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

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== 27e & 87 ==
== 27e & 87 ==


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


Comma list: [[196/195]], [[325/324]], [[441/440]], [[1001/1000]]
[[Comma list]]: [[196/195]], [[325/324]], [[441/440]], [[1001/1000]]


Mapping: [{{val|3 2 2 4 1 10}}, {{val|0 5 9 8 17 2}}]
[[Mapping]]: {{mapping|3 2 2 4 1 10|0 5 9 8 17 2}}


TE generators: ~63/50 = 399.995, ~91/80 = 220.689
[[WE]] generators: ~63/50 = 399.9940, ~91/80 = 220.6882


CTE generators: 1\3, ~91/80 = 220.687
[[CWE]] generators: 1\3, ~91/80 = 220.6899


{{Optimal ET sequence|legend=1|27e, 60e, 87}} (idk how to calculate this)
[[Optimal ET sequence]] ([[TE]]): [[27edo|27e]], [[60edo|60e]], [[87edo|87]]


Badness (Dirichlet): 1.058
Badness ([[TE_logflat_badness|Smith]]): 0.02560
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.05783


== 130 & 181 ==
== 130 & 181 ==


Subgroup: 2.3.5.7.13
[[Subgroup]]: [[2.3.5.7.13_subgroup|2.3.5.7.13]]
 
[[Comma list]]: [[2401/2400]], [[4096/4095]], [[492128/492075]]


Comma list: [[2401/2400]], [[4096/4095]], 492128/492075
[[Mapping]]: {{mapping|1 11 -22 -7 19|0 -24 62 25 -39}}


Mapping: [{{val|1 11 -22 -7 19}}, {{val|0 -24 62 25 -39}}]
[[WE]] generators: ~2/1 = 1199.9727, ~21/16 = 470.7388


TE generators: ~2/1 = 1199.973, ~21/16 = 470.739
[[CWE]] generators: 2/1, ~21/16 = 470.7495


CTE generators: 2/1, ~21/16 = 470.749
[[Optimal ET sequence]] ([[TE]]): [[51edo|51]], [[79edo|79c]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[1453edo|1453]], [[1894edo|1894]], [[2335edo|2335]]


{{Optimal ET sequence|legend=1|130, 441, maybe 571, 1012, sorry idk}}
Badness ([[TE_logflat_badness|Smith]]): 0.01381


Badness (Dirichlet): 0.477
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.47741


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


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


Comma list: [[1575/1573]], [[2080/2079]], [[4096/4095]], [[4459/4455]]
[[Comma list]]: [[1575/1573]], [[2080/2079]], [[4096/4095]], [[4459/4455]]


Mapping: [{{val|1 11 -22 -7 -24 19}}, {{val|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
TE generators: ~2/1 = 1199.939, ~21/16 = 470.722
Line 44: Line 48:
CTE generators: 2/1, ~21/16 = 470.745
CTE generators: 2/1, ~21/16 = 470.745


{{Optimal ET sequence|legend=1|130, 311, 441, idk}}
[[Optimal ET sequence]] ([[TE]]): [[51edo|51]], [[130edo|130]], [[311edo|311]], [[441edo|441]], [[752edo|752e]], [[1193edo|1193e]]
 
Badness ([[TE_logflat_badness|Smith]]): 0.02172


Badness (Dirichlet): 0.897
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.89734


== Badtone (31 & 67) ==
== Badtone (31 & 67) ==


Subgroup: 2.3.5.7.11.13
[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]
 
[[Comma list]]: [[81/80]], [[144/143]], [[176/175]], [[196/195]]


Comma list: [[81/80]], [[144/143]], [[176/175]], [[196/195]]
[[Mapping]]: {{mapping|1 1 0 3 -1 7|0 3 12 -1 23 -17}}


Mapping: [{{val|1 1 0 3 -1 7}}, {{val|0 3 12 -1 23 -17}}]
[[Transversal_generators|Generator preimages]]: [[2/1]], [[8/7]]


Generator tunings:
[[Optimization|Generator tunings]]:


: {| class="wikitable right-1"
: {| class="wikitable right-1"
Line 67: Line 75:
|-
|-
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
|
| ???
|
| 1200.4954{{cc}}, 232.6290{{cc}}
| 1199.935, 232.627
| 1199.9347{{cc}}, 232.6275{{cc}}
| 1199.9460, 232.6297
| 1199.9460{{cc}}, 232.6297{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
|
| ???
|
| 1\1, 232.6732{{cc}}
| 1\1, 232.639
| 1\1, 232.6392{{cc}}
| 1\1, 232.635
| 1\1, 232.6352{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
|
| ???
|
| 1\1, 232.5330{{cc}}
| 1\1, 232.6396
| 1\1, 232.6402{{cc}}
| 1\1, 232.6401
| 1\1, 232.6401{{cc}} <!-- x31eq rounds this to 232.6401 -->
|}
|}


{{Optimal ET sequence|legend=1|31, 67, 98}}
[[Prime_interval|Prime harmonics]] ([[WE]]):


Errors (WE): -0.065{{cent}}, -4.138{{cent}}, 5.216{{cent}}, -1.649{{cent}}, -0.821{{cent}}, 4.348{{cent}}
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 5/1
! 7/1
! 11/1
! 13/1
|-
| [[Tuning_map|Tuning]]
| 1199.9347{{cc}}
| 1897.817{{cc}}
| 2791.5295{{cc}}
| 3367.1765{{cc}}
| 4150.4968{{cc}}
| 4444.8759{{cc}}
|-
| [[Error]]
| −0.0653{{cc}}
| −4.138{{cc}}
| +5.2157{{cc}}
| −1.6494{{cc}}
| −0.8211{{cc}}
| +4.3483{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[31edo|31]], [[67edo|67]], [[98edo|98]]
 
Badness ([[TE_logflat_badness|Smith]]): 0.03686


Badness (Dirichlet): 1.523
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.52300


== Worsetone (12f & 67) ==
== Worsetone (12f & 67) ==


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


Comma list: [[81/80]], [[176/175]], [[196/195]], [[364/363]]
[[Comma list]]: [[81/80]], [[176/175]], [[196/195]], [[364/363]]


Mapping: [{{val|1 1 0 -10 -14 -19}}, {{val|0 1 4 22 30 39}}]
[[Mapping]]: {{mapping|1 0 -4 -32 -44 -58|0 1 4 22 30 39}}


Generator tunings:
[[Transversal_generators|Generator preimages]]: [[2/1]], [[3/1]]
 
[[Optimization|Generator tunings]]:


: {| class="wikitable right-1"
: {| class="wikitable right-1"
Line 110: Line 149:
|-
|-
| [[Optimized]]
| [[Optimized]]
|
| ???
|
| 1199.6846{{cc}}, 1897.7889{{cc}}
| 1199.788, 698.355
| 1199.7882{{cc}}, 1898.1434{{cc}}
| 1199.8021, 698.3632
| 1199.8021{{cc}}, 1898.1654{{cc}}
|-
|-
| [[Constrained]]
| [[Constrained]]
|
| ???
|
| 1\1, 1898.2217{{cc}}
| 1\1, 698.471
| 1\1, 698.4715{{cc}}
| 1\1, 698.455
| 1\1, 698.4553{{cc}}
|-
|-
| [[Destretched]]
| [[Destretched]]
|
| ???
|
| 1\1, 1898.2878{{cc}}
| 1\1, 698.4784
| 1\1, 1898.4785{{cc}}
| 1\1, 698.4784
| 1\1, 1898.4785{{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]]
| 1199.7882{{cc}}
| 1898.1434{{cc}}
| 2793.4206{{cc}}
| 3365.9316{{cc}}
| 4153.6201{{cc}}
| 4439.8756{{cc}}
|-
| [[Error]]
| −0.2118{{cc}}
| −3.8116{{cc}}
| +7.1069{{cc}}
| −2.8943{{cc}}
| +2.3022{{cc}}
| −0.6521{{cc}}
|}
|}


{{Optimal ET sequence|legend=1|12f, 55f, 67}}
{{Optimal ET sequence|legend=1|12f, 55f, 67}}


Errors (WE): −0.21{{cent}}, −3.81{{cent}}, +7.11{{cent}}, −2.89{{cent}}, +2.3{{cent}}, −0.65{{cent}}
[[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]]):


Badness (Dirichlet): 2.041
Badness ([[TE_dirichlet_badness|Dirichlet]]): 2.041


=== 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]], [[273/272]])
 
[[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 1 0 -10 -14 -19 (-32 -33) -24 -16 -14 -22}}, {{val|0 1 4 22 30 39 (62 64) 49 36 33 47}}]
[[Transversal_generators|Generator preimages]]: [[2/1]], [[3/1]]


Generator tunings (no-17 no-19):
[[Optimization|Generator tunings]] ([[2.3.7.11.13.23.31.37.41_subgroup|no-17 no-19]]):


: {| class="wikitable right-1"
: {| class="wikitable right-1"
Line 151: Line 223:
|-
|-
| [[Optimization|Optimized]]
| [[Optimization|Optimized]]
|
| ???
|
| 1201.1304{{cc}}, 1900.1656{{cc}}
| 1200.984, 698.956
| 1200.9840{{cc}}, 1899.9400{{cc}}
| 1200.9879, 698.9583
| 1200.9879{{cc}}, 1899.9461{{cc}}
|-
|-
| [[Constrained_tuning|Constrained]]
| [[Constrained_tuning|Constrained]]
|
| ???
|
| 1\1, 1898.6199{{cc}}
| 1\1, 698.420
| 1\1, 1898.4197{{cc}}
| 1\1, 698.496
| 1\1, 1898.4955{{cc}}
|-
|-
| [[POTE|Destretched]]
| [[POTE|Destretched]]
|
| ???
|
| 1\1, 1898.3773{{cc}}
| 1\1, 698.3833
| 1\1, 1898.3833{{cc}}
| 1\1, 698.3833
| 1\1, 1898.3833{{cc}}
|}
|}


[[Optimal ET sequence]]: [[43edo|43deff(ggghhh)iiikkllmm]], [[55edo|55f(gh)ilm]], [[67edo|67p]], [[122edo|122(g)ilm]] <!-- 311bddf(gg)ikllmm is not a GPV -->
[[Prime_interval|Prime harmonics]] ([[WE]]):


Errors (WE): 0.984{{cent}}, -2.015{{cent}}, -1.635{{cent}}, 3.585{{cent}}, 0.059{{cent}}, (-1.174{{cent}}, 3.197{{cent}}), -3.048{{cent}}, 1.635{{cent}}, 0.427{{cent}}, 0.220{{cent}}
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 7/1
! 11/1
! 13/1
! 23/1
! 31/1
! 37/1
! 41/1
|-
| [[Tuning_map|Tuning]]
| 1200.984{{cc}}
| 1899.940{{cc}}
| 3367.1912{{cc}}
| 4154.903{{cc}}
| 4440.5866{{cc}}
| 5425.2263{{cc}}
| 5946.6708{{cc}}
| 6251.7709{{cc}}
| 6429.2824{{cc}}
|-
| [[Error]]
| +0.984{{cc}}
| −2.015{{cc}}
| −1.6347{{cc}}
| +3.585{{cc}}
| +0.059{{cc}}
| −3.0481{{cc}}
| +1.6352{{cc}}
| +0.4269{{cc}}
| +0.220{{cc}}
|}


Badness (Dirichlet): 1.075 (1.353)
[[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_dirichlet_badness|Dirichlet]]): 1.075 (1.35270)


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


Subgroup: 3.5.7.13
[[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}}
|}


Comma list: [[245/243]], [[2197/2187]]
[[Optimal ET sequence]] ([[TE]]): [[9edt|b9]], [[21edt|b21]], [[30edt|b30]], [[39edt|b39]], [[69edt|b69]], [[108edt|b108]], [[177edt|b177d]]


Badness (Dirichlet): 0.269
Badness ([[TE_logflat_badness|Smith]]): 0.00287
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.26872


=== Hemitri[[BPS|pierce]] (b39 & b60) ===
=== Hemitri[[BPS|pierce]] (b39 & b60) ===


Subgroup: 3.5.7.11.13
[[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]]


Comma list: [[245/243]], [[847/845]], [[1575/1573]]
Badness ([[TE_logflat_badness|Smith]]): 0.00566


Badness (Dirichlet): 0.447
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.44749


=== Tri[[dubhe]] / Semitri[[BPS|pierce]] (b69 & b78) ===
=== Tri[[dubhe]] / Semitri[[BPS|pierce]] (b69 & b78) ===


Subgroup: 3.5.7.13.17.19
[[Subgroup]]: [[3.5.7.13.17.19_subgroup|3.5.7.13.17.19]]
 
[[Comma list]]: [[245/243]], [[325/323]], [[665/663]], [[3213/3211]]
 
[[Mapping]]: {{mapping|3 3 6 7 6 7|0 4 -2 0 5 3}}
 
[[Transversal_generators|Generator preimages]]: [[13/9]], [[17/15]]
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 634.4242{{cc}}, 220.2042{{cc}}
| 634.3781{{cc}}, 220.1438{{cc}}
| 634.3798{{cc}}, 220.1444{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\b3, 220.0518{{cc}}
| 1\b3, 220.0811{{cc}}
| 1\b3, 220.4087{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\b3, 220.0518{{cc}}
| 1\b3, 220.0074{{cc}}
| 1\b3, 220.0074{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 3/1
! 5/1
! 7/1
! 13/1
! 17/1
! 19/1
|-
| [[Tuning_map|Tuning]]
| 1903.1344{{cc}}
| 2783.7095{{cc}}
| 3365.9811{{cc}}
| 4440.6468{{cc}}
| 4906.9877{{cc}}
| 5101.0782{{cc}}
|-
| [[Error]]
| +1.1794{{cc}}
| −2.6042{{cc}}
| −2.8448{{cc}}
| +0.1192{{cc}}
| +2.0323{{cc}}
| +3.5652{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[51edt|b51]], [[60edt|b60]], [[69edt|b69]], [[147edt|b147]]


Comma list: [[245/243]], [[325/323]], [[665/663]], [[3213/3211]]
Badness ([[TE_logflat_badness|Smith]]): 0.00523


Badness (Dirichlet): 0.484
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.48415


=== Hemitri[[dubhe]] / Hemisemitri[[BPS|pierce]] (b60 & b78) ===
=== Hemitri[[dubhe]] / Hemisemitri[[BPS|pierce]] (b60 & b78) ===


Subgroup: 3.5.7.11.13.17.19
[[Subgroup]]: [[3.5.7.11.13.17.19_subgroup|3.5.7.11.13.17.19]]
 
[[Comma list]]: [[245/243]], [[325/323]], [[665/663]], [[847/845]], [[1575/1573]]
 
[[Mapping]]: {{mapping|6 2 14 8 14 7 11|0 4 -2 3 0 5 3}}
 
[[Transversal_generators|Generator preimages]]: [[119/99]], [[15/11]]
 
[[Optimization|Generator tunings]]:
 
: {| 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]]):


Comma list: [[245/243]], [[325/323]], [[665/663]], [[847/845]], [[1575/1573]]
: {| 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 (Dirichlet): 0.950
Badness ([[TE_logflat_badness|Smith]]): 0.01046
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.95032


== 140 & 441 ==
== 140 & 441 ==


Subgroup: 2.3.5.7.13.23
[[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]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 171.4255{{cc}}, 231.2847{{cc}}
| 171.4244{{cc}}, 231.2902{{cc}}
| 171.4244{{cc}}, 231.2902{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\7, 231.2969{{cc}}
| 1\7, 231.2963{{cc}}
| 1\7, 231.2991{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\7, 231.2888{{cc}}
| 1\7, 231.2943{{cc}}
| 1\7, 231.2943{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 5/1
! 7/1
! 13/1
! 23/1
|-
| [[Tuning_map|Tuning]]
| 1199.971{{cc}}
| 1902.0144{{cc}}
| 2786.3108{{cc}}
| 3368.6227{{cc}}
| 4440.6893{{cc}}
| 5428.3714{{cc}}
|-
| [[Error]]
| −0.029{{cc}}
| +0.0594{{cc}}
| −0.0029{{cc}}
| −0.2032{{cc}}
| +0.1616{{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>


Comma list: [[2401/2400]], [[4096/4095]], [[35000/34983]], [[140625/140608]]
Badness ([[TE_logflat_badness|Smith]]): 0.01465 (0.01044)


Badness (Dirichlet): 0.493
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.50663 (0.49340)


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


Subgroup: 2.3.5.7.11.13.23
[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]([[2.3.5.7.11.13.23_subgroup|.23]])
 
[[Comma list]]: [[1288/1287]], [[2080/2079]], [[2401/2400]], [[4096/4095]], [[35000/34983]]
 
[[Mapping]]: {{mapping|7 3 23 21 62 34 (60)|0 6 -5 -1 -28 -6 (-21)}}
 
[[Transversal_generators|Generator preimages]]: [[875/792]], [[8/7]]
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 171.4227, 231.3059{{cc}}
| 171.4242, 231.3085{{cc}}
| 171.4242, 231.3085{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\7, 231.3138{{cc}}
| 1\7, 231.3149{{cc}}
| 1\7, 231.3180{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\7, 231.3138{{cc}}
| 1\7, 231.3144{{cc}}
| 1\7, 231.3144{{cc}}
|}
 
[[Prime_interval|Prime harmonics]] ([[WE]]):
 
: {| class="wikitable right-1"
|-
! Prime
! 2/1
! 3/1
! 5/1
! 7/1
! 11/1
! 13/1
! 23/1
|-
| [[Tuning_map|Tuning]]
| 1199.9697{{cc}}
| 1902.1239{{cc}}
| 2786.2149{{cc}}
| 3368.6006{{cc}}
| 4151.6642{{cc}}
| 4440.5731{{cc}}
| 5427.9754{{cc}}
|-
| [[Error]]
| −0.0303{{cc}}
| +0.1689{{cc}}
| −0.0988{{cc}}
| −0.2253{{cc}}
| +0.3463{{cc}}
| +0.0454{{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>


Comma list: [[1288/1287]], [[2080/2079]], [[2401/2400]], [[4096/4095]], [[35000/34983]]
Badness ([[TE_logflat_badness|Smith]]): 0.02947 (0.01904)


Badness (Dirichlet): 1.010
Badness ([[TE_dirichlet_badness|Dirichlet]]): 1.21770 (1.01017)


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


Subgroup: 2.3.5.7.11.13.17.19
[[Subgroup]]: [[19-limit|2.3.5.7.11.13.17.19]]
 
[[Comma list]]: [[2401/2400]], [[3136/3135]], [[4096/4095]], [[5985/5984]], [[12376/12375]], [[14875/14872]]
 
[[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]]: [[85/77]], [[143/140]]
 
[[Optimization|Generator tunings]] (add-23):
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| 171.4266{{cc}}, 37.1864{{cc}}
| 171.4244{{cc}}, 37.1884{{cc}}
| 171.4244{{cc}}, 37.1884{{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\7, 37.1867{{cc}}
| 1\7, 37.1893{{cc}}
| 1\7, 37.1893{{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\7, 37.1868{{cc}}
| 1\7, 37.1893{{cc}}
| 1\7, 37.1893{{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]] ({{cent}})
| 1199.97{{cc}}
| 1901.97{{cc}}
| 2786.34{{cc}}
| 3368.63{{cc}}
| 4151.37{{cc}}
| 4440.73{{cc}}
| 4905.08{{cc}}
| 5097.39{{cc}}
|-
| [[Error]]
| −0.0291{{cc}}
| +0.0195{{cc}}
| +0.0302{{cc}}
| −0.1966{{cc}}
| +0.0566{{cc}}
| +0.2014{{cc}}
| +0.1289{{cc}}
| −0.1218{{cc}}
|}
 
[[Optimal ET sequence]] ([[TE]]): [[161edo|161]], [[420edo|420]], [[581edo|581]], [[742edo|742]], [[1323edo|1323]]
 
Badness ([[TE_logflat_badness|Smith]]): 0.01260
 
Badness ([[TE_dirichlet_badness|Dirichlet]]): 0.76654
 
<!--
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}}')
 
[[Subgroup]]: [[13-limit|2.3.5.7.11.13]]
 
[[Comma list]]:
 
[[Mapping]]: {{mapping|}}
 
[[Transversal_generators|Generator preimages]]:
 
[[Optimization|Generator tunings]]:
 
: {| class="wikitable right-1"
|-
! Norm
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
| ???
| {{cc}}, {{cc}}
| {{cc}}, {{cc}}
| {{cc}}, {{cc}}
|-
| [[Constrained_tuning|Constrained]]
| ???
| 1\, {{cc}}
| 1\, {{cc}}
| 1\, {{cc}}
|-
| [[POTE|Destretched]]
| ???
| 1\, {{cc}}
| 1\, {{cc}}
| 1\, {{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]]
|
|-
| [[Error]]
|
|}
 
[[Optimal ET sequence]] ([[TE]]):


Comma list: [[2401/2400]], [[3136/3135]], [[4096/4095]], [[5985/5984]], [[12376/12375]], [[14875/14872]]
Badness ([[TE_logflat_badness|Smith]]):


Badness (Dirichlet): 0.767
Badness ([[TE_dirichlet_badness|Dirichlet]]):  
-->
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