TUNING digest 1312

(Graham Breed)
>I've worked out that Paul Erlich's Pentachordal modes can be
>written as 10 JI notes plus three commas of 50/49.

You wouldn't mind posting them?

(Paul Hahn)
>You don't need the tetrahedra to fill space. The lattice fills space
>perfectly fine (if you look at the Voronoi cells of the vertices,
>they're rhombic dodecahedra, which _do_ fill space); but instead of
>dividing space up into cubes you get alternating tetrahedra and
>octahedra.
>
>In crystallography this relationship is called "face-centered cubic
>close-packing" and is quite common.
>
>I believe this structure was actually patented by Buckminster Fuller
>under the name "Octotruss".

The tetrahedra and octahedra space-filling combo is called the
face-centered cubic. Fuller called it both the 'isotropic vector matrix'
(in general) and the 'octet truss' (for architecture). I don't know what a
Voronoi cell is, but if you center a unit sphere on each point in the
face-centered cubic, then each sphere will touch all 12 faces of a rhombic
dodecahedron right in the middle, and the rhombic dodecahedra will fill the
space.

But the face-centered cubic isn't regular, and the rhombic dodecahedron has
too many verticies.

>This isn't right--21/16 should be plotted, not where you have it, but
>like this:
>
> 5/4-------15/8
> / \ /
> / . \ / .
> / \ /
> 1/1-------3/2
>
>in which case the spatial/visual relationship between pitches 3/2 apart
>is preserved.

Ah... I've got a tensegritoy model right here. The tops don't look like
this to me.

Carl


SMTPOriginator: tuning@eartha.mills.edu
From: Paul Hahn
Subject: 60 vs 45 (90, really)
PostedDate: 29-01-98 22:21:40
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