definition of JI - response summary

Re the Harvard Dictionary of Music definition quoted on
EARLYM-L: Just Tuning is "any tuning that incorporates five or
more acoustically pure types of intervals within the octave."
I got the responses I expected from this list - very polite
but very clear! Assuming that "acoustically pure" means
"intervals that can be represented by rational numbers"
(otherwise I'm sure the responses would be even more tart!):
<
If HDM's definition of JI flies, then so does Reagan's assertion
that ketchup is a vegetable.

I wouldn't consider a scale with 5 pure types of intervals and 3
or so impure types to be just intonation.

I haven't heard anyone before consider something a just tuning
with ANY number of ratios that are irrational relative to all
other pitches in the system.

I find that a little silly.

Just Intonation is any tuning in which ALL of the intervals can
be expressed as integer ratios, with a strongly implied
preference for the smallest numbers that are compatible with a
given aesthetic purpose. (Partch)

It's pretty hopeless to ask a couple hundred tuning-heads to
avoid editorializing when somebody as authoritative as the
Harvard guys say something as ... "distasteful" I suppose ...
as that!
>
A few responses noted that if the emphasis in the HDM definition
was on the "more", it was barely acceptable. It was also noted
that the meaning of JI has changed with time - it had to have
meant something different when keyboards were limited to 13 or
14 notes per octave (D# , and sometimes Ab, split).

Thank you for your responses. Now, does anyone have an email
address of the HDM publisher?!

--
John Sankey bf250@freenet.carleton.ca
Music is Beauty, Beauty is Truth, Truth is Freedom

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Thanks Manuel, for the Pierce-Bohlen ratio approximations. Good stuff!

Here's a couple of notes for those of you who might be interested in trying
it out: That 15:7 septimal minor ninth (as I've called it from its appearance
in 88CET) is an interesting-sounding interval. Also, I'm glad to see that
Pierce-Bohlen has a 7:3 (septimal subminor tenth) approximation. That's one
I've wanted to experiment with for a while now.


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