Stellate Hexanies (14-anies)

Neil: The scale is the 14-tone stellated hexany or dekatesserany, Mandala,
or tetradekany invented by Erv Wilson. It is generated by taking any 2)4
hexany and adding 8 new tones to complete the generating tetrad or its
inversion at each facet. That is, if the generator is A.B.C.D, the extra
tones are A^2, B^2, C^2, D^2 and A.B.C/D, A.B.D/C, A.C.D/B and B.C.D/A.
The original hexany tones are A.B, A.C, A.D, B.C, B.D and C.D

When A = 1 as in 1.3.5.7, the math is simpler as 1^2 =1/1 and is a
convenient tonic. The tones thus are 1/1 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 2/1, but actually any of the 14 modes
can be used. The scale is intervallically symmetrical about 21/16 and 15/8.

I don't know which piece is on the tape Brian sent you, but Paul Rapoport
set a poem by Hildegard of Bingen to this scale and recorded it (See
MusicWorks for article and recording). The Sonic Arts players in San
Diego have based improvisations on this scale as well.

--John


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From: "Paul H. Erlich"
Subject: RE: Wilson scale
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I prefer this mode of the stellated hexany, starting from what was
called 6/5 in my previous post, since it has both a 4/3 and a 3/2 above
the tonic:

Ratio cents 31TET
1/1 0 0
49/48 36 1
25/24 71 2
35/32 155 4
7/6 267 7
5/4 386 10
4/3 498 13
7/5 583 15
10/7 617 16
35/24 653 17
3/2 702 18
5/3 884 23
7/4 969 25
35/18 1151 30

Or this mode, starting from what was called 7/4 in my previous post:

Ratio cents 31TET
1/1 0 0
36/35 49 1
8/7 231 6
6/5 316 8
4/3 498 13
48/35 547 14
7/5 583 15
10/7 617 16
3/2 702 18
8/5 814 21
12/7 933 24
64/35 1045 27
48/25 1129 29
96/49 1164 30

Note that these modes are inverses of one another, indicating that the
>scale has mirror symmetry.


SMTPOriginator: tuning@eartha.mills.edu
From: alves@orion.ac.hmc.edu (Bill Alves)
Subject: Greek chords (was RE: 19, 22, etc)
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>}This is the lattice with factors 2 ignored, the zero indicates the 1/1
>}position.
>
>}hor > 3/1 - ver ^ 5/1 - hor >> 7/1
>
>} | * | | |
>} * | * * | * * * | |
>} . | 0 * * | * * | * |
>} | | * | |
>
>}Imagine the four layers on top of one another for a 3D image.
>
>The scale is much more symmetrical when displayed on a lattice where the
>three axes are at 60-degree angles from one another (which I prefer to a
>cubic grid for reasons I have discussed). The hexany is then a regular
>octahedron, and the stellation erects a tetrahedron on each face of the
>octahedron.


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From: "Paul H. Erlich"
Subject: Phonons
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