Tolermic family: Difference between revisions

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== Tolerant ==
== Tolerant ==
Comma: 179200/177147
Subgroup: 2.3.5.7


Map: [<1 0 0 -10|, <0 1 0 11|, <0 0 1 -2|]
[[Comma list]]: 179200/177147


EDOs: 41, 80, 87, 121, 167, 208, 329b, 375b, 537b, 583b, 704bd
[[Mapping]]: [{{val| 1 0 0 -10 }}, {{val| 0 1 0 11 }}, {{val| 0 0 1 -2 }}]


Badness: 0.000165
{{Val list|legend=1| 41, 80, 87, 121, 167, 208, 329b, 375b, 537b, 583b, 704bd }}
 
[[Badness]]: 0.165 × 10<sup>-3</sup>


=== 11-limit ===
=== 11-limit ===
Commas: 896/891, 2200/2187
Subgroup: 2.3.5.7.11
 
Comma list: 896/891, 2200/2187


Map: [&lt;1 0 0 -10 -3|, &lt;0 1 0 11 7|, &lt;0 0 1 -2 -2|]
Mapping: [{{val| 1 0 0 -10 -3 }}, {{val| 0 1 0 11 7 }}, {{val| 0 0 1 -2 -2 }}]


EDOs: 41, 80, 87, 121, 167, 208, 334be, 375be, 542bce
Vals: {{Val list| 41, 80, 87, 121, 167, 208, 334be, 375be, 542bce }}


Badness: 0.001039
Badness: 1.039 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Commas: 325/324, 352/351, 364/363
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 352/351, 364/363


Map: [&lt;1 0 0 -10 -3 2|, &lt;0 1 0 11 7 4|, &lt;0 0 1 -2 -2 -2|]
Mapping: [{{val| 1 0 0 -10 -3 2 }}, {{val| 0 1 0 11 7 4 }}, {{val| 0 0 1 -2 -2 -2 }}]


EDOs: 41, 46, 80, 87, 121, 167, 208, 375be, 583bef
Vals: {{Val list| 41, 46, 80, 87, 121, 167, 208, 375be, 583bef }}


Badness: 0.001021
Badness: 1.021 × 10<sup>-3</sup>


=== 17-limit ===
=== 17-limit ===
Commas: 256/255, 325/324, 352/351, 364/363
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 256/255, 325/324, 352/351, 364/363


Map: [&lt;1 0 0 -10 -3 2 8|, &lt;0 1 0 11 7 4 -1|, &lt;0 0 1 -2 -2 -2 -1|]
Mapping: [{{val| 1 0 0 -10 -3 2 8 }}, {{val| 0 1 0 11 7 4 -1 }}, {{val| 0 0 1 -2 -2 -2 -1 }}]


EDOs: 41, 46, 75e, 80, 87, 121, 167, 288beg
Vals: {{Val list| 41, 46, 75e, 80, 87, 121, 167, 288beg }}


Badness: 0.000982
Badness: 0.982 × 10<sup>-3</sup>


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Tolerant]]
[[Category:Tolerant]]
[[Category:Rank 3]]
[[Category:Rank 3]]

Revision as of 12:31, 14 July 2021

These temper out the tolerma, 179200/177147 = [10 -11 2 1⟩.

Tolerant

Subgroup: 2.3.5.7

Comma list: 179200/177147

Mapping: [⟨1 0 0 -10], ⟨0 1 0 11], ⟨0 0 1 -2]]

Template:Val list

Badness: 0.165 × 10-3

11-limit

Subgroup: 2.3.5.7.11

Comma list: 896/891, 2200/2187

Mapping: [⟨1 0 0 -10 -3], ⟨0 1 0 11 7], ⟨0 0 1 -2 -2]]

Vals: Template:Val list

Badness: 1.039 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 364/363

Mapping: [⟨1 0 0 -10 -3 2], ⟨0 1 0 11 7 4], ⟨0 0 1 -2 -2 -2]]

Vals: Template:Val list

Badness: 1.021 × 10-3

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 256/255, 325/324, 352/351, 364/363

Mapping: [⟨1 0 0 -10 -3 2 8], ⟨0 1 0 11 7 4 -1], ⟨0 0 1 -2 -2 -2 -1]]

Vals: Template:Val list

Badness: 0.982 × 10-3

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