Kleismic rank three family
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
- 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
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
- [|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
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
Enki
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4356
Mapping: [<1 0 1 0 1|, <0 6 5 0 4|, <0 0 0 2 1|]
Mapping generators: 2, 6/5, 66/25
- [|1 0 0 0 0>, |-18/13 0 6/13 -6/13 12/13>, |-2/13 0 5/13 -5/13 10/13>, |-2/13 0 -8/13 8/13 10/13>, |0 0 0 0 1>]
- Eigenmonzos: 2, 11/8, 7/5
Badness: 0.00109
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 625/624
Mapping: [<1 0 1 0 1 0|, <0 6 5 0 4 14|, <0 0 0 2 1 0|]
Mapping generators: 2, 6/5, 66/25
Minimax tuning:
- 13- and 15-odd-limit
- [|1 0 0 0 0 0>, |2/3 0 -2/3 0 0 2/3>, |14/9 0 -5/9 0 0 5/9>, |0 0 0 1 0 0>, |13/9 0 -4/9 1/2 0 4/9>, |14/9 0 -14/9 0 0 14/9>]
- Eigenmonzos: 2, 8/7 13/10
Vals: Template:Val list
Badness: 0.000874
Isimud
Subgroup: 2.3.5.7.11
Comma list: 4125/4096, 8019/8000
Mapping: [<1 0 1 0 9|, <0 6 5 0 -21|, <0 0 0 1 0|]
Badness: 0.003690
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 625/624, 1287/1280
Mapping: [<1 0 1 0 9 0|, <0 6 5 0 -21 14|, <0 0 0 1 0 0|]
Vals: Template:Val list
Badness: 0.002273