5-limit families on bingo-card page

i've just gone thru my bingo-card-lattice calculator
and found every ET up to about 120 which fits into
the different vanishing-comma categories at the very
bottom of my bingo-card lattice page:

http://tonalsoft.com/enc/bingo.htm

would someone please check those and let me know if
it's all correct, or if anything is missing or should
be deleted?

i realize that some of these ETs are inconsistent in
the 5-limit ... for one of them, i've included the
3/2,5/4 mapping (28-ET, in the "Wuerschmidt's comma"
column), and hope to include more later.

thanks.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> would someone please check those and let me know if
> it's all correct, or if anything is missing or should
> be deleted?

I'll repeat my periodic complaint that monzos should include the 2
coordinate unless we are in 2-free territory, such as octave
equivalence classes. Hence, saying that 81/80 is |4 -1> is simply
incorrect, and the most straightforward reading of the claim that
meantone tempers it out is that meantone tempers out 16/3.

I also think saying 50-et "acts as" 7/26 comma meantone is not a good
way to put it. 50-et has 2/7 and 5/18 comma as convergents, but 7/26
is not even a semiconvergent, though to be sure, 29/50 is a convergent
to the 7/26 comma fifth. Can you say it approximates these meantones
instead?

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > would someone please check those and let me know if
> > it's all correct, or if anything is missing or should
> > be deleted?
>
> I'll repeat my periodic complaint that monzos should include the 2
> coordinate unless we are in 2-free territory, such as octave
> equivalence classes. Hence, saying that 81/80 is |4 -1> is simply
> incorrect, and the most straightforward reading of the claim that
> meantone tempers it out is that meantone tempers out 16/3.

i appreciate your complaint and your suggestion. but this
*is* "2-free territory" ... that page is bursting with
lattices, and they're all 2-dimensional 3x5 lattices.
not one of them invokes prime-factor 2.

it's true that i should include 2 in the monzo if i
need mathematical exactitude, but here the exponents
of 3 and 5 suffice to show everything that i'm illustrating
on that page.

i'd like to know what others think of leaving out
the exponent of 2. i think that most of the time
it's OK.

> I also think saying 50-et "acts as" 7/26 comma meantone
> is not a good way to put it. 50-et has 2/7 and 5/18 comma
> as convergents, but 7/26 is not even a semiconvergent,
> though to be sure, 29/50 is a convergent to the 7/26 comma
> fifth. Can you say it approximates these meantones
> instead?

done. yes, that always seemed an awkward phrase to
me and i just never tended to it. thanks.

and how did you guess that i looked at the convergents
from both sides of the equation? ;-)

-monz