Keemic temperaments: Difference between revisions

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m →11-limit: Fix a typo "sugbroup"
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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 14: Line 14:
[[POTE generator]]: ~25/21 = 292.710
[[POTE generator]]: ~25/21 = 292.710


{{Val list|legend=1| 4, 37, 41 }}
{{Optimal ET sequence|legend=1| 4, 37, 41 }}


[[Badness]]: 0.060269
[[Badness]]: 0.060269
Line 27: Line 27:
POTE generator: ~25/21 = 292.547
POTE generator: ~25/21 = 292.547


Vals: {{Val list| 4, 37, 41, 119 }}
{{Optimal ET sequence|legend=1| 4, 37, 41, 119 }}


Badness: 0.043209
Badness: 0.043209
Line 42: Line 42:
POTE generator: ~13/11 = 292.457
POTE generator: ~13/11 = 292.457


Vals: {{Val list| 4, 37, 41, 78, 119f }}
{{Optimal ET sequence|legend=1| 4, 37, 41, 78, 119f }}


Badness: 0.032913
Badness: 0.032913
Line 55: Line 55:
POTE generator: ~25/21 = 292.851
POTE generator: ~25/21 = 292.851


Vals: {{Val list| 41, 127cd, 168cd }}
{{Optimal ET sequence|legend=1| 41, 127cd, 168cd }}


Badness: 0.041170
Badness: 0.041170
Line 68: Line 68:
POTE generator: ~13/11 = 292.928
POTE generator: ~13/11 = 292.928


Vals: {{Val list| 41, 86ce, 127cd }}
{{Optimal ET sequence|legend=1| 41, 86ce, 127cd }}


Badness: 0.030081
Badness: 0.030081
Line 83: Line 83:
[[POTE generator]]: ~25/24 = 53.816
[[POTE generator]]: ~25/24 = 53.816


{{Val list|legend=1| 22, 45, 67c }}
{{Optimal ET sequence|legend=1| 22, 45, 67c }}


[[Badness]]: 0.090769
[[Badness]]: 0.090769
Line 100: Line 100:
[[POTE generator]]: ~3/2 = 708.792
[[POTE generator]]: ~3/2 = 708.792


{{Val list|legend=1| 11c, 22 }}
{{Optimal ET sequence|legend=1| 11c, 22 }}


[[Badness]]: 0.141782
[[Badness]]: 0.141782
Line 113: Line 113:
POTE generator: ~3/2 = 706.768
POTE generator: ~3/2 = 706.768


Vals: {{Val list| 11c, 22 }}
{{Optimal ET sequence|legend=1| 11c, 22 }}


Badness: 0.068672
Badness: 0.068672
Line 126: Line 126:
POTE generator: ~3/2 = 707.764
POTE generator: ~3/2 = 707.764


Vals: {{Val list| 11cf, 22 }}
{{Optimal ET sequence|legend=1| 11cf, 22 }}


Badness: 0.056528
Badness: 0.056528
Line 141: Line 141:
[[POTE generator]]: ~98/75 = 468.331
[[POTE generator]]: ~98/75 = 468.331


{{Val list|legend=1| 18, 23d, 41 }}
{{Optimal ET sequence|legend=1| 18, 23d, 41 }}


[[Badness]]: 0.110448
[[Badness]]: 0.110448
Line 154: Line 154:
POTE generator: ~98/75 = 468.367
POTE generator: ~98/75 = 468.367


Vals: {{Val list| 18e, 23de, 41, 228ccdd }}
{{Optimal ET sequence|legend=1| 18e, 23de, 41, 228ccdd }}


Badness: 0.050105
Badness: 0.050105
Line 167: Line 167:
POTE generator: ~13/10 = 468.270
POTE generator: ~13/10 = 468.270


Vals: {{Val list| 18e, 23de, 41 }}
{{Optimal ET sequence|legend=1| 18e, 23de, 41 }}


Badness: 0.039183
Badness: 0.039183
Line 182: Line 182:
[[POTE generator]]: ~6/5 = 323.780
[[POTE generator]]: ~6/5 = 323.780


{{Val list|legend=1| 26, 37, 63 }}
{{Optimal ET sequence|legend=1| 26, 37, 63 }}


[[Badness]]: 0.157830
[[Badness]]: 0.157830
Line 195: Line 195:
POTE generator: ~6/5 = 323.796<br>
POTE generator: ~6/5 = 323.796<br>


Vals: {{Val list| 26, 37, 63 }}
{{Optimal ET sequence|legend=1| 26, 37, 63 }}


Badness: 0.065356
Badness: 0.065356
Line 208: Line 208:
POTE generator: ~6/5 = 323.790
POTE generator: ~6/5 = 323.790


Vals: {{Val list| 26, 37, 63 }}
{{Optimal ET sequence|legend=1| 26, 37, 63 }}


Badness: 0.035724
Badness: 0.035724
Line 221: Line 221:
[[POTE generator]]: ~3/2 = 705.613
[[POTE generator]]: ~3/2 = 705.613


{{Val list|legend=1| 7, 56, 63, 119 }}
{{Optimal ET sequence|legend=1| 7, 56, 63, 119 }}


[[Badness]]: 0.206592
[[Badness]]: 0.206592
Line 234: Line 234:
POTE generator: ~3/2 = 705.518
POTE generator: ~3/2 = 705.518


Vals: {{Val list| 7, 56, 63, 119 }}
{{Optimal ET sequence|legend=1| 7, 56, 63, 119 }}


Badness: 0.070437
Badness: 0.070437
Line 247: Line 247:
POTE generator: ~3/2 = 705.344
POTE generator: ~3/2 = 705.344


Vals: {{Val list| 7, 56, 63, 119 }}
{{Optimal ET sequence|legend=1| 7, 56, 63, 119 }}


Badness: 0.041238
Badness: 0.041238

Revision as of 18:25, 7 May 2023

These temper out the keema, [-5 -3 3 1⟩ = 875/864. Keemic temperaments include doublewide, flattone, porcupine, superkleismic, magic, keemun, and sycamore. Discussed below are quasitemp and barbad.

Quasitemp

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

Subgroup: 2.3.5.7

Comma list: 875/864, 2401/2400

Mapping: [⟨1 5 5 5], ⟨0 -14 -11 -9]]

Wedgie: ⟨⟨ 14 11 9 -15 -25 -10 ]]

POTE generator: ~25/21 = 292.710

Optimal ET sequence: 4, 37, 41

Badness: 0.060269

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 1375/1372

Mapping: [⟨1 5 5 5 2], ⟨0 -14 -11 -9 6]]

POTE generator: ~25/21 = 292.547

Optimal ET sequence: 4, 37, 41, 119

Badness: 0.043209

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 196/195, 275/273, 385/384

POTE generator: ~13/11 = 292.457

Mapping: [⟨1 5 5 5 2 2], ⟨0 -14 -11 -9 6 7]]

POTE generator: ~13/11 = 292.457

Optimal ET sequence: 4, 37, 41, 78, 119f

Badness: 0.032913

Quato

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 625/616

Mapping: [⟨1 5 5 5 12], ⟨0 -14 -11 -9 -35]]

POTE generator: ~25/21 = 292.851

Optimal ET sequence: 41, 127cd, 168cd

Badness: 0.041170

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 243/242, 275/273, 325/324

Mapping: [⟨1 5 5 5 12 12], ⟨0 -14 -11 -9 -35 -34]]

POTE generator: ~13/11 = 292.928

Optimal ET sequence: 41, 86ce, 127cd

Badness: 0.030081

Chromo

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

Subgroup: 2.3.5.7

Comma list: 875/864, 2430/2401

Mapping: [⟨1 1 2 2], ⟨0 13 7 18]]

POTE generator: ~25/24 = 53.816

Optimal ET sequence: 22, 45, 67c

Badness: 0.090769

Undeka

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

Subgroup: 2.3.5.7

Comma list: 875/864, 3200/3087

Mapping: [⟨11 0 8 31], ⟨0 1 1 0]]

Wedgie: ⟨⟨ 11 11 0 -8 -31 -31 ]]

POTE generator: ~3/2 = 708.792

Optimal ET sequence: 11c, 22

Badness: 0.141782

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 352/343, 385/384

Mapping: [⟨11 0 8 31 38], ⟨0 1 1 0 0]]

POTE generator: ~3/2 = 706.768

Optimal ET sequence: 11c, 22

Badness: 0.068672

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 65/63, 100/99, 169/165, 352/343

Mapping: [⟨11 0 8 31 38 23], ⟨0 1 1 0 0 1]]

POTE generator: ~3/2 = 707.764

Optimal ET sequence: 11cf, 22

Badness: 0.056528

Barbad

Subgroup: 2.3.5.7

Comma list: 875/864, 16875/16807

Mapping: [⟨1 9 7 11], ⟨0 -19 -12 -21]]

Wedgie: ⟨⟨ 19 12 21 -25 -20 15 ]]

POTE generator: ~98/75 = 468.331

Optimal ET sequence: 18, 23d, 41

Badness: 0.110448

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/242, 540/539, 625/616

Mapping: [⟨1 9 7 11 14], ⟨0 -19 -12 -21 -27]]

POTE generator: ~98/75 = 468.367

Optimal ET sequence: 18e, 23de, 41, 228ccdd

Badness: 0.050105

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 245/242, 275/273

Mapping: [⟨1 9 7 11 14 8], ⟨0 -19 -12 -21 -27 -11]]

POTE generator: ~13/10 = 468.270

Optimal ET sequence: 18e, 23de, 41

Badness: 0.039183

Hyperkleismic

Subgroup: 2.3.5.7

Comma list: 875/864, 51200/50421

Mapping: [⟨1 -3 -2 2], ⟨0 17 16 3]]

Wedgie: ⟨⟨ 17 16 3 -14 -43 -38 ]]

POTE generator: ~6/5 = 323.780

Optimal ET sequence: 26, 37, 63

Badness: 0.157830

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 2420/2401

Mapping: [⟨1 -3 -2 2 4], ⟨0 17 16 3 -2]]

POTE generator: ~6/5 = 323.796

Optimal ET sequence: 26, 37, 63

Badness: 0.065356

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 169/168, 275/273, 385/384

Mapping: [⟨1 -3 -2 2 4 1], ⟨0 17 16 3 -2 10]]

POTE generator: ~6/5 = 323.790

Optimal ET sequence: 26, 37, 63

Badness: 0.035724

Sevond

Subgroup: 2.3.5.7

Comma list: 875/864, 327680/321489

Mapping: [⟨7 0 -6 53], ⟨0 1 2 -3]]

POTE generator: ~3/2 = 705.613

Optimal ET sequence: 7, 56, 63, 119

Badness: 0.206592

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 385/384, 6655/6561

Mapping: [⟨7 0 -6 53 2], ⟨0 1 2 -3 2]]

POTE generator: ~3/2 = 705.518

Optimal ET sequence: 7, 56, 63, 119

Badness: 0.070437

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 169/168, 352/351, 385/384

Mapping: [⟨7 0 -6 53 2 37], ⟨0 1 2 -3 2 -1]]

POTE generator: ~3/2 = 705.344

Optimal ET sequence: 7, 56, 63, 119

Badness: 0.041238

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