pitch relationships alone (overtones fall where they will
> relative to the chosen tuning system),

Naah -- most users of these tuning systems are interested primarily in timbres with harmonic or
near-harmonic timbres, which have minimum ambiguity as to pitch.

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:
> --- In tuning@egroups.com, ligonj@n... wrote:
>
> > Now I'm seeing
> > all this as two distinct philosophical approaches to tuning -
(1.)
> > Temperaments, JI etc.., where one is primarily concerned with the
> > fundamental pitch relationships alone (overtones fall where they
will
> > relative to the chosen tuning system),
>
> Naah -- most users of these tuning systems are interested primarily
in timbres with harmonic or
> near-harmonic timbres, which have minimum ambiguity as to pitch.

Paul,

Hi.

True - and whether to use one approach over another, is something
that would greatly effect the sound of a composition. Interestingly,
I,ve found it to be two starkly different sounds: (1.) the sound you
get when you impose a temperament or JI onto an inharmonic timbre
relative to the perceived "fundamental" as opposed to (2.) tuning it
to its' own spectrum scale. Both are extremely useful too.

I'm still actively working with these two approaches, although I have
more experience with the former.

Jacky