source file: mills2.txt
Date: Wed, 9 Jul 1997 19:55:26 +0200

Subject: Re: Muddy waters

From: gbreed@cix.compulink.co.uk (Graham Breed)

>I have not recieved TD 1122, so I write with some tentativeness . . .
Could it be that no-one got that digest?

I've drawn myself some triangular lattices, and I can see how a
lot of nice shapes correspond to a CPS.  I've also tried to
visualise a regular tetrahedral lattice.  The points of this seem
to be in a hexagonal close packed structure.  If I can get a
quantitative formula worked out, I'll change the metric.  Making
the 5/3 dimension infinite turns a triangular into a square
lattice.  What fun!

The saturated 15-limit chords 3:7:15:21 and 5:7:15:35 both make
the same shape on a tetrahedral lattice: two triangles joining at
one edge, not in the same plane.  On a tetrahedral, octave
specific lattice a 4:5:6 chord lies on three corners of the same
shape.  3:4:5 and 5:6:8 don't look as good.  4:5:6:8 doesn't
either, but I still think this is leading somewhere.  I don't see
that we need a new dimension for 9.

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