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

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m adding remaining tuning boxes
rearranging
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== 27e & 87 ==
== Senscape (27e & 87) ==


[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]
[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]
Line 74: Line 74:
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.05783
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.05783


== 130 & 181 ==
== Tri[[BPS|pierce]] (b30 & b39) ==
 
[[Subgroup]]: [[3.5.7.13_subgroup|3.5.7.13]]
 
[[Comma list]]: [[245/243]], [[2197/2187]]
 
[[Mapping]]: {{mapping|3 1 7 7|0 4 -2 0}}
 
[[Transversal_generators|Generator preimages]]: [[13/9]], [[13/7]]
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| ???
| 634.5206{{cc}}, 1075.4459{{cc}}
| 634.5215{{cc}}, 1075.4475{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\b3, 1074.0886{{cc}}
| 1\b3, 1074.6634{{cc}}
| 1\b3, 1075.1282{{cc}}
|-
| [[POTE|Destretched]]
| ???
| ???
| 1\b3, 1074.5381{{cc}}
| 1\b3, 1074.5382{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 3/1
! 5/1
! 7/1
! 13/1
|-
| [[Tuning_map|Tuning]]
| 1903.5617{{cc}}
| 2785.4124{{cc}}
| 3366.1979{{cc}}
| 4441.6439{{cc}}
|-
| [[Error]]
| +1.6067{{cc}}
| −0.9013{{cc}}
| −2.628{{cc}}
| +1.1162{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[9edt|b9]], [[21edt|b21]], [[30edt|b30]], [[39edt|b39]], [[69edt|b69]], [[108edt|b108]], [[177edt|b177d]]
 
Badness ([[TE_logflat_badness|Smith TE]]): 0.00287
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.26872
 
=== Trisemi[[BPS|pierce]] (b39 & b60) ===
 
[[Subgroup]]: [[3.5.7.11.13_subgroup|3.5.7.11.13]]
 
[[Comma list]]: [[245/243]], [[847/845]], [[1575/1573]]
 
[[Mapping]]: {{mapping|3 1 7 4 7|0 4 -2 3 0}}
 
[[Transversal_generators|Generator preimages]]: [[13/9]], [[15/11]]
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 634.4577{{cc}}, 537.4447{{cc}}
| 634.5219{{cc}}, 537.7266{{cc}}
| 634.5229{{cc}}, 537.7274{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\b3, 537.0443{{cc}}
| 1\b3, 537.3589{{cc}}
| 1\b3, 537.7233{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\b3, 537.0443{{cc}}
| 1\b3, 537.2716{{cc}}
| 1\b3, 537.2716{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 3/1
! 5/1
! 7/1
! 11/1
! 13/1
|-
| [[Tuning_map|Tuning]]
| 1903.5658{{cc}}
| 2785.4282{{cc}}
| 3366.2003{{cc}}
| 4151.2674{{cc}}
| 4441.6534{{cc}}
|-
| [[Error]]
| +1.6108{{cc}}
| −0.8855{{cc}}
| −2.6256{{cc}}
| −0.0505{{cc}}
| +1.1258{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[18edt|b18]], [[21edt|b21]], [[39edt|b39]], [[99edt|b99]], [[138edt|b138]], [[177edt|b177d]]
 
Badness ([[TE_logflat_badness|Smith TE]]): 0.00566
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.44749


''See also: [[User:Francium/Miscellaneous_rank-2_temperaments#311_.26_1063|7-limit]]''
=== Tri[[dubhe]] (b69 & b78) ===


[[Subgroup]]: [[2.3.5.7.13_subgroup|2.3.5.7.13]]
[[Subgroup]]: [[3.5.7.13.17.19_subgroup|3.5.7.13.17.19]]


[[Comma list]]: [[2401/2400]], [[4096/4095]], [[492128/492075]]
[[Comma list]]: [[245/243]], [[325/323]], [[665/663]], [[3213/3211]]


[[Mapping]]: {{mapping|1 11 -22 -7 19|0 -24 62 25 -39}}
[[Mapping]]: {{mapping|3 3 6 7 6 7|0 4 -2 0 5 3}}


[[Transversal_generators|Generator preimages]]: [[2/1]], [[21/16]]
[[Transversal_generators|Generator preimages]]: [[13/9]], [[17/15]]


[[Optimization|Generator tunings]]:
[[Optimization|Generator tunings]]:
Line 98: Line 235:
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
| ???
| ???
| 1199.983{{cc}}, 470.7428{{cc}}
| 634.4242{{cc}}, 220.2042{{cc}}
| 1199.9727{{cc}}, 470.7388{{cc}}
| 634.3781{{cc}}, 220.1438{{cc}}
| 1199.9727{{cc}}, 470.7388{{cc}}
| 634.3798{{cc}}, 220.1444{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
| ???
| ???
| 1\1, 470.7495{{cc}}
| 1\b3, 220.0518{{cc}}
| 1\1, 470.7495{{cc}}
| 1\b3, 220.0811{{cc}}
| 1\1, 470.7493{{cc}}
| 1\b3, 220.4087{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
| ???
| ???
| 1\1, 470.7495{{cc}}
| 1\b3, 220.0518{{cc}}
| 1\1, 470.7495{{cc}}
| 1\b3, 220.0074{{cc}}
| 1\1, 470.7495{{cc}}
| 1\b3, 220.0074{{cc}}
|}
|}


Line 120: Line 257:
|-
|-
! Prime
! Prime
! 2/1
! 3/1
! 3/1
! 5/1
! 5/1
! 7/1
! 7/1
! 13/1
! 13/1
! 17/1
! 19/1
|-
|-
| [[Tuning_map|Tuning]]
| [[Tuning_map|Tuning]]
| 1199.9727{{cc}}
| 1903.1344{{cc}}
| 1901.9687{{cc}}
| 2783.7095{{cc}}
| 2786.4055{{cc}}
| 3365.9811{{cc}}
| 3368.6607{{cc}}
| 4440.6468{{cc}}
| 4440.6683{{cc}}
| 4906.9877{{cc}}
| 5101.0782{{cc}}
|-
|-
| [[Error]]
| [[Error]]
| −0.0273{{cc}}
| +1.1794{{cc}}
| +0.0137{{cc}}
| −2.6042{{cc}}
| +0.0918{{cc}}
| −2.8448{{cc}}
| −0.1652{{cc}}
| +0.1192{{cc}}
| +0.1407{{cc}}
| +2.0323{{cc}}
| +3.5652{{cc}}
|}
|}


[[Optimal ET sequence]] ([[TE]]): [[51edo|51]], [[79edo|79c]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[1453edo|1453]], [[1894edo|1894]], [[2335edo|2335]]
[[Optimal ET sequence]] ([[TE]]): [[51edt|b51]], [[60edt|b60]], [[69edt|b69]], [[147edt|b147]]


Badness ([[TE_logflat_badness|Smith TE]]): 0.01381
Badness ([[TE_logflat_badness|Smith TE]]): 0.00523


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.47741
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.48415


=== 13-limit ===
=== Trisemi[[dubhe]] (b60 & b78) ===


[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]
[[Subgroup]]: [[3.5.7.11.13.17.19_subgroup|3.5.7.11.13.17.19]]


[[Comma list]]: [[1575/1573]], [[2080/2079]], [[4096/4095]], [[4459/4455]]
[[Comma list]]: [[245/243]], [[325/323]], [[665/663]], [[847/845]], [[1575/1573]]


[[Mapping]]: {{mapping|1 11 -22 -7 -24 19|0 -24 62 25 70 -39}}
[[Mapping]]: {{mapping|6 2 14 8 14 7 11|0 4 -2 3 0 5 3}}


[[Transversal_generators|Generator preimages]]: [[2/1]], [[21/16]]
[[Transversal_generators|Generator preimages]]: [[119/99]], [[15/11]]


[[Optimization|Generator tunings]]:
[[Optimization|Generator tunings]]:
Line 169: Line 309:
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
| ???
| ???
| 1199.9305{{cc}}, 470.7167{{cc}}
| ???
| 1199.9386{{cc}}, 470.7221{{cc}}
| 317.2028{{cc}}, 537.3966{{cc}}
| 1199.9387{{cc}}, 470.7221{{cc}}
| 317.2037{{cc}}, 537.3981{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
| ???
| ???
| 1\1, 470.7411{{cc}}
| 1\b6, 537.0443{{cc}}
| 1\1, 470.746{{cc}}
| 1\b6, 537.1261{{cc}}
| 1\1, 470.745{{cc}}
| 1\b6, 537.5291{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
| ???
| ???
| 1\1, 470.744{{cc}}
| ???
| 1\1, 470.7462{{cc}}
| 1\b6, 1074.0806{{cc}}
| 1\1, 470.7461{{cc}}
| 1\b6, 1074.0806{{cc}}
|}
|}


Line 191: Line 331:
|-
|-
! Prime
! Prime
! 2/1
! 3/1
! 3/1
! 5/1
! 5/1
Line 197: Line 336:
! 11/1
! 11/1
! 13/1
! 13/1
! 17/1
! 19/1
|-
|-
| [[Tuning_map|Tuning]]
| [[Tuning_map|Tuning]]
| 1199.9386{{cc}}
| 1903.2168{{cc}}
| 1901.9946{{cc}}
| 2783.9919{{cc}}
| 2786.1202{{cc}}
| 3366.0459{{cc}}
| 3368.482{{cc}}
| 4149.8121{{cc}}
| 4152.0197{{cc}}
| 4440.8391{{cc}}
| 4440.6721{{cc}}
| 4907.4024{{cc}}
| 5101.4204{{cc}}
|-
|-
| [[Error]]
| [[Error]]
| −0.0614{{cc}}
| +1.2618{{cc}}
| +0.0396{{cc}}
| −2.3218{{cc}}
| −0.1936{{cc}}
| −2.780{{cc}}
| −0.3439{{cc}}
| −1.5059{{cc}}
| +0.7017{{cc}}
| +0.3114{{cc}}
| +0.1445{{cc}}
| +2.447{{cc}}
| +3.9074{{cc}}
|}
|}


[[Optimal ET sequence]] ([[TE]]): [[51edo|51]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[752edo|752e]], [[1193edo|1193e]]
[[Optimal ET sequence]] ([[TE]]): [[18edt|b18]], [[60edt|b60]], [[78edt|b78]], [[138edt|b138]], [[216edt|b216]]


Badness ([[TE_logflat_badness|Smith TE]]): 0.02172
Badness ([[TE_logflat_badness|Smith TE]]): 0.01046


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.89734
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.95032


== Badtone (31 & 67) ==
== Badtone (31 & 67) ==
Line 296: Line 439:


== Worsetone (12f & 67) ==
== Worsetone (12f & 67) ==
<p style="margin-bottom:1em">[[User:Lucius_Chiaraviglio|Lucas Chiaraviglio]] suggests the name ''[[Talk:Meantone#Unlisted_strong_7-limit_Meantone_extension_.28provisional_name_Mildtone.29.3F|mildtone]]''.</p>


[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]
[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]
Line 450: Line 595:
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.07545 (1.35270)
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.07545 (1.35270)


== Tri[[BPS|pierce]] (b30 & b39) ==
== Cyanide (140 & 441) ==


[[Subgroup]]: [[3.5.7.13_subgroup|3.5.7.13]]
[[Subgroup]]: [[2.3.5.7.13_subgroup|2.3.5.7.13]]([[2.3.5.7.13.23_subgroup|.23]])


[[Comma list]]: [[245/243]], [[2197/2187]]
[[Comma list]]: [[2401/2400]], [[4096/4095]], ([[35000/34983]]), [[140625/140608]]


[[Mapping]]: {{mapping|3 1 7 7|0 4 -2 0}}
[[Mapping]]: {{mapping|7 3 23 21 34 (60)|0 6 -5 -1 -6 (-21)}}


[[Transversal_generators|Generator preimages]]: [[13/9]], [[13/7]]
[[Transversal_generators|Generator preimages]]: [[3675/3328]], [[8/7]]


[[Optimization|Generator tunings]]:
[[Optimization|Generator tunings]]:
Line 472: Line 617:
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
| ???
| ???
| ???
| 171.4255{{cc}}, 231.2847{{cc}}
| 634.5206{{cc}}, 1075.4459{{cc}}
| 171.4244{{cc}}, 231.2902{{cc}}
| 634.5215{{cc}}, 1075.4475{{cc}}
| 171.4244{{cc}}, 231.2902{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
| ???
| ???
| 1\b3, 1074.0886{{cc}}
| 1\7, 231.2969{{cc}}
| 1\b3, 1074.6634{{cc}}
| 1\7, 231.2963{{cc}}
| 1\b3, 1075.1282{{cc}}
| 1\7, 231.2991{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
| ???
| ???
| ???
| 1\7, 231.2888{{cc}}
| 1\b3, 1074.5381{{cc}}
| 1\7, 231.2943{{cc}}
| 1\b3, 1074.5382{{cc}}
| 1\7, 231.2943{{cc}}
|}
|}


Line 494: Line 639:
|-
|-
! Prime
! Prime
! 2/1
! 3/1
! 3/1
! 5/1
! 5/1
! 7/1
! 7/1
! 13/1
! 13/1
! 23/1
|-
|-
| [[Tuning_map|Tuning]]
| [[Tuning_map|Tuning]]
| 1903.5617{{cc}}
| 1199.971{{cc}}
| 2785.4124{{cc}}
| 1902.0144{{cc}}
| 3366.1979{{cc}}
| 2786.3108{{cc}}
| 4441.6439{{cc}}
| 3368.6227{{cc}}
| 4440.6893{{cc}}
| 5428.3714{{cc}}
|-
|-
| [[Error]]
| [[Error]]
| +1.6067{{cc}}
| −0.029{{cc}}
| −0.9013{{cc}}
| +0.0594{{cc}}
| −2.628{{cc}}
| −0.0029{{cc}}
| +1.1162{{cc}}
| −0.2032{{cc}}
| +0.1616{{cc}}
| +0.097{{cc}}
|}
|}


[[Optimal ET sequence]] ([[TE]]): [[9edt|b9]], [[21edt|b21]], [[30edt|b30]], [[39edt|b39]], [[69edt|b69]], [[108edt|b108]], [[177edt|b177d]]
[[Optimal ET sequence]] ([[TE]]): [[21edo|21]], [[119edo|119]], [[140edo|140]], [[301edo|301]], [[441edo|441]] <small>(add-23: [[21edo|21ii]], [[140edo|140]], [[301edo|301]], [[441edo|441]], [[3227edo|3227f]])</small>


Badness ([[TE_logflat_badness|Smith TE]]): 0.00287
Badness ([[TE_logflat_badness|Smith TE]]): 0.01465 (0.01044)


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.26872
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.50663 (0.49340)


=== Trisemi[[BPS|pierce]] (b39 & b60) ===
=== 13-limit ===


[[Subgroup]]: [[3.5.7.11.13_subgroup|3.5.7.11.13]]
[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]([[2.3.5.7.11.13.23_subgroup|.23]])


[[Comma list]]: [[245/243]], [[847/845]], [[1575/1573]]
[[Comma list]]: [[1288/1287]], [[2080/2079]], [[2401/2400]], [[4096/4095]], [[35000/34983]]


[[Mapping]]: {{mapping|3 1 7 4 7|0 4 -2 3 0}}
[[Mapping]]: {{mapping|7 3 23 21 62 34 (60)|0 6 -5 -1 -28 -6 (-21)}}


[[Transversal_generators|Generator preimages]]: [[13/9]], [[15/11]]
[[Transversal_generators|Generator preimages]]: [[875/792]], [[8/7]]


[[Optimization|Generator tunings]]:
[[Optimization|Generator tunings]]:
Line 540: Line 691:
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
| ???
| ???
| 634.4577{{cc}}, 537.4447{{cc}}
| 171.4227, 231.3059{{cc}}
| 634.5219{{cc}}, 537.7266{{cc}}
| 171.4242, 231.3085{{cc}}
| 634.5229{{cc}}, 537.7274{{cc}}
| 171.4242, 231.3085{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
| ???
| ???
| 1\b3, 537.0443{{cc}}
| 1\7, 231.3138{{cc}}
| 1\b3, 537.3589{{cc}}
| 1\7, 231.3149{{cc}}
| 1\b3, 537.7233{{cc}}
| 1\7, 231.3180{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
| ???
| ???
| 1\b3, 537.0443{{cc}}
| 1\7, 231.3138{{cc}}
| 1\b3, 537.2716{{cc}}
| 1\7, 231.3144{{cc}}
| 1\b3, 537.2716{{cc}}
| 1\7, 231.3144{{cc}}
|}
|}


Line 562: Line 713:
|-
|-
! Prime
! Prime
! 2/1
! 3/1
! 3/1
! 5/1
! 5/1
Line 567: Line 719:
! 11/1
! 11/1
! 13/1
! 13/1
! 23/1
|-
|-
| [[Tuning_map|Tuning]]
| [[Tuning_map|Tuning]]
| 1903.5658{{cc}}
| 1199.9697{{cc}}
| 2785.4282{{cc}}
| 1902.1239{{cc}}
| 3366.2003{{cc}}
| 2786.2149{{cc}}
| 4151.2674{{cc}}
| 3368.6006{{cc}}
| 4441.6534{{cc}}
| 4151.6642{{cc}}
| 4440.5731{{cc}}
| 5427.9754{{cc}}
|-
|-
| [[Error]]
| [[Error]]
| +1.6108{{cc}}
| −0.0303{{cc}}
| −0.8855{{cc}}
| +0.1689{{cc}}
| −2.6256{{cc}}
| −0.0988{{cc}}
| −0.0505{{cc}}
| −0.2253{{cc}}
| +1.1258{{cc}}
| +0.3463{{cc}}
| +0.0454{{cc}}
| −0.2989{{cc}}
|}
|}


[[Optimal ET sequence]] ([[TE]]): [[18edt|b18]], [[21edt|b21]], [[39edt|b39]], [[99edt|b99]], [[138edt|b138]], [[177edt|b177d]]
[[Optimal ET sequence]] ([[TE]]): [[140edo|140]], [[301edo|301e]], [[441edo|441]], [[581edo|581]], [[1022edo|1022]], [[1603edo|1603e]] <small>(same sequence for add-23)</small>


Badness ([[TE_logflat_badness|Smith TE]]): 0.00566
Badness ([[TE_logflat_badness|Smith TE]]): 0.02947 (0.01904)


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.44749
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.21770 (1.01017)


=== Tri[[dubhe]] (b69 & b78) ===
=== 581 & 742 <small style="font-weight:400">(weak extension)</small> ===


[[Subgroup]]: [[3.5.7.13.17.19_subgroup|3.5.7.13.17.19]]
[[Subgroup]]: [[19-limit|2.3.5.7.11.13.17.19]]


[[Comma list]]: [[245/243]], [[325/323]], [[665/663]], [[3213/3211]]
[[Comma list]]: [[2401/2400]], [[3136/3135]], [[4096/4095]], [[5985/5984]], [[12376/12375]], [[14875/14872]]


[[Mapping]]: {{mapping|3 3 6 7 6 7|0 4 -2 0 5 3}}
[[Mapping]]: {{mapping|7 15 13 19 24 22 31 28|0 -18 15 3 1 18 -11 8}} &nbsp;<small>(23/1: {{mapping|18|63}})</small>


[[Transversal_generators|Generator preimages]]: [[13/9]], [[17/15]]
[[Transversal_generators|Generator preimages]]: [[85/77]], [[143/140]]


[[Optimization|Generator tunings]]:
[[Optimization|Generator tunings]] (add-23):


: {| class="wikitable right-1"
: {| class="wikitable right-1"
Line 611: Line 768:
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
| ???
| ???
| 634.4242{{cc}}, 220.2042{{cc}}
| 171.4266{{cc}}, 37.1864{{cc}}
| 634.3781{{cc}}, 220.1438{{cc}}
| 171.4244{{cc}}, 37.1884{{cc}}
| 634.3798{{cc}}, 220.1444{{cc}}
| 171.4244{{cc}}, 37.1884{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
| ???
| ???
| 1\b3, 220.0518{{cc}}
| 1\7, 37.1867{{cc}}
| 1\b3, 220.0811{{cc}}
| 1\7, 37.1893{{cc}}
| 1\b3, 220.4087{{cc}}
| 1\7, 37.1893{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
| ???
| ???
| 1\b3, 220.0518{{cc}}
| 1\7, 37.1868{{cc}}
| 1\b3, 220.0074{{cc}}
| 1\7, 37.1893{{cc}}
| 1\b3, 220.0074{{cc}}
| 1\7, 37.1893{{cc}}
|}
|}


Line 633: Line 790:
|-
|-
! Prime
! Prime
! 2/1
! 3/1
! 3/1
! 5/1
! 5/1
! 7/1
! 7/1
! 11/1
! 13/1
! 13/1
! 17/1
! 17/1
! 19/1
! 19/1
|-
|-
| [[Tuning_map|Tuning]]
| [[Tuning_map|Tuning]] ({{cent}})
| 1903.1344{{cc}}
| 1199.97{{cc}}
| 2783.7095{{cc}}
| 1901.97{{cc}}
| 3365.9811{{cc}}
| 2786.34{{cc}}
| 4440.6468{{cc}}
| 3368.63{{cc}}
| 4906.9877{{cc}}
| 4151.37{{cc}}
| 5101.0782{{cc}}
| 4440.73{{cc}}
| 4905.08{{cc}}
| 5097.39{{cc}}
|-
|-
| [[Error]]
| [[Error]]
| +1.1794{{cc}}
| −0.0291{{cc}}
| −2.6042{{cc}}
| +0.0195{{cc}}
| −2.8448{{cc}}
| +0.0302{{cc}}
| +0.1192{{cc}}
| −0.1966{{cc}}
| +2.0323{{cc}}
| +0.0566{{cc}}
| +3.5652{{cc}}
| +0.2014{{cc}}
| +0.1289{{cc}}
| −0.1218{{cc}}
|}
|}


[[Optimal ET sequence]] ([[TE]]): [[51edt|b51]], [[60edt|b60]], [[69edt|b69]], [[147edt|b147]]
[[Optimal ET sequence]] ([[TE]]): [[161edo|161]], [[420edo|420]], [[581edo|581]], [[742edo|742]], [[1323edo|1323]]


Badness ([[TE_logflat_badness|Smith TE]]): 0.00523
Badness ([[TE_logflat_badness|Smith TE]]): 0.01260


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.48415
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.76654


=== Trisemi[[dubhe]] (b60 & b78) ===
== 130 & 181 ==


[[Subgroup]]: [[3.5.7.11.13.17.19_subgroup|3.5.7.11.13.17.19]]
''See also: [[User:Francium/Miscellaneous_rank-2_temperaments#311_.26_1063|7-limit]]''


[[Comma list]]: [[245/243]], [[325/323]], [[665/663]], [[847/845]], [[1575/1573]]
[[Subgroup]]: [[2.3.5.7.13_subgroup|2.3.5.7.13]]


[[Mapping]]: {{mapping|6 2 14 8 14 7 11|0 4 -2 3 0 5 3}}
[[Comma list]]: [[2401/2400]], [[4096/4095]], [[492128/492075]]


[[Transversal_generators|Generator preimages]]: [[119/99]], [[15/11]]
[[Mapping]]: {{mapping|1 11 -22 -7 19|0 -24 62 25 -39}}


[[Optimization|Generator tunings]]:
[[Transversal_generators|Generator preimages]]: [[2/1]], [[21/16]]
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| ???
| 317.2028{{cc}}, 537.3966{{cc}}
| 317.2037{{cc}}, 537.3981{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\b6, 537.0443{{cc}}
| 1\b6, 537.1261{{cc}}
| 1\b6, 537.5291{{cc}}
|-
| [[POTE|Destretched]]
| ???
| ???
| 1\b6, 1074.0806{{cc}}
| 1\b6, 1074.0806{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 3/1
! 5/1
! 7/1
! 11/1
! 13/1
! 17/1
! 19/1
|-
| [[Tuning_map|Tuning]]
| 1903.2168{{cc}}
| 2783.9919{{cc}}
| 3366.0459{{cc}}
| 4149.8121{{cc}}
| 4440.8391{{cc}}
| 4907.4024{{cc}}
| 5101.4204{{cc}}
|-
| [[Error]]
| +1.2618{{cc}}
| −2.3218{{cc}}
| −2.780{{cc}}
| −1.5059{{cc}}
| +0.3114{{cc}}
| +2.447{{cc}}
| +3.9074{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[18edt|b18]], [[60edt|b60]], [[78edt|b78]], [[138edt|b138]], [[216edt|b216]]
 
Badness ([[TE_logflat_badness|Smith TE]]): 0.01046
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.95032
 
== 140 & 441 ==
 
[[Subgroup]]: [[2.3.5.7.13_subgroup|2.3.5.7.13]]([[2.3.5.7.13.23_subgroup|.23]])
 
[[Comma list]]: [[2401/2400]], [[4096/4095]], ([[35000/34983]]), [[140625/140608]]
 
[[Mapping]]: {{mapping|7 3 23 21 34 (60)|0 6 -5 -1 -6 (-21)}}
 
[[Transversal_generators|Generator preimages]]: [[3675/3328]], [[8/7]]


[[Optimization|Generator tunings]]:
[[Optimization|Generator tunings]]:
Line 762: Line 850:
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
| ???
| ???
| 171.4255{{cc}}, 231.2847{{cc}}
| 1199.983{{cc}}, 470.7428{{cc}}
| 171.4244{{cc}}, 231.2902{{cc}}
| 1199.9727{{cc}}, 470.7388{{cc}}
| 171.4244{{cc}}, 231.2902{{cc}}
| 1199.9727{{cc}}, 470.7388{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
| ???
| ???
| 1\7, 231.2969{{cc}}
| 1\1, 470.7495{{cc}}
| 1\7, 231.2963{{cc}}
| 1\1, 470.7495{{cc}}
| 1\7, 231.2991{{cc}}
| 1\1, 470.7493{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
| ???
| ???
| 1\7, 231.2888{{cc}}
| 1\1, 470.7495{{cc}}
| 1\7, 231.2943{{cc}}
| 1\1, 470.7495{{cc}}
| 1\7, 231.2943{{cc}}
| 1\1, 470.7495{{cc}}
|}
|}


Line 789: Line 877:
! 7/1
! 7/1
! 13/1
! 13/1
! 23/1
|-
|-
| [[Tuning_map|Tuning]]
| [[Tuning_map|Tuning]]
| 1199.971{{cc}}
| 1199.9727{{cc}}
| 1902.0144{{cc}}
| 1901.9687{{cc}}
| 2786.3108{{cc}}
| 2786.4055{{cc}}
| 3368.6227{{cc}}
| 3368.6607{{cc}}
| 4440.6893{{cc}}
| 4440.6683{{cc}}
| 5428.3714{{cc}}
|-
|-
| [[Error]]
| [[Error]]
| −0.029{{cc}}
| −0.0273{{cc}}
| +0.0594{{cc}}
| +0.0137{{cc}}
| −0.0029{{cc}}
| +0.0918{{cc}}
| −0.2032{{cc}}
| −0.1652{{cc}}
| +0.1616{{cc}}
| +0.1407{{cc}}
| +0.097{{cc}}
|}
|}


[[Optimal ET sequence]] ([[TE]]): [[21edo|21]], [[119edo|119]], [[140edo|140]], [[301edo|301]], [[441edo|441]] <small>(add-23: [[21edo|21ii]], [[140edo|140]], [[301edo|301]], [[441edo|441]], [[3227edo|3227f]])</small>
[[Optimal ET sequence]] ([[TE]]): [[51edo|51]], [[79edo|79c]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[1453edo|1453]], [[1894edo|1894]], [[2335edo|2335]]


Badness ([[TE_logflat_badness|Smith TE]]): 0.01465 (0.01044)
Badness ([[TE_logflat_badness|Smith TE]]): 0.01381


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.50663 (0.49340)
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.47741


=== 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]]


[[Comma list]]: [[1288/1287]], [[2080/2079]], [[2401/2400]], [[4096/4095]], [[35000/34983]]
[[Comma list]]: [[1575/1573]], [[2080/2079]], [[4096/4095]], [[4459/4455]]


[[Mapping]]: {{mapping|7 3 23 21 62 34 (60)|0 6 -5 -1 -28 -6 (-21)}}
[[Mapping]]: {{mapping|1 11 -22 -7 -24 19|0 -24 62 25 70 -39}}


[[Transversal_generators|Generator preimages]]: [[875/792]], [[8/7]]
[[Transversal_generators|Generator preimages]]: [[2/1]], [[21/16]]


[[Optimization|Generator tunings]]:
[[Optimization|Generator tunings]]:
Line 836: Line 921:
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
| ???
| ???
| 171.4227, 231.3059{{cc}}
| 1199.9305{{cc}}, 470.7167{{cc}}
| 171.4242, 231.3085{{cc}}
| 1199.9386{{cc}}, 470.7221{{cc}}
| 171.4242, 231.3085{{cc}}
| 1199.9387{{cc}}, 470.7221{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
| ???
| ???
| 1\7, 231.3138{{cc}}
| 1\1, 470.7411{{cc}}
| 1\7, 231.3149{{cc}}
| 1\1, 470.746{{cc}}
| 1\7, 231.3180{{cc}}
| 1\1, 470.745{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
| ???
| ???
| 1\7, 231.3138{{cc}}
| 1\1, 470.744{{cc}}
| 1\7, 231.3144{{cc}}
| 1\1, 470.7462{{cc}}
| 1\7, 231.3144{{cc}}
| 1\1, 470.7461{{cc}}
|}
|}


Line 864: Line 949:
! 11/1
! 11/1
! 13/1
! 13/1
! 23/1
|-
|-
| [[Tuning_map|Tuning]]
| [[Tuning_map|Tuning]]
| 1199.9697{{cc}}
| 1199.9386{{cc}}
| 1902.1239{{cc}}
| 1901.9946{{cc}}
| 2786.2149{{cc}}
| 2786.1202{{cc}}
| 3368.6006{{cc}}
| 3368.482{{cc}}
| 4151.6642{{cc}}
| 4152.0197{{cc}}
| 4440.5731{{cc}}
| 4440.6721{{cc}}
| 5427.9754{{cc}}
|-
|-
| [[Error]]
| [[Error]]
| −0.0303{{cc}}
| −0.0614{{cc}}
| +0.1689{{cc}}
| +0.0396{{cc}}
| −0.0988{{cc}}
| −0.1936{{cc}}
| −0.2253{{cc}}
| −0.3439{{cc}}
| +0.3463{{cc}}
| +0.7017{{cc}}
| +0.0454{{cc}}
| +0.1445{{cc}}
| −0.2989{{cc}}
|}
|}


[[Optimal ET sequence]] ([[TE]]): [[140edo|140]], [[301edo|301e]], [[441edo|441]], [[581edo|581]], [[1022edo|1022]], [[1603edo|1603e]] <small>(same sequence for add-23)</small>
[[Optimal ET sequence]] ([[TE]]): [[51edo|51]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[752edo|752e]], [[1193edo|1193e]]


Badness ([[TE_logflat_badness|Smith TE]]): 0.02947 (0.01904)
Badness ([[TE_logflat_badness|Smith TE]]): 0.02172


Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.21770 (1.01017)
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.89734


=== 581 & 742 <small style="font-weight:400">(weak extension)</small> ===
== Whooshlet (441 & 3072) ==


[[Subgroup]]: [[19-limit|2.3.5.7.11.13.17.19]]
[[Subgroup]]: [[2.3.5.7.13_subgroup|2.3.5.7.13]]


[[Comma list]]: [[2401/2400]], [[3136/3135]], [[4096/4095]], [[5985/5984]], [[12376/12375]], [[14875/14872]]
[[Comma list]]: [[140625/140608]], [[250047/250000]], [[1990656/1990625]] &nbsp;<small>([[9801/9800]] can be added if the full 13-limit is desired)</small>


[[Mapping]]: {{mapping|7 15 13 19 24 22 31 28|0 -18 15 3 1 18 -11 8}} &nbsp;<small>(23/1: {{mapping|18|63}})</small>
[[Mapping]]: {{mapping|3 18 17 2 40|0 -33 -25 16 -72}}


[[Transversal_generators|Generator preimages]]: [[85/77]], [[143/140]]
[[Transversal_generators|Generator preimages]]: [[63/50]], [[192/175]]


[[Optimization|Generator tunings]] (add-23):
[[Optimization|Generator tunings]]:


: {| class="wikitable right-1"
: {| class="wikitable right-1"
Line 913: Line 995:
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
| ???
| ???
| 171.4266{{cc}}, 37.1864{{cc}}
| 400.0024{{cc}}, 160.5488{{cc}}
| 171.4244{{cc}}, 37.1884{{cc}}
| 400.0034{{cc}}, 160.5495{{cc}}
| 171.4244{{cc}}, 37.1884{{cc}}
| 400.0034{{cc}}, 160.5495{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
| ???
| ???
| 1\7, 37.1867{{cc}}
| 1\, 160.5478{{cc}}
| 1\7, 37.1893{{cc}}
| 1\, 160.5480{{cc}}
| 1\7, 37.1893{{cc}}
| 1\, 160.5476{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
| ???
| ???
| 1\7, 37.1868{{cc}}
| 1\3, 160.5478{{cc}}
| 1\7, 37.1893{{cc}}
| 1\3, 160.5481{{cc}}
| 1\7, 37.1893{{cc}}
| 1\3, 160.5481{{cc}}
|}
|}


Line 941: Line 1,023:
! 11/1
! 11/1
! 13/1
! 13/1
! 17/1
! 19/1
|-
|-
| [[Tuning_map|Tuning]] ({{cent}})
| [[Tuning_map|Tuning]]
| 1199.97{{cc}}
| 1200.0102{{cc}}
| 1901.97{{cc}}
| 1901.9291{{cc}}
| 2786.34{{cc}}
| 2786.3213{{cc}}
| 3368.63{{cc}}
| 3368.7981{{cc}}
| 4151.37{{cc}}
| 4440.575{{cc}}
| 4440.73{{cc}}
| 4905.08{{cc}}
| 5097.39{{cc}}
|-
|-
| [[Error]]
| [[Error]]
| −0.0291{{cc}}
| +0.0102{{cc}}
| +0.0195{{cc}}
| −0.0259{{cc}}
| +0.0302{{cc}}
| +0.0076{{cc}}
| −0.1966{{cc}}
| −0.0278{{cc}}
| +0.0566{{cc}}
| +0.0473{{cc}}
| +0.2014{{cc}}
| +0.1289{{cc}}
| −0.1218{{cc}}
|}
|}


[[Optimal ET sequence]] ([[TE]]): [[161edo|161]], [[420edo|420]], [[581edo|581]], [[742edo|742]], [[1323edo|1323]]
[[Optimal ET sequence]] ([[TE]]): [[15edo|15]], [[411edo|411f]], [[426edo|426]], [[441edo|441]], [[1308edo|1308]], [[1749edo|1749]], [[2190edo|2190]], [[6129edo|6129]], [[8319edo|8319]], [[10509edo|10509]] &nbsp;<small>(full 13-limit: [[426edo|426]], [[882edo|882]], [[1308edo|1308]], [[2190edo|2190]], [[5688edo|5688]], [[7878edo|7878]], [[17946edo|17946bde]])</small>


Badness ([[TE_logflat_badness|Smith TE]]): 0.01260
Badness ([[TE_logflat_badness|Smith TE]]): 0.0142139


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.76654
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.4914805


<!--
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console.log(``.split(/\s+/).reduce((a,b)=>a+'{{cc}}\n| '+b)+'{{cc}}')
console.log(``.split(/\s+/).reduce((a,b)=>a+'{{cc}}\n| '+b)+'{{cc}}')
console.log(``.split(/\s+/).reduce((a,b)=>a+'{{cc}}\n| +'+b).replaceAll('+-', '−')+'{{cc}}')
console.log(``.split(/\s+/).reduce((a,b)=>a+'{{cc}}\n| +'+b).replaceAll('+-', '−')+'{{cc}}')
Line 1,036: Line 1,111:


Badness ([[TE_dirichlet_badness|Dirichlet]]):  
Badness ([[TE_dirichlet_badness|Dirichlet]]):  
-->
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