A 58 tone epimorphic scale containing Genesis

Genesis is not epimorphic, so we should find non-CS, inconsistent properties. We would also not be able to produce it as any kind of block. I took the steps of Genesis which were mapped to 2 by h58,
which are 45/44, 49/48, 50/49 and 55/54, and split them in two as follows:

45/44 = 81/80 100/99
49/48 = 245/242 121/120
50/49 = 99/98 100/99
55/54 = 100/99 121/120

I then picked the one of the two possibilites presented in each case for filling the "gap" by choosing the option of least Tenney height, and obtained the following:

1, 81/80, 45/44, 33/32, 21/20, 16/15, 27/25, 12/11, 11/10, 10/9,
9/8, 8/7, 121/105, 7/6, 32/27, 6/5, 40/33, 11/9, 99/80, 5/4, 14/11, 9/7, 315/242, 21/16, 4/3, 27/20, 15/11, 11/8, 7/5, 99/70, 10/7, 16/11, 22/15, 40/27, 3/2, 32/21, 484/315, 14/9, 11/7, 8/5, 81/50, 18/11, 33/20, 5/3, 27/16, 12/7, 121/70, 7/4, 16/9, 9/5, 20/11, 11/6, 50/27, 15/8, 40/21, 64/33, 88/45, 160/81

It is readily verified that this *is* epimorphic, with map h58.

The set of steps for this scale is 121/120, 100/99, 99/98, 245/242, 81/80, 64/63, and 56/55. Geometrically it is more complex than Genesis, with 30 verticies and 65 facets. However, a 4D parallepiped would have 16 verticies and 8 facets so there is a limit to how simple this can get, and I suppose Genesis is not so bad.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

>Genesis is not epimorphic, so we should find non-CS, inconsistent
>properties. We would also not be able to produce it as any kind of
>block.

i thought my original question made it clear that we were to take
11/10 and 20/11 as auxillaries, not as part of the block.

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> i thought my original question made it clear that we were to take
> 11/10 and 20/11 as auxillaries, not as part of the block.

I don't know how to take something as an auxillary, but we can certainly look at the scale we get by leaving 11/10 and 20/11 out of
Genesis. Is this what you mean? Perhaps you could tell us again what you are actually looking for.

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...>
wrote:
>
> > i thought my original question made it clear that we were to take
> > 11/10 and 20/11 as auxillaries, not as part of the block.
>
> I don't know how to take something as an auxillary, but we can
certainly look at the scale we get by leaving 11/10 and 20/11 out of
> Genesis. Is this what you mean?

yes, or whatever choice is best. there should be only 41 notes inside
the parallelepiped and whatever other shape you may happen to
investigate (what's the 4-dimensional analogue of a 3-d rhombic
dodecahedron or a 2-d hexagon? i feel that should be the most general
case, and certain vertices may coincide in specific instances,
causing some edges/faces/cells to disappear).