Aline Honingh

Hi Aline!
Scales are concerned with melodic qualites of a series of notes ( as opposed to harmonic ). The properties of a scale applies regardless of size of the intervals.
Moments of Symetry though usually are not found in just intonation scales because you have many different size intervals. It close relative, constant structures, do apply.
The original papers in the authors handwriting can be found here
http://www.anaphoria.com/mos.PDF

Of couse all of these are just theoretical constructs, and what makes a scale is determined by ones ear. So there are things that lie outside of all the above.
On the other hand, I do not know of any of the above being heard not as a scale. At least not anyone who has spoken up.

>
>Message: 2 > Date: Fri, 20 May 2005 08:27:45 -0000
> From: "ahoningh2000" <ahoningh@science.uva.nl>
>Subject: question about just intonation scales
>
>Dear all,
>
>I was wondering what makes a sequence of notes a (just intonation)
>scale. Maybe somebody can tell me about properties of just intonation
>scales, like conditions they have to satisfy? >In the Encyclopaedia of Tuning I did find some properties of scales.
>Under 'scale' is written: "Scales often, but not always, exhibit
>tetrachordal similarity, and other properties such as MOS, propriety,
>distributional evenness, etc."
>However, all these properties are only valid for equal tempered scales
>(or am I wrong?). >Are there similar properties for just intonation scales? I hope
>somebody can help me. Thanks in advance.
>
>Best regards,
>Aline Honingh
>
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--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Kraig makes good points, as did Yaya. Maybe I see it a bit differently, from
a different perspective.

If a scale is a mere ordering of notes from low to high from which we extract
tones to compose, then yes, there can be such a thing as a just intonation
scale.

But really, scale seems more of a metaphor when applied to just intonation.
First off, it is anathema to melody, as Kraig pointed out. For in just
intonation, when all notes are perfectly tapped from the overtone series, a
stupendous blend of harmony ensues. This is not the stuff of a melodic scale.

A second reason to avoid a term like "scale" or "mode" in favor of "limit" is
that just intonation is a fabric of intervalic relationships, as noted by
Harry Partch. It's a musical chain reaction of numbers. Choices are the human
contribution to the majesty of definitive consonance, timbre made livid, that
which we call just intonation harmonies.

Limits seem the best fit for describing just intonation choices:

3-limit pythagorean tuning (cycle of fifths)
5-limit modern tuning, although tempered
7-limit Terry Riley, Johann Philipp Kirnberger, ancient Greek
11-limit Harry Partch...others would explain 11-limit as the rationale for
quartertones
13-limit Jon Catler...extended ji of Ben Johnston

all best, Johnny Reinhard