Re: For Jacky Ligon -- JI, HI, and/or RI?

Hello, there, and what an engaging experience this thread on just
intonation (JI) and rational intonation (RI) has been! What a
privilege it is to partake of such a dialogue, enriched by some very
practical musical experience as well as theoretical prowess and a due
infusion of humor from various quarters.

Here I would like especially to thank Jacky Ligon for exploring an
area which may lie on the interstices or border regions between what
some of us have been describing as "[small-integer] JI" and RI
involving large integer ratios not conceived in terms of partials.

What I might read some of your articles to describe is an approach
where some large ratios (e.g. 29:23) might be conceived as harmonic or
subharmonic constructs, although this derivation might in many timbres
or contexts be beyond the discrete perception of the listener. In
other words, am I right to understand that the complex as well as
simple intervals -- the former often favored in your music mainly from
a melodic point of view -- have a common harmonic/subharmonic design,
although not all facets of that design may be explicitly heard in
specifically "harmonic/locking-in-partials" terms?

How moving it has been, Jacky, to share with you the exciting and
sometimes arduous adventure of confronting at least one widespread
definition of "JI," understanding its very significant and ably argued
appeal, and asking what alternative categories and paradigms might
bring out the distinctive musical qualities of other approaches to
integer-based music.

From the viewpoint of typology, your articles in combination with
those of Bill Alves and Dave Keenan, among others, suggest to me that
"JI" in a generic or wide sense may have at least subgenera, so to
speak, either of which might invite a comparably concise acronym:

Harmonic Intonation (HI): JI where harmonicity and the
purest or most beatless tuning of sonorities possible
is the ideal -- or, from another view, the Partch/Doty
ideal that ratios should be kept as small as is fitting
for the musical context

Rational Intonation (RI): JI where integer-based ratios,
simple or complex, are the distinguishing feature, many
of these ratios possibly having little if any obvious
connection with relations between partials, and with
beatlessness not necessarily a pervasive ideal,
especially for complex or unstable sonorities (e.g.
Gothic/neo-Gothic), or in primarily melodic rather than
polyphonic textures (e.g. ancient Greece a la Bill Alves).

It is easy to recognize Dave Keenan's JI as synonymous with HI, and
indeed the two concepts are mostly synonymous in the late 15th-19th
century era where "Just" seems a recognized category of tunings (your
very important point of historical usage, Monz).

It also seems easy to recognize the JI of Bill Alves (who nicely expresses
my accustomed concept also) as synonymous with RI, as you, Bill, yourself
suggest. Themes such as superparticular ratios for tetrachord divisions,
applying for example to melodic whole-tones and sometimes also to
semitones (Archytus, Ptolemy), do seem to me a vital part of what I am
used to calling "the JI approach" in ancient Greece.

The obvious bridge between the HI and RI facets of JI is that certain
basic rational ratios prevalent in various world musics (2:1, 3:2,
4:3) do produce pure vertical intervals -- or _consonantiae_ in the
theory of Boethius (who takes _simultaneous_ intervals as the focus of
the consonance concept).

Jacky, your approach maybe suggests how a musical style or
intonational system can straddle these HI and RI approaches, for
example by taking an HI outlook on some sonorities with small integer
ratios, and an RI approach on melodic intervals or other vertical
sonorities (possibly conceived in terms of some harmonic/subharmonic
series).

An advantage to the "JI as HI or RI" approach is that it lets us -- to
allude to some of your very moving words, Jacky -- joyously wear our
chosen flags over our hearts, affirming that the same concept can mean
different things to different people.

For Dave Keenan, barbershop is JI because, as we might say, it has an
"HI sound," however its intonational fine structure might be analyzed
mathematically.

For some of us, large integer ratios are also JI because they have an
artful "RI design," manifesting itself in complexity as well as
simplicity, although the effect may often be quite different than HI.

Taking this outlook, we might discuss a given piece of music as either
HI or RI -- or possibly some creative fusion of the two constructs --
while recognizing that either concept may reflect part of the semantic
territory often associated with the JI category.

Again, Jacky, thank you alike for some great ratios and creative
musical ideas seasoned with passion, humor, and friendly wisdom.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:
>
> What I might read some of your articles to describe is an approach
> where some large ratios (e.g. 29:23) might be conceived as harmonic
or
> subharmonic constructs, although this derivation might in many
timbres
> or contexts be beyond the discrete perception of the listener. In
> other words, am I right to understand that the complex as well as
> simple intervals -- the former often favored in your music mainly
from
> a melodic point of view -- have a common harmonic/subharmonic
design,
> although not all facets of that design may be explicitly heard in
> specifically "harmonic/locking-in-partials" terms?

Margo and all,

This is true, and I should make the important point that at the core
of it all - and running like a connecting thread throughout my ratio
web; I routinely consider all superparticular ratios from 2/1 to
38/37 in my "master scale" (144 pitches at this point in time, from
which I create myriad of subset scales), which would of course
encompass many of the most important JI intervals, while easily
exceeding this set, and allowing a much larger palette of complex
ratio which are harmonically related (many intervals found by
addition of sequential members of the harmonic series are imployed).
The harmonic series represents the "trunk" of my rational tuning tree.

>
> How moving it has been, Jacky, to share with you the exciting and
> sometimes arduous adventure of confronting at least one widespread
> definition of "JI," understanding its very significant and ably
argued
> appeal, and asking what alternative categories and paradigms might
> bring out the distinctive musical qualities of other approaches to
> integer-based music.

Most inspiring to me is that others, like yourself Margo, make as a
part of their regular musical practice, to consider a number of ratio
within the range of each pitch class. And by viewing and dividing up
the pitch continuum in this manner, the composer is able to harness a
spectrum of simple to complex "flavors", which have at their "root
system" the primary simple ratios of JI. Usually, when I'm
considering the division of a given pitch class into a number of
harmonically related ratio, I'm seeking to divide the range from
roughly 1/4 tone, or neutral interval, below and above the primary
ratio (currently I'm dividing each pitch class into 12 parts with
ratios). Working in this manner also has practical implications,
related to mapping the tunings onto the instruments for which I am
fated to make music with (I believe these scales would sit well on a
MicroZone!).

As a result, my interest in this area has led me to explore, as one
kind of rational construction; scales which have inversional
symmetry. This scale type has always had a special allure in its
sound for me, as I enjoy the evenness of the scale step sizes
ascending from 1/1 and descending from 2/1. Beatlessness of intervals
is but one feature of the kinds of scales assembled in such a manner.

The idea that I need the ability to freely call upon the most simple
ratios for this beatless quality, and at the same time, strategically
choose to use more complex intervals which lie above or below a
simple ratio, has much to do with my compositional need to control
the musical energies of tension and relaxation that is created by
changing the tunings of instruments over the course of a composition.
I need many varieties of seconds, thirds fourths, etc., to fulfill
the requirements of a given composition, and enjoy the complete
freedom to choose from the infinite spectrum of integer ratios for
this purpose (although I rarely wander beyond the boundaries of 37
prime with these RI tunings.). I believe that once a composer has
command over the vocabulary of a broad range of ratios, by repeatedly
experiencing them in a musical context, both the music and the
experience of creating it, becomes significantly more meaningful.

>
> Jacky, your approach maybe suggests how a musical style or
> intonational system can straddle these HI and RI approaches, for
> example by taking an HI outlook on some sonorities with small
integer
> ratios, and an RI approach on melodic intervals or other vertical
> sonorities (possibly conceived in terms of some harmonic/subharmonic
> series).

As above, the need to harness the music power from the extreme poles
of simplicity and complexity in compositional settings, leads me
toward rational tuning systems which would encompass both an HI and
RI aesthetic. This is such a rich land of possibilities that even if
I never went outside of this to explore things like the spectrum
tunings, my musical diet of RI flavors, would be sufficient to
sustain me for a very long time. Sometimes I seek to justly intone
chords, other times to tune a single flute voice to a highly complex
scale, which would not likely be harmonically functional (in the
chordal sense). Even in the area neighboring around 4/3 and 3/2,
there are many wonderful melodic, and or harmonic possibilities for
either flattening or sharpening of these primary intervals. In my
mind and experience, all of these represent valid choices depending
on the musical context.

>
> An advantage to the "JI as HI or RI" approach is that it lets us --
to
> allude to some of your very moving words, Jacky -- joyously wear our
> chosen flags over our hearts, affirming that the same concept can
mean
> different things to different people.

Inspired by the above, and Bill Alves' post:

http://www.egroups.com/message/tuning/16477

I would like to inject the following analogy:

Suppose that the Oxford Dictionary contained a frozen entry
for "Jazz" that was based on what this term meant during the 1930s.
Would any of us accept that this definition would have any meaning
for what Jazz became in the decades following? I really think not.
Words, meanings and definitions do undergo subtle, or not so subtle
transformations over time. I realize there will be some out there who
will find difference with this analogy, but it is a point about the
evolution of the meanings of terms and language, not definitions. I
personally am able to withstand this reality, and openly embrace the
evolution of the term JI. I won't take it upon myself to correct
those that use this to describe their rational tuning systems when
they don't conform to the accepted definition, as my humble feeling
is that our dialog about all this, is happening in a sort of
isolated "test-tube" amidst a real-world musical reality, in which
there are many worthy composers who do happen to see this in a
different light (whether naive about the Oxford definition or not is
irrelevant).

In light of the above, some part of me is troubled by a feeling that
I "caved" to quickly on this, but since I have now eaten from "The
Tree of The Knowledge of Justness", I cannot return to my prior state
of innocence. Ah, booted out of the JI Garden - but that fruit sure
was tasty! Also, highly ironic to me is that I've ended up in this
discussion at all, since these things always disappear into their
proper background when I set down to compose with - well - whatever
you like to call it! All the same, I've found it highly instructive
and enriching to become involved (however unwittingly). To see this
amazing discussion take place; with all of those that I deepest
revere; has been worth all the effort to follow along (I sense it's
not over yet either!).

>
> For some of us, large integer ratios are also JI because they have
an
> artful "RI design," manifesting itself in complexity as well as
> simplicity, although the effect may often be quite different than
HI.

Certainly speaks to my direction with the above analogy.

>
> Taking this outlook, we might discuss a given piece of music as
either
> HI or RI -- or possibly some creative fusion of the two constructs -
-
> while recognizing that either concept may reflect part of the
semantic
> territory often associated with the JI category.

Yes, in my mind, the concept of RI, with its range of simple to
complex structures is a direct extension of the constructs of JI
tuning systems (in the classic "Oxford" definition sense). I would
personally be unable to conceive of the extended complexity of an "RI-
type" of system without the foundation provided by the aesthetic of
beatlessness offered by a HI/JI conception. It would be like trying
to walk without gravity!

Kind Thanks,

Jacky Ligon