A 41-limit temperament

The 140&171 7-limit temperament has a 311-et generator of 20/311;
extending that to the 41-limit gives a mapping of

[<1, 3, 2, 3, -4, 1, 1, 11, -3, 1, 11, 0, 6|,
<0, -22, 5, -3, 116, 42, 48, -105, 117, 60, -94, 81, -10|]

An LLL-reduced basis is

{703/702, 784/783, 875/874, 1000/999, 1625/1624, 1729/1728, 8092/8073,
10557/10556, 68921/68894, 177023/177008, 11670750/11648281}

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> The 140&171 7-limit temperament has a 311-et generator of 20/311;
> extending that to the 41-limit gives a mapping of
>
>
> [<1, 3, 2, 3, -4, 1, 1, 11, -3, 1, 11, 0, 6|,
> <0, -22, 5, -3, 116, 42, 48, -105, 117, 60, -94, 81, -10|]
>
> An LLL-reduced basis is
>
> {703/702, 784/783, 875/874, 1000/999, 1625/1624, 1729/1728, 8092/8073,
> 10557/10556, 68921/68894, 177023/177008, 11670750/11648281}

It seems this isn't a basis for the whole temperament; it has
3-torsion. I need to find non-cube products which are cubes, and take
the cube root

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> It seems this isn't a basis for the whole temperament; it has
> 3-torsion. I need to find non-cube products which are cubes, and take
> the cube root

A correct LLL reduced basis for the temperament is

{6290/6279, 714/713, 820/819, 1015/1014, 1105/1104, 1365/1364,
2002/2001, 2146/2145, 2185/2184, 16530/16523, 4060/4059}

4000/3993 is zero steps of 311, one step of 140, and 385/384 is one
step of 311, zero steps of 140; adding the correct one of these gives
us a basis for 311 or 140, and adding both gives us a "notation". This
one has three different versions of 87-et, which seems excessive, but
it does easily allow us to compute a 311 Fokker block (I just did it,
so I know its easy) in case anyone is tired of piddling around with
tiny 11-limit scales of size 43 or so. That 6290/6279 is not very
nice, so maybe that could be reduced. An ambitious person might want
to TM reduce the whole thing. Booting it would give us a planar
temperament, in case anyone knows what to do with a 41-limit planar.