"JI" considered ambiguous; introducing "JIS"

Paul Erlich wrote in
/tuning/topicId_28978.html#29090

"I think Dave Keenan is the only one who considers 81:64 not to be JI.
It comes up in the simplest JI tuning systems from a chain of four
3:2s."

I objected to this, and so, bless his soul, did John deLaubenfels, in
/tuning/topicId_28978.html#29100

And so, I believe, would the authors of the Oxford English Dictionary entry for "just".

"/Mus/. in /just interval/, etc.: Harmonically pure; sounding perfectly in tune.

But this did point out to me that Margo Schulter's otherwise excellent suggestion of RI vs. JI had been unsatisfying to many.

Paul Erlich has been my greatest teacher in this field and so in private email with Paul I tried to get to the bottom of this. It was like getting blood out of a stone. :-) Paul really didn't want to discuss it because he quite understandably didn't want to take sides in what had previously been a somewhat acrimonious discussion. But I pushed and prodded until eventually I think I came up with something useful.

Here is the (slightly edited) text of my final message to Paul on the topic, which he has asked me to share with you.

------------------------------------------------------------------------
DK:
>>What do you call that perceptual property that an 8:11 +-0.5c has, but a
>>35:48 does not (assuming a suitable harmonic timbre)? "Consonant" won't
>>do. Many people agree with me that while a bare 8:11 may be JI, it is a >>stretch to call it consonant.

PE:
>It's a form of concordance. I'd tend to spell out the fact that it has
>nearly coinciding partials.

DK:
Well Paul, I have to say I have very little respect for this position. I really don't think many people who hear them (with a suitable harmonic timbre) would have trouble agreeing that 8:11 +-0.5c is a justly intoned super-fourth while 35:48 is a super-fourth which is not justly intoned, in the same way as they would agree that a 4:5 +-0.5c is a justly intoned major third while a 64:81 is not.

DK:
>>So you would say "64:81 is JI when it is in a Pythagorean scale".

PE:
>Agnostic.

DK:
>>But what could "JI" stand for here, if not "justly intoned"?

PE:
>Just Intonation.

DK:
That doesn't even seem quite gramatically correct "The interval 64:81 is just intonation"? What could this mean?

So, do you respect the view of people who say that some interval is JI (just intonation) merely because it is in a Pythagorean (or other JI) tuning system? Despite the fact that _any_ interval will be within 0.5c (or whatever tolerance you like) of some interval in such a system, if it is sufficently extended.

And what about that "or other JI [system]" above. We both agree that Pythagorean systems are JI systems. But how do you decide (or how do you think these people decide) what is a JI tuning system in general. They can't logically use JI intervals to define JI systems, since they have already used JI systems to define JI intervals. That is unless _some_ JI intervals are defined without reference to JI systems, in which case _those_ JI intervals are somewhat special aren't they? And they deserve a different adjective don't they?

It seems that people use the abbreviation "JI" in a very ambiguous manner when using it as an adjective to describe intervals or chords. It can be an abbreviation for either "justly intoned" (the perceptual property) or "just-intonation-systemic" (i.e. contained within a just intonation system). This leads to a great deal of confusion, particularly for the poor newbies. I think the tuning list can do better than to allow this confusing state of affairs to continue. And I think it can be addressed without acrimony.

Wouldn't it be a lot simpler and less confusing to agree that those special intervals (such as 4:5 +-some tolerance) are the justly intoned intervals (= JI intervals) while the others (such as 64:81 +-some tolerance) are merely just intonation system intervals (= JI-system intervals or JI-scale intervals = JIS intervals).

I think JIS is a better term than RI because it allows that these intervals may have a tolerance too, and don't have to be precisely rational (which can only be achieved by extraordinary digital means in any case).
-----------------------------------------------------------------------

Just so we know what we're talking about, the following URL is for a graph that models quite well, my perception of the justness (JI-ness) of intervals using typical harmonic timbres. I'd prefer not to tell you how it was derived until after you've had a look at it and thought about how well it models _your_ perception of justness. Many thanks to Paul Erlich for computing and plotting it.

/tuning/files/Erlich/keenan.jpg

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

> And so, I believe, would the authors of the Oxford English
Dictionary entry for "just".
>
> "/Mus/. in /just interval/, etc.: Harmonically pure; sounding
perfectly in tune.

But what does "harmonically pure" mean, exactly? Let's play
Dictionary Wars:

Just intonation. (Mus.) (a) The correct sounding of notes or
intervals; true pitch. (b) The giving all chords and intervals in
their purity or their exact mathematical ratio, or without
temperament; a process in which the number of notes and intervals
required in the various keys is much greater than the twelve to the
octave used in systems of temperament. --H. W. Poole.

Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.

> But this did point out to me that Margo Schulter's otherwise
excellent suggestion of RI vs. JI had been unsatisfying to many.

Until someone comes up with a different defintion for "just", why not?

> And what about that "or other JI [system]" above. We both agree
that Pythagorean systems are JI systems. But how do you decide (or
how do you think these people decide) what is a JI tuning system in
general.

If it seems to be using rational numbers structurally, rather than as
approximations.

> It seems that people use the abbreviation "JI" in a very ambiguous
manner when using it as an adjective to describe intervals or chords.
It can be an abbreviation for either "justly intoned" (the perceptual
property) or "just-intonation-systemic" (i.e. contained within a just
intonation system). This leads to a great deal of confusion,
particularly for the poor newbies. I think the tuning list can do
better than to allow this confusing state of affairs to continue. And
I think it can be addressed without acrimony.

Then there's "effectively just" to deal with.

> I think JIS is a better term than RI because it allows that these
intervals may have a tolerance too, and don't have to be precisely
rational (which can only be achieved by extraordinary digital means
in any case).

Precisely anything can never be achieved by any means whatever.

Dave, I like your "JIS" proposal. Let's see if it catches on!

[Dave:]
>Just so we know what we're talking about, the following URL is for a
>graph that models quite well, my perception of the justness (JI-ness)
>of intervals using typical harmonic timbres. I'd prefer not to tell you
>how it was derived until after you've had a look at it and thought
>about how well it models _your_ perception of justness. Many thanks to
>Paul Erlich for computing and plotting it.

>/tuning/files/Erlich/keenan.jpg

Hate to tell you, but Paul let the cat out of the bag with the caption
to the jpg! So, I'm going to use it in this response as well.

I think the 2nd derivative of the harmonic entropy curve is interesting,
but don't consider it ideal for a description of "justness". I'd rather
use the original H.E. curve (turned upside down, of course).

For example, note that for the major third, 400 cents is shown as worse
than 408 cents (I think; it's kinda hard to see clearly), whereas to
my ear, 408 cents is definitely worse.

Also the dips at about 333 cents and 368 cents - I'm not sure my ear
finds them worse than 350 cents (a small peak on your graph).

Maybe some combination of 2nd derivative and the original curve? I
_do_ think there is some justification for the dips adjacent to the
peaks, and these are missing from the original.

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> For example, note that for the major third, 400 cents is shown as
worse
> than 408 cents (I think; it's kinda hard to see clearly), whereas to
> my ear, 408 cents is definitely worse.

According to this chart, the major and minor thirds of 12-et are
about as bad as possible--so bad they presumably shouldn't be usable.
Of course, some people may agree with this assessment. :)

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
>
> > For example, note that for the major third, 400 cents is shown as
> worse
> > than 408 cents (I think; it's kinda hard to see clearly), whereas to
> > my ear, 408 cents is definitely worse.
>
> According to this chart, the major and minor thirds of 12-et are
> about as bad as possible--so bad they presumably shouldn't be usable.
> Of course, some people may agree with this assessment. :)

Well, Gene, recall that Dave is seeking to distinguish "justness" from "consonance" here; and
although I don't fully understand the use of the 2nd derivative, I certainly see no logical
contradiction if one wanted to say that 400 cents is more _consonant_ than 408 cents (which the
original (0th derivative) harmonic entropy curve, which Dave uses for "consonance", tells us), but
400 cents has the least "justness" of any major third.

Gene:
"Precisely anything can never be achieved by any means whatever."

This is a highly amusing little piece of wisdom. (I do understand it
in the context in which it was stated.) It is a memorable quote and I
will keep it among my suite of verbal armaments for confusing my
opponents on any and all issues.

- Bob Wendell

P.S. - Translation: Nothing can be achieved with total precision no
matter what means are chosen in the attempt.

[Gene wrote:]
>>Precisely anything can never be achieved by any means whatever.

[Bob Wendell:]
P.S. - Translation: Nothing can be achieved with total precision no
matter what means are chosen in the attempt.

Thanks, Bob! I tried to parse Gene's original sentence for several
minutes, and just got cross-eyed! Now finally the light comes on.

JdL