Mint temperaments: Difference between revisions

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m →13-limit: Fix a typo (period to comma)
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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 14: Line 14:
[[POTE generator]]: ~15/14 = 140.927
[[POTE generator]]: ~15/14 = 140.927


{{Val list|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}


[[Badness]]: 0.048356
[[Badness]]: 0.048356
Line 27: Line 27:
POTE generators: ~12/11 = 140.747
POTE generators: ~12/11 = 140.747


Optimal GPV sequence: {{Val list| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}


Badness: 0.026050
Badness: 0.026050
Line 40: Line 40:
POTE generators: ~13/12 = 140.751
POTE generators: ~13/12 = 140.751


Optimal GPV sequence: {{Val list| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}


Badness: 0.018158
Badness: 0.018158
Line 53: Line 53:
POTE generators: ~13/12 = 141.404
POTE generators: ~13/12 = 141.404


Optimal GPV sequence: {{Val list| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=1| 8d, 9, 17cg }}


Badness: 0.016743
Badness: 0.016743
Line 66: Line 66:
POTE generators: ~13/12 = 140.479
POTE generators: ~13/12 = 140.479


Optimal GPV sequence: {{Val list| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=1| 8d, 9, 17cg }}


Badness: 0.016841
Badness: 0.016841
Line 83: Line 83:
[[POTE generator]]: ~21/20 = 99.483
[[POTE generator]]: ~21/20 = 99.483


{{Val list|legend=1| 12 }}
{{Optimal ET sequence|legend=1| 12 }}


[[Badness]]: 0.059735
[[Badness]]: 0.059735
Line 96: Line 96:
POTE generator: ~21/20 = 99.385
POTE generator: ~21/20 = 99.385


Optimal GPV sequence: {{Val list| 12 }}
{{Optimal ET sequence|legend=1| 12 }}


Badness: 0.038811
Badness: 0.038811
Line 109: Line 109:
POTE generator: ~21/20 = 98.572
POTE generator: ~21/20 = 98.572


Optimal GPV sequence: {{Val list| 12f }}
{{Optimal ET sequence|legend=1| 12f }}


Badness: 0.031639
Badness: 0.031639
Line 126: Line 126:
[[POTE generator]]: ~5/4 = 422.275
[[POTE generator]]: ~5/4 = 422.275


{{Val list|legend=1| 3d, 11d, 14, 17c, 37ccdd }}
{{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, 37ccdd }}


[[Badness]]: 0.077871
[[Badness]]: 0.077871
Line 139: Line 139:
POTE generator: ~5/4 = 422.217
POTE generator: ~5/4 = 422.217


Optimal GPV sequence: {{Val list| 3de, 14, 17c, 37ccddee }}
{{Optimal ET sequence|legend=1| 3de, 14, 17c, 37ccddee }}


Badness: 0.042518
Badness: 0.042518
Line 152: Line 152:
POTE generator: ~5/4 = 423.020
POTE generator: ~5/4 = 423.020


Optimal GPV sequence: {{Val list| 3de, 14, 17c }}
{{Optimal ET sequence|legend=1| 3de, 14, 17c }}


Badness: 0.036836
Badness: 0.036836
Line 169: Line 169:
[[POTE generator]]: ~6/5 = 284.219
[[POTE generator]]: ~6/5 = 284.219


{{Val list|legend=1| 4, 17c, 21, 38c }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}


[[Badness]]: 0.061101
[[Badness]]: 0.061101
Line 182: Line 182:
POTE generator: ~6/5 = 283.253
POTE generator: ~6/5 = 283.253


Optimal GPV sequence: {{Val list| 17c, 55ccd }}
{{Optimal ET sequence|legend=1| 17c, 55ccd }}


Badness: 0.044651
Badness: 0.044651
Line 197: Line 197:
POTE generator: ~6/5 = 282.856
POTE generator: ~6/5 = 282.856


Optimal GPV sequence: {{Val list| 17c }}
{{Optimal ET sequence|legend=1| 17c }}


Badness: 0.032324
Badness: 0.032324
Line 210: Line 210:
POTE generator: ~6/5 = 283.822
POTE generator: ~6/5 = 283.822


Optimal GPV sequence: {{Val list| 4, 17c, 21, 38ce, 55ccde }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38ce, 55ccde }}


Badness: 0.047247
Badness: 0.047247
Line 223: Line 223:
POTE generator: ~6/5 = 283.882
POTE generator: ~6/5 = 283.882


Optimal GPV sequence: {{Val list| 4, 17c, 21, 38ce, 55ccde }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38ce, 55ccde }}


Badness: 0.036701
Badness: 0.036701
Line 240: Line 240:
[[POTE generator]]: ~21/20 = 72.303
[[POTE generator]]: ~21/20 = 72.303


{{Val list|legend=1| 16, 17c, 33, 50cd, 83bccd }}
{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}


[[Badness]]: 0.114869
[[Badness]]: 0.114869
Line 253: Line 253:
POTE generator: ~21/20 = 72.297
POTE generator: ~21/20 = 72.297


Optimal GPV sequence: {{Val list| 16, 17c, 33, 50cd, 83bccd }}
{{Optimal ET sequence|legend=1| 16, 17c, 33, 50cd, 83bccd }}


Badness: 0.050514
Badness: 0.050514
Line 266: Line 266:
POTE generator: ~21/20 = 72.409
POTE generator: ~21/20 = 72.409


Optimal GPV sequence: {{Val list| 16, 17c, 33, 83bccd }}
{{Optimal ET sequence|legend=1| 16, 17c, 33, 83bccd }}


Badness: 0.033102
Badness: 0.033102
Line 283: Line 283:
[[POTE generator]]: ~6/5 = 239.977
[[POTE generator]]: ~6/5 = 239.977


{{Val list|legend=1| 1bd, 5 }}
{{Optimal ET sequence|legend=1| 1bd, 5 }}


[[Badness]]: 0.046882
[[Badness]]: 0.046882

Revision as of 16:12, 7 May 2023

These are low complexity, high error temperaments tempering out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.

Progression

For the 5-limit version of this temperament, see High badness temperaments #Lafayette.

Subgroup: 2.3.5.7

Comma list: 36/35, 392/375

Mapping: [⟨1 1 2 2], ⟨0 5 3 7]]

Wedgie: ⟨⟨ 5 3 7 -7 -3 8 ]]

POTE generator: ~15/14 = 140.927

Optimal ET sequence: 8d, 9, 17c

Badness: 0.048356

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 77/75

Mapping: [⟨1 1 2 2 3], ⟨0 5 3 7 4]]

POTE generators: ~12/11 = 140.747

Optimal ET sequence: 8d, 9, 17c

Badness: 0.026050

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 56/55, 66/65

Mapping: [⟨1 1 2 2 3 3], ⟨0 5 3 7 4 6]]

POTE generators: ~13/12 = 140.751

Optimal ET sequence: 8d, 9, 17c

Badness: 0.018158

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 26/25, 36/35, 51/50, 56/55, 66/65

Mapping: [⟨1 1 2 2 3 3 4], ⟨0 5 3 7 4 6 1]]

POTE generators: ~13/12 = 141.404

Optimal ET sequence: 8d, 9, 17cg

Badness: 0.016743

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65

Mapping: [⟨1 1 2 2 3 3 4 4], ⟨0 5 3 7 4 6 1 2]]

POTE generators: ~13/12 = 140.479

Optimal ET sequence: 8d, 9, 17cg

Badness: 0.016841

Ripple

See also: Ripple family § Ripple

Subgroup: 2.3.5.7

Comma list: 36/35, 2560/2401

Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]

Wedgie: ⟨⟨ 5 8 2 1 -11 -18 ]]

POTE generator: ~21/20 = 99.483

Optimal ET sequence: 12

Badness: 0.059735

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 80/77, 126/121

Mapping: [⟨1 2 3 3 4], ⟨0 -5 -8 -2 -6]]

POTE generator: ~21/20 = 99.385

Optimal ET sequence: 12

Badness: 0.038811

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 40/39, 66/65, 147/143

Mapping: [⟨1 2 3 3 4 4], ⟨0 -5 -8 -2 -6 -3]]

POTE generator: ~21/20 = 98.572

Optimal ET sequence: 12f

Badness: 0.031639

Smate

See also: Smate family § Smate

Subgroup: 2.3.5.7

Comma list: 36/35, 2048/1875

Mapping: [⟨1 3 2 6], ⟨0 -4 1 -9]]

Wedgie: ⟨⟨ 4 -1 9 -11 3 24 ]]

POTE generator: ~5/4 = 422.275

Optimal ET sequence: 3d, 11d, 14, 17c, 37ccdd

Badness: 0.077871

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 243/242

Mapping: [⟨1 3 2 6 7], ⟨0 -4 1 -9 -10]]

POTE generator: ~5/4 = 422.217

Optimal ET sequence: 3de, 14, 17c, 37ccddee

Badness: 0.042518

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 56/55, 243/242

Mapping: [⟨1 3 2 6 7 3], ⟨0 -4 1 -9 -10 2]]

POTE generator: ~5/4 = 423.020

Optimal ET sequence: 3de, 14, 17c

Badness: 0.036836

Subklei

For the 5-limit version of this temperament, see High badness temperaments #Delorean.

Subgroup: 2.3.5.7

Comma list: 36/35, 1029/1000

Mapping: [⟨1 3 4 4], ⟨0 -6 -7 -5]]

Wedgie: ⟨⟨ 6 7 5 -3 -9 -8 ]]

POTE generator: ~6/5 = 284.219

Optimal ET sequence: 4, 17c, 21, 38c

Badness: 0.061101

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 77/75, 352/343

Mapping: [⟨1 3 4 4 7], ⟨0 -6 -7 -5 -15]]

POTE generator: ~6/5 = 283.253

Optimal ET sequence: 17c, 55ccd

Badness: 0.044651

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 66/65, 352/343

POTE generator: ~6/5 = 282.856

Mapping: [⟨1 3 4 4 7 7], ⟨0 -6 -7 -5 -15 -14]]

POTE generator: ~6/5 = 282.856

Optimal ET sequence: 17c

Badness: 0.032324

Subkla

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 1029/1000

Mapping: [⟨1 3 4 4 3], ⟨0 -6 -7 -5 2]]

POTE generator: ~6/5 = 283.822

Optimal ET sequence: 4, 17c, 21, 38ce, 55ccde

Badness: 0.047247

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 56/55, 66/65, 640/637

Mapping: [⟨1 3 4 4 3 3], ⟨0 -6 -7 -5 2 3]]

POTE generator: ~6/5 = 283.882

Optimal ET sequence: 4, 17c, 21, 38ce, 55ccde

Badness: 0.036701

Slurpee

For the 5-limit version of this temperament, see High badness temperaments #Slurpee.

Subgroup: 2.3.5.7

Comma list: 36/35, 51200/50421

Mapping: [⟨1 2 3 3], ⟨0 -7 -11 -3]]

Wedgie: ⟨⟨ 7 11 3 1 -15 -24 ]]

POTE generator: ~21/20 = 72.303

Optimal ET sequence: 16, 17c, 33, 50cd, 83bccd

Badness: 0.114869

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 121/120, 352/343

Mapping: [⟨1 2 3 3 4], ⟨0 -7 -11 -3 -9]]

POTE generator: ~21/20 = 72.297

Optimal ET sequence: 16, 17c, 33, 50cd, 83bccd

Badness: 0.050514

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 66/65, 143/140, 352/343

Mapping: [⟨1 2 3 3 4 4], ⟨0 -7 -11 -3 -9 -5]]

POTE generator: ~21/20 = 72.409

Optimal ET sequence: 16, 17c, 33, 83bccd

Badness: 0.033102

Penta

See also: Gamelismic clan § Gidorah

Subgroup: 2.3.5.7

Comma list: 28/25, 36/35

Mapping: [⟨1 1 2 2], ⟨0 3 2 4]]

Wedgie: ⟨⟨ 3 2 4 -4 -2 4 ]]

POTE generator: ~6/5 = 239.977

Optimal ET sequence: 1bd, 5

Badness: 0.046882

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