5-limit Haluska commas

Here is how the (infinite) list of 5-limit Haluska commas less than
81/80 starts out:

diaschisma
2048/2025
|11 -4 -2>

kleisma
15625/15552
|-6 -5 6>

schisma
32805/32768
|-15 8 1>

semithirds comma
274877906944/274658203125
|38 -2 -15>

ennealimma
7629394531250/7625597484987
|1 -27 18>

kwazma
9010162353515625/9007199254740992
|-53 10 16>

monzisma
450359962737049600/450283905890997363
|54 -37 2>

senior comma
381520424476945831628649898809/381469726562500000000000000000
|-17 62 -35>

piratic comma
17763568394002504646778106689453125/17763086495282268024161967871623168
|-90 -15 49>

Taking them in adjacent pairs gives
34, 53, 118, 441, 612, 612, 1171, 2513...

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> Taking them in adjacent pairs gives
> 34, 53, 118, 441, 612, 612, 1171, 2513...

Back to the good old zoom diagrams! (Sorry for a dumb question):
Can the temperament for adjacent pairs of commas be found from
the wedgie? Or is it done from [0 0 1], [comma], [comma] by
inverting the matrix...

Paul Hj

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@u...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> >
> > Taking them in adjacent pairs gives
> > 34, 53, 118, 441, 612, 612, 1171, 2513...
>
> Back to the good old zoom diagrams! (Sorry for a dumb question):
> Can the temperament for adjacent pairs of commas be found from
> the wedgie? Or is it done from [0 0 1], [comma], [comma] by
> inverting the matrix...

You can get it from the wedge product, which in this case is
equivalent to saying you can get it from the 3D vector cross product.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> <paul.hjelmstad@u...> wrote:
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
> > >
> > > Taking them in adjacent pairs gives
> > > 34, 53, 118, 441, 612, 612, 1171, 2513...
> >
> > Back to the good old zoom diagrams! (Sorry for a dumb question):
> > Can the temperament for adjacent pairs of commas be found from
> > the wedgie? Or is it done from [0 0 1], [comma], [comma] by
> > inverting the matrix...
>
> You can get it from the wedge product, which in this case is
> equivalent to saying you can get it from the 3D vector cross
product.

Right, thanks. Regarding the matrix method: of course I meant [1 0
0]. That method works pretty slick for any limit. (Someday I hope to
understand the underlying logic between using matrices and using
wedgies):)