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

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


Badness: 1.058 (Sintel)
Badness (Dirichlet): 1.058


== 130 & 181 ==
== 130 & 181 ==
Line 30: Line 30:
{{Optimal ET sequence|legend=1|130, 441, maybe 571, 1012, sorry idk}}
{{Optimal ET sequence|legend=1|130, 441, maybe 571, 1012, sorry idk}}


Badness: 0.477 (Sintel)
Badness (Dirichlet): 0.477


=== 13-limit ===
=== 13-limit ===
Line 46: Line 46:
{{Optimal ET sequence|legend=1|130, 311, 441, idk}}
{{Optimal ET sequence|legend=1|130, 311, 441, idk}}


Badness: 0.897 (Sintel)
Badness (Dirichlet): 0.897
 
== Badtone (31 & 67) ==
 
Subgroup: 2.3.5.7.11.13
 
Comma list: [[81/80]], [[144/143]], [[176/175]], [[196/195]]
 
Mapping: [{{val|1 1 0 3 -1 7}}, {{val|0 3 12 -1 23 -17}}]
 
{{Optimal ET sequence|legend=1|31, 67, 98}}
 
Errors (WE): -0.065{{cent}}, -4.138{{cent}}, 5.216{{cent}}, -1.649{{cent}}, -0.821{{cent}}, 4.348{{cent}}
 
Badness (Dirichlet): 1.523


== Worsetone (12f & 67) ==
== Worsetone (12f & 67) ==
Line 89: Line 103:
Errors (WE): −0.21{{cent}}, −3.81{{cent}}, +7.11{{cent}}, −2.89{{cent}}, +2.3{{cent}}, −0.65{{cent}}
Errors (WE): −0.21{{cent}}, −3.81{{cent}}, +7.11{{cent}}, −2.89{{cent}}, +2.3{{cent}}, −0.65{{cent}}


Badness: 2.041 (Sintel)
Badness (Dirichlet): 2.041
 
=== 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]])
 
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}}]
 
Generator tunings (no-17 no-19):
 
: {| class="wikitable right-1"
|-
!
! [[Minimax-lils-S|Weil]]
! [[TOP|Tenney]]
! [[WE]]
! [[TE]]
|-
| [[Optimization|Optimized]]
|
|
| 1200.984, 698.956
| 1200.9879, 698.9583
|-
| [[Constrained_tuning|Constrained]]
|
|
| 1\1, 698.420
| 1\1, 698.496
|-
| [[POTE|Destretched]]
|
|
| 1\1, 698.3833
| 1\1, 698.3833
|}
 
{{Optimal ET sequence|legend=1|12f, 55f, 67, 122(g)ilm}} <!-- 311bddf(gg)ikllmm is not a GPV -->
 
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}}
 
Badness (Dirichlet): 1.075 (1.353)

Revision as of 18:54, 17 November 2024

27e & 87

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨3 2 2 4 1 10], ⟨0 5 9 8 17 2]]

TE generators: ~63/50 = 399.995, ~91/80 = 220.689

CTE generators: 1\3, ~91/80 = 220.687

Optimal ET sequence: 27e, 60e, 87 (idk how to calculate this)

Badness (Dirichlet): 1.058

130 & 181

Subgroup: 2.3.5.7.13

Comma list: 2401/2400, 4096/4095, 492128/492075

Mapping: [⟨1 11 -22 -7 19], ⟨0 -24 62 25 -39]]

TE generators: ~2/1 = 1199.973, ~21/16 = 470.739

CTE generators: 2/1, ~21/16 = 470.749

Optimal ET sequence: 130, 441, maybe 571, 1012, sorry idk

Badness (Dirichlet): 0.477

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 11 -22 -7 -24 19], ⟨0 -24 62 25 70 -39]]

TE generators: ~2/1 = 1199.939, ~21/16 = 470.722

CTE generators: 2/1, ~21/16 = 470.745

Optimal ET sequence: 130, 311, 441, idk

Badness (Dirichlet): 0.897

Badtone (31 & 67)

Subgroup: 2.3.5.7.11.13

Comma list: 81/80, 144/143, 176/175, 196/195

Mapping: [⟨1 1 0 3 -1 7], ⟨0 3 12 -1 23 -17]]

Optimal ET sequence: 31, 67, 98

Errors (WE): -0.065 ¢, -4.138 ¢, 5.216 ¢, -1.649 ¢, -0.821 ¢, 4.348 ¢

Badness (Dirichlet): 1.523

Worsetone (12f & 67)

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 1 0 -10 -14 -19], ⟨0 1 4 22 30 39]]

Generator tunings:

Weil Tenney WE TE
Optimized 1199.788, 698.355 1199.8021, 698.3632
Constrained 1\1, 698.471 1\1, 698.455
Destretched 1\1, 698.4784 1\1, 698.4784

Optimal ET sequence: 12f, 55f, 67

Errors (WE): −0.21 ¢, −3.81 ¢, +7.11 ¢, −2.89 ¢, +2.3 ¢, −0.65 ¢

Badness (Dirichlet): 2.041

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)

Mapping: [⟨1 1 0 -10 -14 -19 (-32 -33) -24 -16 -14 -22], ⟨0 1 4 22 30 39 (62 64) 49 36 33 47]]

Generator tunings (no-17 no-19):

Weil Tenney WE TE
Optimized 1200.984, 698.956 1200.9879, 698.9583
Constrained 1\1, 698.420 1\1, 698.496
Destretched 1\1, 698.3833 1\1, 698.3833

Optimal ET sequence: 12f, 55f, 67, 122(g)ilm

Errors (WE): 0.984 ¢, -2.015 ¢, -1.635 ¢, 3.585 ¢, 0.059 ¢, (-1.174 ¢, 3.197 ¢), -3.048 ¢, 1.635 ¢, 0.427 ¢, 0.220 ¢

Badness (Dirichlet): 1.075 (1.353)

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