Diversity of Microtonal explorations

I feel that we are now in a position in time where it is possible for
each of us to indulge in whatever musical specialty we may feel a passion
for, without holding back the course of musical evolution in other
realms. Ivor was indeed pressed for time. But thanks to his work, (and
the internet) we
are now able to communicate with each other about a multitude of
subjects, in as much detail as we choose. Each post from each person
contributes to the whole from which each of us may glean whatever may be
of value to us. Though I have been primarily interested in higher
harmonics in the past, and now in an expanded version of Partch's
tonality diamond, I find the discourse on other systems to be
stimulating. The whole of knowledge is a better resource than any
militant subset (at least for me). Specialized systems like 88cet might
never be documented
at all if it weren't for Garys enthusiasm. Marions exploration of the
subharmonic series is profound. Even though Charles Lucie's ideas are
hard to accept as the perfect system, I find his perspective fascinating.
Now, Brian is challenging everything that comes before him, and
presenting evidence for his objections. We all win!
Ivor was one of the most open minded people I ever met. He was
allways in favor of exploration. He encouraged work in any new field, and
applauded all developments, no matter how unusual they were. In his
kinder moments, he even acknowledged 12 tet as useful for certain purposes.
I guess I'm rambling. But my point is: I'm glad to be in a position to
communicate directly with such a diverse group of astute colleagues, and
to have access to so much valuable information.
For those of you who think that I'm not being militant enough on the
side of just intonation, I would like to point out something that Easly
Blackwood once said: "There is no such thing as just intonation. All you
can do is approximate a ratio by some standard of precision. It all
depends on the tolorance that you are willing to accept". I think that the
same thing could be said about equal temperaments, as well. This all
comes to a head with David Canright's early work in which he showed that
any equal tempered scale could be described as an array of just ratios
when sufficiently high numbers are accepted in the ratios.
I find limits on just intonation components to be useful for
compositional purposes as well as necessary for instrument construction,
but I cannot imagine why I would ever say "No music should be made using
intervals beyond the x limit". Unless I was concerned about the
playability of that music by someone other than it's creator. But even
that should not stop anyone from exploring the interest in their heart.
Go, Xenharmonikers!

Denny Genovese


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"John H. Chalmers" writes:
> See also Neubauer , Otto (?, Neuberger, etc.) The Exact Sciences in
> Antiquity. Sorry I don't have a better reference to this book.

That would be Otto Neugebauer, who I believe founded the Brown department
of the History of Mathematics.

AUTHOR Neugebauer, O. (Otto), 1899-
TITLE The exact sciences in antiquity.
EDITION 2d ed.
PUBLISHED New York, Harper & Brothers [1962]
DESCRIPT'N vii,240 p. illus., facsims. 21 cm.
SERIES Harper Torchbooks, TB 552.
NOTE Includes bibliographical references and index.
LC SUBJECT Mathematics, Ancient.
Astronomy, Ancient.
LCCN 57012342.
RLIN/OCLC RIBG0626061-B.

Enjoy!

---josh

Joshua Brandon Holden Brown Math Department holden@math.brown.edu
"It's never too late to have a happy childhood!" ---Cutter John
YAZ/socrates

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