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

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VisualWikitext
fixing names
m adding remaining tuning boxes
Line 8: Line 8:
[[Mapping]]: {{mapping|3 2 2 4 1 10|0 5 9 8 17 2}}
[[Mapping]]: {{mapping|3 2 2 4 1 10|0 5 9 8 17 2}}


[[WE]] generators: ~63/50 = 399.9940, ~91/80 = 220.6882
[[Transversal_generators|Generator preimages]]: [[63/50]], [[91/80]]


[[CWE]] generators: 1\3, ~91/80 = 220.6899
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 400.3122{{cc}}, 220.5893{{cc}}
| 399.994{{cc}}, 220.6882{{cc}}
| 399.9947{{cc}}, 220.6886{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\3, 220.729{{cc}}
| 1\3, 220.6899{{cc}}
| 1\3, 220.6873{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\3, 220.4173{{cc}}
| 1\3, 220.6915{{cc}}
| 1\3, 220.6915{{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]]
| 1199.982{{cc}}
| 1903.4292{{cc}}
| 2786.1822{{cc}}
| 3365.482{{cc}}
| 4151.6942{{cc}}
| 4441.3165{{cc}}
|-
| [[Error]]
| -0.018{{cc}}
| +1.4742{{cc}}
| −0.1315{{cc}}
| −3.3439{{cc}}
| +0.3762{{cc}}
| +0.7889{{cc}}
|}


[[Optimal ET sequence]] ([[TE]]): [[27edo|27e]], [[60edo|60e]], [[87edo|87]]
[[Optimal ET sequence]] ([[TE]]): [[27edo|27e]], [[60edo|60e]], [[87edo|87]]


Badness ([[TE_logflat_badness|Smith]]): 0.02560
Badness ([[TE_logflat_badness|Smith TE]]): 0.02560


Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.05783
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.05783


== 130 & 181 ==
== 130 & 181 ==
''See also: [[User:Francium/Miscellaneous_rank-2_temperaments#311_.26_1063|7-limit]]''


[[Subgroup]]: [[2.3.5.7.13_subgroup|2.3.5.7.13]]
[[Subgroup]]: [[2.3.5.7.13_subgroup|2.3.5.7.13]]
Line 26: Line 84:
[[Mapping]]: {{mapping|1 11 -22 -7 19|0 -24 62 25 -39}}
[[Mapping]]: {{mapping|1 11 -22 -7 19|0 -24 62 25 -39}}


[[WE]] generators: ~2/1 = 1199.9727, ~21/16 = 470.7388
[[Transversal_generators|Generator preimages]]: [[2/1]], [[21/16]]


[[CWE]] generators: 2/1, ~21/16 = 470.7495
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 1199.983{{cc}}, 470.7428{{cc}}
| 1199.9727{{cc}}, 470.7388{{cc}}
| 1199.9727{{cc}}, 470.7388{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\1, 470.7495{{cc}}
| 1\1, 470.7495{{cc}}
| 1\1, 470.7493{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\1, 470.7495{{cc}}
| 1\1, 470.7495{{cc}}
| 1\1, 470.7495{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 5/1
! 7/1
! 13/1
|-
| [[Tuning_map|Tuning]]
| 1199.9727{{cc}}
| 1901.9687{{cc}}
| 2786.4055{{cc}}
| 3368.6607{{cc}}
| 4440.6683{{cc}}
|-
| [[Error]]
| −0.0273{{cc}}
| +0.0137{{cc}}
| +0.0918{{cc}}
| −0.1652{{cc}}
| +0.1407{{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]]): [[51edo|51]], [[79edo|79c]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[1453edo|1453]], [[1894edo|1894]], [[2335edo|2335]]


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.47741
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.47741
Line 44: Line 155:
[[Mapping]]: {{mapping|1 11 -22 -7 -24 19|0 -24 62 25 70 -39}}
[[Mapping]]: {{mapping|1 11 -22 -7 -24 19|0 -24 62 25 70 -39}}


TE generators: ~2/1 = 1199.939, ~21/16 = 470.722
[[Transversal_generators|Generator preimages]]: [[2/1]], [[21/16]]
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 1199.9305{{cc}}, 470.7167{{cc}}
| 1199.9386{{cc}}, 470.7221{{cc}}
| 1199.9387{{cc}}, 470.7221{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\1, 470.7411{{cc}}
| 1\1, 470.746{{cc}}
| 1\1, 470.745{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\1, 470.744{{cc}}
| 1\1, 470.7462{{cc}}
| 1\1, 470.7461{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):


CTE generators: 2/1, ~21/16 = 470.745
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 5/1
! 7/1
! 11/1
! 13/1
|-
| [[Tuning_map|Tuning]]
| 1199.9386{{cc}}
| 1901.9946{{cc}}
| 2786.1202{{cc}}
| 3368.482{{cc}}
| 4152.0197{{cc}}
| 4440.6721{{cc}}
|-
| [[Error]]
| −0.0614{{cc}}
| +0.0396{{cc}}
| −0.1936{{cc}}
| −0.3439{{cc}}
| +0.7017{{cc}}
| +0.1445{{cc}}
|}


[[Optimal ET sequence]] ([[TE]]): [[51edo|51]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[752edo|752e]], [[1193edo|1193e]]
[[Optimal ET sequence]] ([[TE]]): [[51edo|51]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[752edo|752e]], [[1193edo|1193e]]


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.89734
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.89734
Line 124: Line 291:
[[Optimal ET sequence]] ([[TE]]): [[31edo|31]], [[67edo|67]], [[98edo|98]]
[[Optimal ET sequence]] ([[TE]]): [[31edo|31]], [[67edo|67]], [[98edo|98]]


Badness ([[TE_logflat_badness|Smith]]): 0.03686
Badness ([[TE_logflat_badness|Smith TE]]): 0.03686


Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.52300
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.52300
Line 198: Line 365:
{{Optimal ET sequence|legend=1|12f, 55f, 67}}
{{Optimal ET sequence|legend=1|12f, 55f, 67}}


[[Error]]s (WE): −0.21{{c}}, −3.81{{c}}, +7.11{{c}}, −2.89{{c}}, +2.3{{c}}, −0.65{{c}}
Badness ([[TE_logflat_badness|Smith TE]]): 0.04940
 
Badness ([[TE_logflat_badness|Smith]]):


Badness ([[TE_dirichlet_badness|Dirichlet]]): 2.041
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 ===
Line 281: Line 446:
[[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|12f(ghh)ikm]], [[43edo|43deff(ggghhh)iiikkllmm]], [[55edo|55f(gh)ilm]], [[67edo|67p]], [[122edo|122(g)ilm]]


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.075 (1.35270)
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.07545 (1.35270)


== Tri[[BPS|pierce]] (b30 & b39) ==
== Tri[[BPS|pierce]] (b30 & b39) ==
Line 349: Line 514:
[[Optimal ET sequence]] ([[TE]]): [[9edt|b9]], [[21edt|b21]], [[30edt|b30]], [[39edt|b39]], [[69edt|b69]], [[108edt|b108]], [[177edt|b177d]]
[[Optimal ET sequence]] ([[TE]]): [[9edt|b9]], [[21edt|b21]], [[30edt|b30]], [[39edt|b39]], [[69edt|b69]], [[108edt|b108]], [[177edt|b177d]]


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.26872
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.26872
Line 420: Line 585:
[[Optimal ET sequence]] ([[TE]]): [[18edt|b18]], [[21edt|b21]], [[39edt|b39]], [[99edt|b99]], [[138edt|b138]], [[177edt|b177d]]
[[Optimal ET sequence]] ([[TE]]): [[18edt|b18]], [[21edt|b21]], [[39edt|b39]], [[99edt|b99]], [[138edt|b138]], [[177edt|b177d]]


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.44749
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.44749
Line 494: Line 659:
[[Optimal ET sequence]] ([[TE]]): [[51edt|b51]], [[60edt|b60]], [[69edt|b69]], [[147edt|b147]]
[[Optimal ET sequence]] ([[TE]]): [[51edt|b51]], [[60edt|b60]], [[69edt|b69]], [[147edt|b147]]


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.48415
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.48415
Line 571: Line 736:
[[Optimal ET sequence]] ([[TE]]): [[18edt|b18]], [[60edt|b60]], [[78edt|b78]], [[138edt|b138]], [[216edt|b216]]
[[Optimal ET sequence]] ([[TE]]): [[18edt|b18]], [[60edt|b60]], [[78edt|b78]], [[138edt|b138]], [[216edt|b216]]


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.95032
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.95032
Line 645: Line 810:
[[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]]): [[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]]): 0.01465 (0.01044)
Badness ([[TE_logflat_badness|Smith TE]]): 0.01465 (0.01044)


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.50663 (0.49340)
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.50663 (0.49340)
Line 722: Line 887:
[[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]]): [[140edo|140]], [[301edo|301e]], [[441edo|441]], [[581edo|581]], [[1022edo|1022]], [[1603edo|1603e]] <small>(same sequence for add-23)</small>


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.21770 (1.01017)
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.21770 (1.01017)
Line 802: Line 967:
[[Optimal ET sequence]] ([[TE]]): [[161edo|161]], [[420edo|420]], [[581edo|581]], [[742edo|742]], [[1323edo|1323]]
[[Optimal ET sequence]] ([[TE]]): [[161edo|161]], [[420edo|420]], [[581edo|581]], [[742edo|742]], [[1323edo|1323]]


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


Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.76654
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.76654
Line 868: Line 1,033:
[[Optimal ET sequence]] ([[TE]]):  
[[Optimal ET sequence]] ([[TE]]):  


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


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