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User:Recentlymaterialized/Miscellaneous rank-2 temperaments: Difference between revisions

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worsetone 19-limit mapping changed from 55fgh & 67 to 55f & 67
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== Tri[[BPS|pierce]] (b30 & b39) ==
== Tri[[BPS|pierce]] (b30 & b39) ==
: ''See also: [[User:Dummy_index/3rd-tritave_temperaments#BPS_III_.28b30_.26_b9.2C_b39_.26_b9.29|BPS III]]''


[[Subgroup]]: [[3.5.7.13_subgroup|3.5.7.13]]
[[Subgroup]]: [[3.5.7.13_subgroup|3.5.7.13]]
Line 80: Line 82:
[[Comma list]]: [[245/243]], [[2197/2187]]
[[Comma list]]: [[245/243]], [[2197/2187]]


[[Mapping]]: {{mapping|3 1 7 7|0 4 -2 0}}
[[Mapping]]: {{mapping|3 1 7 7|0 2 -1 0}}


[[Transversal_generators|Generator preimages]]: [[13/9]], [[13/7]]
[[Transversal_generators|Generator preimages]]: [[13/9]], [[13/7]]
Line 143: Line 145:


=== Trisemi[[BPS|pierce]] (b39 & b60) ===
=== Trisemi[[BPS|pierce]] (b39 & b60) ===
: ''See also: [[User:Dummy_index/3rd-tritave_temperaments#weak_extension_3.5.7.11.13_.28b39_.26_b60.29|BPS III - weak extension]]''


[[Subgroup]]: [[3.5.7.11.13_subgroup|3.5.7.11.13]]
[[Subgroup]]: [[3.5.7.11.13_subgroup|3.5.7.11.13]]
Line 514: Line 517:
Badness ([[TE_dirichlet_badness|Dirichlet]]): 2.04145
Badness ([[TE_dirichlet_badness|Dirichlet]]): 2.04145


=== 2.3.7.11.13(.17.19).23.31.37.41 subgroup ===
==== 2.3.7.11.13(.17.19).23.31.37.41 subgroup ====


[[Comma list]]: [[287/286]], [[297/296]], [[364/363]], [[483/481]], [[621/616]], [[3627/3626]], [[4797/4774]], ([[153/152]], [[273/272]])
[[Comma list]]: [[287/286]], [[297/296]], [[364/363]], [[483/481]], [[621/616]], [[3627/3626]], [[4797/4774]], ([[153/152]], [[189/187]])


[[Mapping]]: [{{val|1 0 -32 -44 -58 (-94 -97) -73 -52 -47 -69}}, {{val|0 1 22 30 39 (62 64) 49 36 33 47}}]
[[Mapping]]: [{{val|1 0 -32 -44 -58 (12 9) -73 -52 -47 -69}}, {{val|0 1 22 30 39 (-5 -3) 49 36 33 47}}]


[[Transversal_generators|Generator preimages]]: [[2/1]], [[3/1]]
[[Transversal_generators|Generator preimages]]: [[2/1]], [[3/1]]
Line 589: Line 592:
|}
|}


[[Optimal ET sequence]]: [[12edo|12f(ghh)ikm]], [[43edo|43deff(ggghhh)iiikkllmm]], [[55edo|55f(gh)ilm]], [[67edo|67p]], [[122edo|122(g)ilm]]
[[Optimal ET sequence]]: [[12edo|12fikm]], [[43edo|43deffiiikkllmm]], [[55edo|55film]], [[67edo|67]], [[122edo|122(h)ilm]]
 
Badness ([[TE_logflat_badness|Smith TE]]): 0.01056 (0.01515)
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.07545 (1.77384)
 
== Hemififive (68 & 94) ==
 
[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]
 
[[Comma list]]: [[275/273]], [[325/324]], [[385/384]], [[1716/1715]]
 
[[Mapping]]: {{mapping|2 7 10 6 5 12|0 -10 -14 -1 5 -12}}
 
[[Transversal_generators|Generator preimages]]: [[99/70]], [[8/7]]
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 599.9903{{cc}}, 229.6835{{cc}}
| 600.0198{{cc}}, 229.7451{{cc}}
| 600.0210{{cc}}, 229.7456{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\2, 229.6914{{cc}}
| 1\2, 229.7361{{cc}}
| 1\2, 229.7307{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\2, 229.6872{{cc}}
| 1\2, 229.7375{{cc}}
| 1\2, 229.7376{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 5/1
! 7/1
! 11/1
! 13/1
|-
| [[Tuning_map|Tuning]]
| 1200.0396{{cc}}
| 1902.6876{{cc}}
| 2783.7665{{cc}}
| 3370.3738{{cc}}
| 4148.8246{{cc}}
| 4443.2964{{cc}}
|-
| [[Error]]
| +0.0396{{cc}}
| +0.7326{{cc}}
| −2.5472{{cc}}
| +1.5479{{cc}}
| −2.4933{{cc}}
| +2.7687{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[26edo|26]], [[68edo|68]], [[94edo|94]]
 
Badness ([[TE_logflat_badness|Smith TE]]): 0.03418
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.41232
 
==== 19-limit ====
 
[[Subgroup]]: [[19-limit|2.3.5.7.11.13.17.19]]
 
[[Comma list]]: [[190/189]], [[275/273]], [[325/324]], [[385/384]], [[561/560]], [[595/594]]
 
[[Mapping]]: {{mapping|2 7 10 6 5 12 12 15|0 -10 -14 -1 5 -12 -10 -17}}
 
[[Transversal_generators|Generator preimages]]: [[17/12]], [[8/7]]
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 599.9903{{cc}}, 229.6835{{cc}}
| 600.0751{{cc}}, 229.7512{{cc}}
| 600.0765{{cc}}, 229.7517{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\2, 229.6914{{cc}}
| 1\2, 229.7168{{cc}}
| 1\2, 229.6935{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\2, 229.6872{{cc}}
| 1\2, 229.7224{{cc}}
| 1\2, 229.7224{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 5/1
! 7/1
! 11/1
! 13/1
! 17/1
! 19/1
|-
| [[Tuning_map|Tuning]]
| 1200.1502{{cc}}
| 1903.0139{{cc}}
| 2784.2344{{cc}}
| 3370.6993{{cc}}
| 4149.1313{{cc}}
| 4443.8869{{cc}}
| 4903.3893{{cc}}
| 5095.3563{{cc}}
|-
| [[Error]]
| +0.1502{{cc}}
| +1.0589{{cc}}
| −2.0793{{cc}}
| +1.8734{{cc}}
| −2.1867{{cc}}
| +3.3593{{cc}}
| −1.5661{{cc}}
| −2.1567{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[26edo|26]], [[68edo|68]], [[94edo|94]]
 
Badness ([[TE_logflat_badness|Smith TE]]): 0.01725
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.04955
 
==== 23-limit ====
 
[[Subgroup]]: [[23-limit|2.3.5.7.11.13.17.19.23]]
 
[[Comma list]]: [[190/189]], [[253/252]], [[275/273]], [[325/324]], [[385/384]], [[561/560]], [[595/594]]
 
[[Mapping]]: {{mapping|2 7 10 6 5 12 12 15 19|0 -10 -14 -1 5 -12 -10 -17 -26}}
 
[[Transversal_generators|Generator preimages]]: [[17/12]], [[8/7]]
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 599.9903{{cc}}, 229.6835{{cc}}
| 600.0744{{cc}}, 229.7474{{cc}}
| 600.0758{{cc}}, 229.7480{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\2, 229.6914{{cc}}
| 1\2, 229.7135{{cc}}
| 1\2, 229.6908{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\2, 229.6872{{cc}}
| 1\2, 229.7189{{cc}}
| 1\2, 229.7190{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 5/1
! 7/1
! 11/1
! 13/1
! 17/1
! 19/1
! 23/1
|-
| [[Tuning_map|Tuning]]
| 1200.1488{{cc}}
| 1903.0465{{cc}}
| 2784.28{{cc}}
| 3370.6991{{cc}}
| 4149.1094{{cc}}
| 4443.9237{{cc}}
| 4903.4186{{cc}}
| 5095.4097{{cc}}
| 5427.9804{{cc}}
|-
| [[Error]]
| +0.1488{{cc}}
| +1.0915{{cc}}
| −2.0337{{cc}}
| +1.8732{{cc}}
| −2.2086{{cc}}
| +3.3961{{cc}}
| −1.5368{{cc}}
| −2.1033{{cc}}
| −0.2939{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[26edo|26i]], [[68edo|68]], [[94edo|94]]


Badness ([[TE_logflat_badness|Smith TE]]): 0.01056 (0.01156)
Badness ([[TE_logflat_badness|Smith TE]]): 0.01458


Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.07545 (1.35270)
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.04399


== Cyanide (140 & 441) ==
== Cyanide (140 & 441) ==
Line 669: Line 909:
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.50663 (0.49340)
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.50663 (0.49340)


=== 13-limit ===
==== 13-limit ====


[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]([[2.3.5.7.11.13.23_subgroup|.23]])
[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]([[2.3.5.7.11.13.23_subgroup|.23]])
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