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Definitions suggestions, Kleisma

🔗John Chalmers <jhchalmers@xxxx.xxxx>

4/22/1999 5:40:00 AM

Re Paul Erlich's definitions:

The proposed definitions are well written. If I make a suggestion, I
recommend we distinguish between "sensory consonance" (aka roughness,
sonance etc.) and "contextual consonance" as Tenney does in his History
of Consonance and Dissonance, somewhere in the glossary or FAQ.

Also, I think we should call the various lattice diagrams "tonal
lattices" to distinguish them from the partially ordered sets subject to
certain requirements of greatest lower and least upper bounds on pairs
of elements that other mathematicians call lattices.

>Another problem in the latter: the 225/224 is not a septimal schisma (which
>is 33554432/33480783) but I think it's a kleisma.

I suggest this definition:

The Kleisma is a small interval composed of 6 major thirds up and 5
fifths down. Its ratio is 15635/15552 or approximately 8.10728 cents.
The term was introduced by Shohe' Tanaka.

determinant: I suggest the folowing minor changes.

A calculation made on a square matrix. When the rows of the matrix
represent independent unison vectors, the absolute value of the
determinant indicates the number of pitches contained within the
corresponding periodicity block. This was documented by Fokker.

--John