Re: [tuning-math] More on chord geometry
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Wed, 10 Jul 2002 22:53:20 -0700
The symmetrical 7-limit note lattice has "deep holes" which are
geometrically octahedra, and musically hexanies. The dual cubic lattice
of 7-limit tetrads just discussed has eight-tetrad cubes as holes; if we
look at the corresponding notes we have a 14-note stellated octahedron.
Fans of superparticular ratios may be interested to hear that considered
as a scale, this has all of its steps superparticular rations, though of
highly variable size:
1-21/20-15/14-35/32-9/8-5/4-21/16-35/24-3/2-49/32-25/16-105/64-7/4-15/8
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