source file: mills2.txt
Date: Sat, 5 Jul 1997 23:19:45 +0200

Subject: The Outer Limits

From: DFinnamore@aol.com

So far, all of the limits I have seen discussed have been _upper_ limits.
 Has anyone explored the idea of lower limits - say, a lower 3-limit, which
would not allow a power-of-two to stand alone in a numerator or denominator?
 I think that would mean that every note of the scale, every interval created
by notes of the scale, would have at least a certain degree of complexity.  I
drew up a few of these scales on paper but haven't yet listened to them.
 Using a lower limit of 5 and an upper limit of 7 looks very strange on
paper!

BTW, I like a concept that Graham Breed introduced me to: harmonic
dimensionality using prime limits.  As I understand it, using all octaves
(like P. D. Q. Bach's Don Octave) would be 1-dimensional, Pythagorean scales
(3-limit in practice) would be 2-dimensional, 5-limit would be 3-dimensional.
 So a lower limit of 3 with an upper limit of 5 would insure that every
member of the scale except the tonic itself would have a 3-dimensional
relationship to the tonic; and I think it might insure that every interval
created with the scale members would also be 3-dimensional (with respect to
the tonic; 2-D standing alone, right?).

Any comments?

David J. Finnamore

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