Hemimage family: Difference between revisions

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m Cleanup (2/2)
Edo lists reviewed
Line 18: Line 18:
: [[Eigenmonzo]]s: 2, 10/9, 8/7
: [[Eigenmonzo]]s: 2, 10/9, 8/7


{{Val list|legend=1| 14, 19, 41, 58, 77, 80, 99, 118, 140, 217, 316, 338, 357, 415, 456, 654, 695 }}
{{Val list|legend=1| 17c, 19, 39d, 41, 58, 77, 80, 99, 217, 239, 338, 357, 456, 695 }}


[[Badness]]: 0.199 × 10<sup>-3</sup>
[[Badness]]: 0.199 × 10<sup>-3</sup>
Line 36: Line 36:
: [[Eigenmonzo]]s: 2, 11/9, 5/4
: [[Eigenmonzo]]s: 2, 11/9, 5/4


{{Val list|legend=1| 19, 22, 41, 58, 80, 121 }}
{{Val list|legend=1| 17c, 19, 22, 39d, 41, 58, 80, 99e, 121, 179e, 220e, 300bdee, 399bcdeee }}


[[Badness]]: 0.702 × 10<sup>-3</sup>
[[Badness]]: 0.702 × 10<sup>-3</sup>
Line 47: Line 47:
Mapping: [{{val| 1 0 2 -1 6 11 }}, {{val| 0 1 2 3 -1 -4 }}, {{val| 0 0 -3 -1 -1 -1 }}]
Mapping: [{{val| 1 0 2 -1 6 11 }}, {{val| 0 1 2 3 -1 -4 }}, {{val| 0 0 -3 -1 -1 -1 }}]


Vals: {{Val list| 22, 41, 58, 80, 121 }}
Vals: {{Val list| 17c, 22, 36f, 39d, 41, 58, 80, 99ef, 121, 179ef, 300bdeef }}


Badness: 1.06 × 10<sup>-3</sup>
Badness: 1.06 × 10<sup>-3</sup>
Line 58: Line 58:
Mapping: [{{val| 1 0 2 -1 6 -2 }}, {{val| 0 1 2 3 -1 3 }}, {{val| 0 0 -3 -1 -1 1 }}]
Mapping: [{{val| 1 0 2 -1 6 -2 }}, {{val| 0 1 2 3 -1 3 }}, {{val| 0 0 -3 -1 -1 1 }}]


Vals: {{Val list| 19, 36, 41, 58 }}
Vals: {{Val list| 17c, 19, 22f, 36, 39df, 41, 58, 99ef, 157eff }}


Badness: 1.07 × 10<sup>-3</sup>
Badness: 1.07 × 10<sup>-3</sup>
Line 74: Line 74:
: [[Eigenmonzo]]s: 2, 10/9, 11/9
: [[Eigenmonzo]]s: 2, 10/9, 11/9


{{Val list|legend=1| 41, 58, 118, 159, 217, 335 }}
{{Val list|legend=1| 17c, 19, 36, 39d, 41, 58, 99e, 118, 159, 217, 335 }}


[[Badness]]: 0.936 × 10<sup>-3</sup>
[[Badness]]: 0.936 × 10<sup>-3</sup>

Revision as of 08:42, 10 May 2021

The hemimage family of temperaments are rank-3 temperaments tempering out 10976/10935.

Hemimage

Subgroup: 2.3.5.7

Comma list: 10976/10935

Mapping: [1 0 2 -1], 0 1 2 3], 0 0 -3 -1]]

Mapping generators: ~2, ~3, ~27/14

Minimax tuning:

[[1 0 0 0, [5/8 1/8 -1/8 3/8, [5/8 -7/8 7/8 3/8, [0 0 0 1]
Eigenmonzos: 2, 8/7, 6/5
[[1 0 0 0, [5/9 2/9 -1/9 1/3, [10/9 -14/9 7/9 2/3, [0 0 0 1]
Eigenmonzos: 2, 10/9, 8/7

Template:Val list

Badness: 0.199 × 10-3

Projection pair: 5 10976/2187 to 2.3.7

Uni

Subgroup: 2.3.5.7.11

Comma list: 540/539, 896/891

Mapping: [1 0 2 -1 6], 0 1 2 3 -1], 0 0 -3 -1 -1]]

Minimax tuning:

[[1 0 0 0 0, [16/11 6/11 1/11 0 -3/11, [0 0 1 0 0, [19/11 14/11 6/11 0 -7/11, [32/11 -10/11 2/11 0 5/11]
Eigenmonzos: 2, 11/9, 5/4

Template:Val list

Badness: 0.702 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 364/363, 540/539

Mapping: [1 0 2 -1 6 11], 0 1 2 3 -1 -4], 0 0 -3 -1 -1 -1]]

Vals: Template:Val list

Badness: 1.06 × 10-3

Tin

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 729/728

Mapping: [1 0 2 -1 6 -2], 0 1 2 3 -1 3], 0 0 -3 -1 -1 1]]

Vals: Template:Val list

Badness: 1.07 × 10-3

Turan

Subgroup: 2.3.5.7.11

Comma list: 441/440, 10976/10935

Mapping: [1 0 2 -1 -7], 0 1 2 3 6], 0 0 -3 -1 1]]

Minimax tuning:

[[1 0 0 0 0, [19/12 -2/3 1/12 0 1/4, [19/6 -10/3 7/6 0 1/2, [37/12 -8/3 7/12 0 3/4, [19/6 -10/3 1/6 0 3/2]
Eigenmonzos: 2, 10/9, 11/9

Template:Val list

Badness: 0.936 × 10-3