Re: [tuning-math] More on chord geometry
- From: Carl Lumma <carl@xxxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxx
- Date: Wed, 10 Jul 2002 22:58:27 -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
That's what Wilson calls the Stellated Hexany. Highly varying size, as
you say. It rivals the diamond in tetrads/notes, but has no tonal
center.
The 12-tone subset with the most 3:2's is a scale I've improvised in,
and posted to tuning-math in the past.
-Carl
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