Multiple Fokker blocks

This is not the same as a wakalix; rather, consider this: the 13 notes of the 7-limit tonality diamond have at least 11 different vals with which they define a weakly epimorphic scale (this is the number Scala finds.) Each of these vals makes the diamond into a Fokker block, although, sadly, none of these blocks are wakalixes. What's the deal with this?

On Wed, Mar 28, 2012 at 12:47 AM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> This is not the same as a wakalix; rather, consider this: the 13 notes of
> the 7-limit tonality diamond have at least 11 different vals with which they
> define a weakly epimorphic scale (this is the number Scala finds.) Each of
> these vals makes the diamond into a Fokker block, although, sadly, none of
> these blocks are wakalixes. What's the deal with this?

Wow, what? What are the vals?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Mar 28, 2012 at 12:47 AM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > This is not the same as a wakalix; rather, consider this: the 13 notes of
> > the 7-limit tonality diamond have at least 11 different vals with which they
> > define a weakly epimorphic scale (this is the number Scala finds.) Each of
> > these vals makes the diamond into a Fokker block, although, sadly, none of
> > these blocks are wakalixes. What's the deal with this?
>
> Wow, what? What are the vals?

<13 21 27 36|
<13 21 28 38|
<13 21 32 35|
<13 21 33 37|
<13 22 28 36|
<13 22 32 34|
<13 22 33 38|
<13 23 27 34|
<13 23 28 35|
<13 23 30 38|
<13 23 32 37|

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

This madness also includes wakalixes and superwakalixes. I've got this example

28/27, 35/32, 10/9, 7/6, 32/27, 5/4, 35/27, 21/16, 4/3, 35/24, 40/27, 3/2, 14/9, 5/3, 7/4, 16/9, 15/8, 35/18, 2

for which there are four different vals, for each of which it is a superwakalix.

On Wed, Mar 28, 2012 at 4:02 PM, genewardsmith <genewardsmith@sbcglobal.net>
wrote:
>
> --- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...>
> wrote:
>
> This madness also includes wakalixes and superwakalixes. I've got this
> example
>
> 28/27, 35/32, 10/9, 7/6, 32/27, 5/4, 35/27, 21/16, 4/3, 35/24, 40/27, 3/2,
> 14/9, 5/3, 7/4, 16/9, 15/8, 35/18, 2
>
> for which there are four different vals, for each of which it is a
> superwakalix.

Now that I'm more awake, what I was trying to say last night was:
consider a string of 7 5/4's on the 5-limit lattice, all reduced
within the octave. There's going to be (at least) two vals starting
with <7 ... | under which this set is weakly epimorphic, correct?
There will be one supporting dicot, one supporting magic, one
supporting wuerschmidt, etc etc. The only difference is going to be in
which generic interval class 3/2 appears.

<7 10 16| is a horrific val, much like the ones we're looking at now.
But, it still makes sense if you think of it as being a "magic-based"
organization of the above scale. It's what you get if you temper out
the chroma for magic[7]. This should make sense, because the "chroma"
is 75/64, so you obviously get ridiculous results if you temper it
out.

Your examples appear to me to be just a more advanced version of this
concept; they're ways to organize the 7-limit tonality diamond into
different scales that have the property that each interval in the
tonality diamond fits into a unique generic interval class in this
scale. The interval doesn't even have to appear in the MOS, but the
tonality diamond will be a MODMOS of the 13-note MOS of this
temperament. I suspect the "chromas" for these MOS's will also be very
large, like 75/64, and so we should expect to see lots of improper
scales result.

The key point is that <7 10 16|, which looks nonsensical at first,
actually has magic lurking within it somewhere. I suspect a similar
situation will happen for these other vals. So it would be good to
search, within each val, for commas that have the property that their
POTE tuning generates a 13-note MOS which is -strongly- epimorphic to
the val in question. Those scales will have really cool properties in
the way that they organize the tonality diamond.

-Mike

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> This madness also includes wakalixes and superwakalixes. I've got this example
>
> 28/27, 35/32, 10/9, 7/6, 32/27, 5/4, 35/27, 21/16, 4/3, 35/24, 40/27, 3/2, 14/9, 5/3, 7/4, 16/9, 15/8, 35/18, 2
>
> for which there are four different vals, for each of which it is a superwakalix.

Sorry, made a mistake here. :(