JI definitions and concepts (for Monz's dictionary)

Hello, there, everyone, and I might add a few comments on the "What is
JI?" question that seems to come up here from time to time.

A basic problem is that different people use the "JI" concept in very
different musical contexts, as Kraig has eloquently observed. Here I
can come up with at least five definitions, maybe ranging from the
most encompassing to the narrowest or most "culture/style-specific":

(1) Just intonation could be taken as synonymous with
rational intonation (RI), the use of integer ratios
(simple or complex) to build a complete tuning system;

(2) Just intonation could additionally be taken to imply
that some intervals, especially those which may be
regarded as "fully consonant" or "stable," have
_simple_ interval ratios (e.g. 3:2 and 4:3);

(3) Just intonation could be yet further taken to suggest
a system featuring or tending toward superparticular
or epimore ratios for melodic steps and other types
of intervals, as with many Greek tetrachord schemes;

(4) Just intonation could be taken to imply that ratios
based on two or more simple primes larger than two
are combined in a single system, giving rise to the
intricacy and frequent "asymmetry" associated with
a "JI" system (other than 3-limit or Pythagorean);
and

(5) Most narrowly, but very commonly in a certain
perspective centered on composed European music
of c. 1480-1900, "JI" could be taken to imply
specifically "5-limit JI," where the intervals
deemed to be stable concords in the styles of
this region and period are pure.

As it happens, my own perspective often focuses on intonational
systems with 3:2 and 4:3 as the primary concords, so that a "JI"
system means one where these concords are realized in many or most
positions in pure form, and all intervals are rational (RI).

Thus I would regard any tetrachord based on a pure 4:3, divided in
rational fashion, as "JI," for example the 12:11:10:9 of Ptolemy, or
also the 28:27:24:21 of Archytas. These divisions have lots of epimore
steps -- 12:11, 11:10, 10:9; or 28:27, 9:8, 8:7.

With Monz, I can confirm that many books oriented mainly to European
harmony in a late 15th-19th century style use the term "just scale" to
describe specifically a 5-limit scale of the kind introduced by Ramos
(1482) and made an ideal standard for vocal intonation by people such
as Fogliano (1529) and Zarlino (1558).

However, this seems to me a very specific definition, having more to
do with the nature of consonance/dissonance concepts in conventional
music of this era than anything concerned with a more general concept
of "justness," "purity," "rational epimore structure," or whatever.

Indeed the "n-limit" concept may be most relevant for styles building
on a Partchian kind of paradigm seeking to use _all_ primes and ratios
up to a certain odd-limit, with Zarlino's senario or 5-limit scheme as
one historical precedent.

This has led me to coin terms like "7-flavor JI" or "3-7 JI" for a
system where the pure ratios are based on factors of 2-3-7-9, for
example.

As it happens, Renaissance-Romantic European practice is based on
4:5:6 rather than 12:14:18:21, for example; but I'm not sure why, in
the early 21st century, the former should be regarded as "more just,"
or "more typically just," except of course for discussions where that
specific practice is the most salient.

Certainly it makes sense to alert a newcomer, or even a more
experienced reader, that many books speak of _the_ "just scale" as
specifically Zarlino's version of the 5-limit diatonic.

However, I see the range of perspectives as much larger, with the best
solution maybe being simply to make explicit the different assumptions
and levels of meaning often attached to the "JI" category.

Incidentally, I might speak specifically of RI -- as opposed to "JI"
-- for a system which seems mainly designed to emulate some kind of
irrational temperament. If a system features some pure versions of
simple ratios, and especially if it has an epimoric kind of structure,
then I'd freely call it either JI or RI. A Pythagorean or 3-limit RI
system I also consider JI, since it includes pure concords of 3:2 and
4:3, and also epimore steps of 9:8.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and I might add a few comments on the "What
is
> JI?" question that seems to come up here from time to time.
>
> A basic problem is that different people use the "JI" concept in
very
> different musical contexts, as Kraig has eloquently observed. Here I
> can come up with at least five definitions, maybe ranging from the
> most encompassing to the narrowest or most "culture/style-specific":
>
> (1) Just intonation could be taken as synonymous with
> rational intonation (RI), the use of integer ratios
> (simple or complex) to build a complete tuning system;
>
> (2) Just intonation could additionally be taken to imply
> that some intervals, especially those which may be
> regarded as "fully consonant" or "stable," have
> _simple_ interval ratios (e.g. 3:2 and 4:3);
>
> (3) Just intonation could be yet further taken to suggest
> a system featuring or tending toward superparticular
> or epimore ratios for melodic steps and other types
> of intervals, as with many Greek tetrachord schemes;
>
> (4) Just intonation could be taken to imply that ratios
> based on two or more simple primes larger than two
> are combined in a single system, giving rise to the
> intricacy and frequent "asymmetry" associated with
> a "JI" system (other than 3-limit or Pythagorean);
> and
>
> (5) Most narrowly, but very commonly in a certain
> perspective centered on composed European music
> of c. 1480-1900, "JI" could be taken to imply
> specifically "5-limit JI," where the intervals
> deemed to be stable concords in the styles of
> this region and period are pure.

What happened to Dave Keenan's definition of JI? Taken from the
dictionary, no less?

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, January 27, 2002 9:11 PM
> Subject: [tuning] Re: JI definitions and concepts (for Monz's dictionary)
>
>
> --- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> > Hello, there, everyone, and I might add a few comments on the "What
> > is JI?" question that seems to come up here from time to time.
>
> <excellent definitions snipped here ... but now in the Dictionary>
>
>
> What happened to Dave Keenan's definition of JI? Taken from the
> dictionary, no less?

Dave Keenan:
message 15836 (Thu Nov 23, 2000 11:39pm)
/tuning/topicId_15836.html#15836?expand=1

>> The Shorter Oxford English Dictionary on Historical Principles.
>> Just
>> /Mus./ in /just interval/, etc. : Harmonically pure; sounding perfectly
in tune. 1811.

This post is the one which began the big discussion over
the definition of "just intonation", to which I've been referring.

This, Margo's definitions, and a few other things are now in
my webpage. I've also taken out "insist" as a result of Gene's
comment, and clarified the bit about ancient Greek JI.

Really, the only reason I announced the update to this webpage
on the list was because of the lattice I added. I didn't see
any reason to put in an entry for "pental", since "JI" often
means that anyway, so that's where I put the 5-limit lattice.
I'll eventually have entries for "septimal", "nonadecimal",
etc., and they'll have the 7-, 11-, etc.-limit lattices.

But anyway, thanks to Kraig for the criticism, because now
I finally have a page for "just intonation" that I can be
proud of. And much, much more on the way.

-monz

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> What happened to Dave Keenan's definition of JI? Taken from the
> dictionary, no less?

Er yeah? The one based on the Oxford English Dictionary definition.
The one that doesn't talk about numbers at all, but about how it
_sounds_.