Re: hexany degeneracy

Kraig, Joseph: While having less than 6 tones would seem to destroy the
hexany structure, actually it is still there underneath the surface. In
a 5-tone degenerate hexany such as 1.3.11.33, the two notes of the same
pitch (1.33 and 3.11) are in different triadic environments and in fact
function as polar opposites. To see this, place the products 1.3 1.11
1.33 3.11 3.33 and 11.33 on the hexagram and examine the triads. This
might not be the best hexany to demonstrate degeneracy, however, you
might try 1.3.5.15, 1.3.7.21 or 1.5.7.35, or any other of the form A.B.C.BC.

--John

--- In tuning@egroups.com, John Chalmers <JHCHALMERS@U...> wrote:
> Kraig, Joseph: While having less than 6 tones would seem to destroy
the
> hexany structure, actually it is still there underneath the
surface. In
> a 5-tone degenerate hexany such as 1.3.11.33, the two notes of the
same
> pitch (1.33 and 3.11) are in different triadic environments and in
fact
> function as polar opposites. To see this, place the products 1.3
1.11
> 1.33 3.11 3.33 and 11.33 on the hexagram and examine the triads.
This
> might not be the best hexany to demonstrate degeneracy, however, you
> might try 1.3.5.15, 1.3.7.21 or 1.5.7.35, or any other of the form
A.B.C.BC.

John, isn't 1.3.11.33 exactly of this form?