User:Dummy index/3rd-tritave temperaments: Difference between revisions
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== "Threedie family" start from 3.5.7.13 == | == "Threedie family" start from 3.5.7.13 == | ||
=== BPS III (b30 & b9, b39 & b9) === | === BPS III (b30 & b9, b39 & b9) === | ||
: ''Proposed names: [[User:Recentlymaterialized/Miscellaneous rank-2 temperaments #Tripierce (b30 & b39)]]'' | : ''Proposed names: [[User:Recentlymaterialized/Miscellaneous rank-2 temperaments #Tripierce (b30 & b39)]]'' | ||
[[Subgroup]]: 3.5.7.13 | [[Subgroup]]: 3.5.7.13 | ||
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Badness (Dirichlet): 0.269 | Badness (Dirichlet): 0.269 | ||
* {{mos scalesig|3L 6s<3/1>|link=1}} | |||
* {{mos scalesig|9L 3s<3/1>|link=1}} – This has 5:7:9:13. | |||
==== 3.5.7.11.13 ==== | ==== 3.5.7.11.13 ==== | ||
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Badness (Dirichlet): 0.525 | Badness (Dirichlet): 0.525 | ||
==== strong extension 3.5.7.11.13 (b39 & b30e) ==== | ==== strong extension 3.5.7.11.13 (b39 & b30e) ==== | ||
Subgroup: 3.5.7.11.13 | Subgroup: 3.5.7.11.13 | ||
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Badness (Dirichlet): 0.713 | Badness (Dirichlet): 0.713 | ||
==== weak extension 3.5.7.11.13 (b39 & b60) ==== | ==== weak extension 3.5.7.11.13 (b39 & b60) ==== | ||
Subgroup: 3.5.7.11.13 | Subgroup: 3.5.7.11.13 | ||
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Badness (Dirichlet): 0.447 | Badness (Dirichlet): 0.447 | ||
=== Sirius III (b39 & b6, b39 & b45) === | * {{mos scalesig|3L 15s<3/1>|link=1}} | ||
* {{mos scalesig|18L 3s<3/1>|link=1}} – This has 5:7:9:11:13. | |||
=== Sirius III (b39 & b6, b39 & b45) === | |||
[[Subgroup]]: 3.5.7.13 | [[Subgroup]]: 3.5.7.13 | ||
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Badness (Dirichlet): 0.832 | Badness (Dirichlet): 0.832 | ||
* {{mos scalesig|3L 3s<3/1>|link=1}} | |||
* {{mos scalesig|6L 3s<3/1>|link=1}} | |||
==== 3.5.7.11.13 (also deneb III) ==== | ==== 3.5.7.11.13 (also deneb III) ==== | ||
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Badness (Dirichlet): 0.551 | Badness (Dirichlet): 0.551 | ||
=== Canopus III (b39 & b36, b39 & b75) === | === Canopus III (b39 & b36, b39 & b75) === | ||
[[Subgroup]]: 3.5.7.13 | [[Subgroup]]: 3.5.7.13 | ||
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{{main|Suhail}} | {{main|Suhail}} | ||
=== b9 & b6 === | === b9 & b6 === | ||
[[Subgroup]]: 3.5.7.13 | [[Subgroup]]: 3.5.7.13 | ||
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== "Threedie family" start from 3.7.11.13 == | == "Threedie family" start from 3.7.11.13 == | ||
=== Mintaka III (b39 & b66) === | === Mintaka III (b39 & b66) === | ||
[[Subgroup]]: 3.7.11.13 | [[Subgroup]]: 3.7.11.13 | ||
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Badness (Dirichlet): 0.237 | Badness (Dirichlet): 0.237 | ||
* {{mos scalesig|3L 9s<3/1>|link=1}} – This and the following have 7:9:11:13. | |||
* {{mos scalesig|12L 3s<3/1>|link=1}} | |||
==== 3.5.7.11.13 (also procyon III) ==== | ==== 3.5.7.11.13 (also procyon III) ==== | ||
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Badness (Dirichlet): 0.459 | Badness (Dirichlet): 0.459 | ||
==== | ==== Weak extension 3.5.7.11.13 (b39 & b15, also arcturus III) ==== | ||
: ''See also: [[Tetrahanson #b39 & b15]]'' | |||
Subgroup: 3.5.7.11.13 | Subgroup: 3.5.7.11.13 | ||
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Badness (Dirichlet): 0.588 | Badness (Dirichlet): 0.588 | ||
* {{mos scalesig|6L 3s<3/1>|link=1}} | |||
* {{mos scalesig|9L 6s<3/1>|link=1}} – This has 5:9:11:13. | |||
* {{mos scalesig|15L 9s<3/1>|link=1}} – This has 5:7:9:11:13. | |||
=== b27 & b21 === | |||
Subgroup: 3.7.11.13 | |||
Comma list: 9477/9317, 2197/2187 | |||
Sval mapping: {{mapping| 3 1 8 7 | 0 3 -1 0 }} | |||
Sval mapping (mingen): {{mapping| 3 4 7 7 | 0 3 -1 0 }} | |||
Sval mapping generators: ~13/9, ~243/143 | |||
Optimal tuning (CWE): ~13/9 = 1\3edt, ~243/143 = 912.556 | |||
Supporting ETs: 27, 6, 21, 48, 75, 15[-7], 33[+7], 69, 102, 123[+11], 60[+7], 129[+7], 90[+11], 117[+11] | |||
Badness (Dirichlet): 0.830 | |||
== External links == | == External links == | ||
*[https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_13&error=6.2] | * [https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_13&error=6.2] | ||
*[https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_11_13&error=4.0] | * [https://x31eq.com/pyscript/more.html?r=2&limit=3_5_7_11_13&error=4.0] | ||
<!-- b30 & b6, b30 & b45, b9 & b45 --> | <!-- b30 & b6, b30 & b45, b9 & b45 --> | ||