Re: "Pentatonic JI" -- repartee and reason

Hello, there, and I just want to acknowledge a point made in a
response by Paul Erlich to my remarks offered in the course of last
Friday's rather rowsing repartee on the Tuning List about such
questions as a pentatonic scales "in JI."

While seeking to promote reconciliation and humor in my response, I
might indeed also have sought more lucidly to promote clarity by
making my own assumptions on the "pentatonic JI" issue clear, and
making more explicit the often different assumptions involved in the
discussion of such issues.

As Paul very correctly points out, this less epigrammatic and more
explanatory approach might have better made readers (including
newcomers to the list) aware not only of my point but of the context
and of the likely intentions of other contributors. As an advocate of
"peace," I might well have sought with equal passion to promote the
associated goal of "understanding."

It was very clear to me from the thread that the "JI" pentatonic scale
was intended to be 5-limit or higher, with 5:4 and 6:5 major thirds.
As Paul correctly noted, defining the problem in this way, we run into
the syntonic comma problem: four pure 3:2 fifths give an 81:64 major
third (wider than 5:4 by the syntonic comma of 81:80, ~21.51 cents),
while three such fifths give a 32:27 minor third (a syntonic comma
narrower than 6:5).

However, taking this repartee somewhat in the style of a riddle, I
seemed to notice that the discussion was simply of "JI," not of
"5-limit or higher JI," although the reference to the syntonic comma
as a problem made the 5-limit _assumptions_ very clear.

Since a lot of the dialogue seemed to concern categories and
assumptions, I couldn't resist solving the "riddle" by suggesting that
3-limit or Pythagorean tuning is also a kind of "JI," and that here,
of course, 81:64 and 32:27 thirds are a normal way of life, not a
"problem." Since pentatonic scales are often analyzed in terms of
3-limit musics and tunings, the point seemed not so artificial to me.

However, if my purpose was to communicate these concepts, I might have
done so more patiently and informatively, discussing the distinction
between 3-limit and 5-limit JI, and also the common default assumption
that "JI" implies "5-limit or higher."

In a way, the repartee reminded me of a story about an astronomer who
was told that a certain proposition would not be valid because there
was one too few stars within a certain radius of earth. The astronomer
(Pickering, as I recall) replied, "But you're forgetting the sun!"

In that case, as I recall (having read about it likely some 35 years
ago), the omission of the sun may have really affected the
astronomical issue in question. Here, of course, if the problem is to
have a pentatonic scale with pure fifths _and_ 5:4 and 6:5 thirds,
then the syntonic comma problem remains -- and pointing out that such
a scale may also be tuned in 3-limit "JI" is more of a point of
semantics or "intonational politics," which is how I intended it.

However, if the point was worth making, it was worth making in a clear
and educative manner. Repartee can be intoxicating, but adequate
explanation more informative.

Most respectfully,

Margo Schulter
mschulter@value.net