These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

Kleismic

Subgroup: 2.3.5.7

Comma list: 15625/15552

Mapping: [<1 0 1 0|, <0 6 5 0|, <0 0 0 1|]

Mapping generators: ~2, ~6/5, ~7

Minimax tuning:

7- and 9-odd-limit

[|1 0 0 0>, |0 1 0 0>, |1 5/6 0 0>, |0 0 0 1>]

Eigenmonzos: 2, 7/6, 4/3

Template:Val list

Enlil

Subgroup: 2.3.5.7.11

Comma list: 385/384, 6250/6237

Mapping: [<1 0 1 0 6|, <0 6 5 0 1|, <0 0 0 1 -1|]

Mapping generators: ~2, ~6/5, ~7

Minimax tuning:

11-odd-limit

[|1 0 0 0 0>, |0 1 0 0 0>, |1 5/6 0 0 0>, |3 1/12 0 1/2 -1/2>, |3 1/12 0 -1/2 1/2>]

Eigenmonzos: 2, 4/3, 14/11

Template:Val list

Badness: 0.000798

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 385/384, 625/624

Mapping: [<1 0 1 0 6 0|, <0 6 5 0 1 14|, <0 0 0 1 -1 0|]

Mapping generators: 2, 6/5, 7

Minimax tuning

13- and 15-odd-limit

[|1 0 0 0 0 0>, |4/3 0 0 -2/9 -2/9 4/9>, |19/9 0 0 -5/27 -5/27 10/27>, |28/9 0 0 13/27 -14/27 1/27>, |28/9 0 0 -14/27 13/27 1/27>, |28/9 0 0 -14/27 -14/27 28/27>]

Eigenmonzos: 2, 13/11, 14/11

Vals: Template:Val list

Badness: 0.000680

Scales: enlil19_13