Mario's cells and some temperaments they define

I've uploaded Mario's progression of cells here, in monzo form:

/tuning/files/MarioPizarro/cells.csv

Each row of the csv defines a monzo with 2.3.5 coordinates.

Now then, the following cells are mistakenly said to differ by an exact 4/3:

Cell 288, which is |29 -18 0>
Cell 542, which is |-23 18 2>

The difference between these cells is |-52 36 -2>, which is not 4/3.
The difference between |-52 36 -2> and |2 -1 0> is |54 -37 2>, or
450359962737049600/450283905890997363, which defines "Monzismic"
temperament:

http://x31eq.com/cgi-bin/rt.cgi?ets=612_1171&limit=5

Mario has also made the claim that every cell has to differ from the
cell 254 cells up by 4/3, which would define this temperament without
a name:

http://x31eq.com/cgi-bin/rt.cgi?ets=306_612&limit=5

It tempers out |485 -306 0>, or
99895953610111751404211111353381321783955140565279076827493022708011895642232499843849795298031743077114461795885011932654335221737225129801285632/99793888233710926097676673961542382339552034110870991187709058567130998942396826836880350287497238272034603157195937657211050782186192219658614729.

These two together define the p612 val. (I'm going to start putting
the patent "p" before the number from now on because people complain
about confusion with the 53-limit)

I'm not sure if this is the canonical tempering of Mario's progression
of cells, though: it would appear that the notion that every cell is
separate from every other by 4/3 is a simple error. However, if that
claim is removed, there may be another, deeper 5-limit temperament
lurking in the progression somewhere.

-Mike

On Sun, Apr 8, 2012 at 9:54 PM, Mike Battaglia <battaglia01@...> wrote:
>
> Now then, the following cells are mistakenly said to differ by an exact 4/3:
>
> Cell 288, which is |29 -18 0>
> Cell 542, which is |-23 18 2>
>
> The difference between these cells is |-52 36 -2>, which is not 4/3.
> The difference between |-52 36 -2> and |2 -1 0> is |54 -37 2>, or
> 450359962737049600/450283905890997363, which defines "Monzismic"
> temperament:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=612_1171&limit=5

By the way, for those who are curious about where I got this, this is
what I got by tracing the spiral of 4/3's until the stated monzo broke
from what it was expected to be. If you instead trace the spiral of
3/2's, you get a break at

Cell 278 |-36 23 0>

and

Cell 24 |16 -13 2>

If cell 24 were 4/3 less than cell 278, the value here should be |-38
24 0>. Instead, it's |16 -13 2>. These differ by |54 -37 2>, which
brings us back to Monzismic temperament again.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I've uploaded Mario's progression of cells here, in monzo form:
>
> /tuning/files/MarioPizarro/cells.csv

Neither you nor Mario seems to have grasped the concept of an ascii file. :)

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > I've uploaded Mario's progression of cells here, in monzo form:
> >
> > /tuning/files/MarioPizarro/cells.csv
>
> Neither you nor Mario seems to have grasped the concept of an ascii file. :)

What do you mean? This file here, cells.csv, is ASCII.

Keenan

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Mario has also made the claim that every cell has to differ from the
> cell 254 cells up by 4/3, which would define this temperament without
> a name:

It has a name, sasktel:
http://xenharmonic.wikispaces.com/Comma

On Mon, Apr 9, 2012 at 12:00 AM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I've uploaded Mario's progression of cells here, in monzo form:
> >
> > /tuning/files/MarioPizarro/cells.csv
>
> Neither you nor Mario seems to have grasped the concept of an ascii file.
> :)

By popular demand!

/tuning/files/MarioPizarro/cells.txt

-Mike