Semaphoresmic clan: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 20: Line 20:
[[POTE generator]]: ~7/6 = 250.385
[[POTE generator]]: ~7/6 = 250.385


{{Val list|legend=1| 5, 14, 19, 24, 67dd, 91dd }}
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67dd, 91dd }}


Scales: [[semaphore5]], [[semaphore9]], [[semaphore14]]
Scales: [[semaphore5]], [[semaphore9]], [[semaphore14]]
Line 33: Line 33:
[[POTE generator]]: ~16/15 = 80.9538
[[POTE generator]]: ~16/15 = 80.9538


{{Val list|legend=1| 14, 15, 44cd }}
{{Optimal ET sequence|legend=1| 14, 15, 44cd }}


[[Badness]]: 0.129339
[[Badness]]: 0.129339
Line 46: Line 46:
POTE generator: ~16/15 = 80.8171
POTE generator: ~16/15 = 80.8171


Optimal GPV sequence: {{Val list| 14e, 15 }}
{{Optimal ET sequence|legend=1| 14e, 15 }}


Badness: 0.069398
Badness: 0.069398
Line 59: Line 59:
POTE generator: ~16/15 = 81.0243
POTE generator: ~16/15 = 81.0243


Optimal GPV sequence: {{Val list| 14e, 15, 44cdeff }}
{{Optimal ET sequence|legend=1| 14e, 15, 44cdeff }}


Badness: 0.048553
Badness: 0.048553
Line 76: Line 76:
[[POTE generator]]: ~75/56 = 529.667
[[POTE generator]]: ~75/56 = 529.667


{{Val list|legend=1| 9, 25, 34 }}
{{Optimal ET sequence|legend=1| 9, 25, 34 }}


[[Badness]]: 0.133638
[[Badness]]: 0.133638
Line 89: Line 89:
POTE generator: ~15/11 = 529.729
POTE generator: ~15/11 = 529.729


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}


Badness: 0.061501
Badness: 0.061501
Line 102: Line 102:
POTE generator: ~15/11 = 529.763
POTE generator: ~15/11 = 529.763


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}


Badness: 0.037270
Badness: 0.037270
Line 115: Line 115:
POTE generator: ~15/11 = 529.695
POTE generator: ~15/11 = 529.695


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}


Badness: 0.031888
Badness: 0.031888
Line 128: Line 128:
POTE generator: ~15/11 = 529.736
POTE generator: ~15/11 = 529.736


Optimal GPV sequence: {{Val list| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}


Badness: 0.026981
Badness: 0.026981
Line 145: Line 145:
[[POTE generator]]: ~36/35 = 50.826
[[POTE generator]]: ~36/35 = 50.826


{{Val list|legend=1| 23d, 24, 47d, 71bdd }}
{{Optimal ET sequence|legend=1| 23d, 24, 47d, 71bdd }}


[[Badness]]: 0.175113
[[Badness]]: 0.175113
Line 158: Line 158:
POTE generator: ~36/35 = 50.826
POTE generator: ~36/35 = 50.826


Optimal GPV sequence: {{Val list| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}


Badness: 0.066834
Badness: 0.066834
Line 171: Line 171:
POTE generator: ~36/35 = 50.635
POTE generator: ~36/35 = 50.635


Optimal GPV sequence: {{Val list| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}


Badness: 0.046588
Badness: 0.046588

Revision as of 16:12, 7 May 2023

This clan tempers out the slendro diesis, 49/48, a triprime comma with factors of 2, 3 and 7.

Discussed elsewhere are baba, decimal, beep, blacksmith, godzilla, keemun, triforce, superpelog, negri, nautilus, spell and immunity.

Semaphore

Main article: Semaphore and Godzilla

Subgroup: 2.3.7

Comma list: 49/48

Sval Mapping: [⟨1 0 2], ⟨0 2 1]]

Sval mapping generators: ~2, ~7/4

Gencom mapping: [⟨1 2 0 3], ⟨0 -2 0 -1]]

Gencom: [2 7/6; 49/48]

POTE generator: ~7/6 = 250.385

Optimal ET sequence: 5, 14, 19, 24, 67dd, 91dd

Scales: semaphore5, semaphore9, semaphore14

Nuke

Subgroup: 2.3.5.7

Comma list: 49/48, 3584/3375

Mapping: [⟨1 2 2 3], ⟨0 -6 5 -3]]

POTE generator: ~16/15 = 80.9538

Optimal ET sequence: 14, 15, 44cd

Badness: 0.129339

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 77/75, 512/495

Mapping: [⟨1 2 2 3 3], ⟨0 -6 5 -3 7]]

POTE generator: ~16/15 = 80.8171

Optimal ET sequence: 14e, 15

Badness: 0.069398

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 66/65, 77/75, 448/429

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

POTE generator: ~16/15 = 81.0243

Optimal ET sequence: 14e, 15, 44cdeff

Badness: 0.048553

Mabila

See also: Mabila family

Subgroup: 2.3.5.7

Comma list: 49/48, 28672/28125

Mapping: [⟨1 6 1 5], ⟨0 -10 3 -5]]

Wedgie: ⟨⟨ 10 -3 5 -28 -20 20 ]]

POTE generator: ~75/56 = 529.667

Optimal ET sequence: 9, 25, 34

Badness: 0.133638

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 56/55, 1350/1331

Mapping: [⟨1 6 1 5 7], ⟨0 -10 3 -5 -8]]

POTE generator: ~15/11 = 529.729

Optimal ET sequence: 9, 25e, 34

Badness: 0.061501

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 56/55, 91/90, 847/845

Mapping: [⟨1 6 1 5 7 9], ⟨0 -10 3 -5 -8 -12]]

POTE generator: ~15/11 = 529.763

Optimal ET sequence: 9, 25e, 34

Badness: 0.037270

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 49/48, 56/55, 91/90, 154/153, 375/374

Mapping: [⟨1 6 1 5 7 9 1], ⟨0 -10 3 -5 -8 -12 7]]

POTE generator: ~15/11 = 529.695

Optimal ET sequence: 9, 25e, 34

Badness: 0.031888

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187

Mapping: [⟨1 6 1 5 7 9 1 6], ⟨0 -10 3 -5 -8 -12 7 -4]]

POTE generator: ~15/11 = 529.736

Optimal ET sequence: 9, 25e, 34

Badness: 0.026981

Hemiripple

See also: Ripple family § Hemiripple

Subgroup: 2.3.5.7

Comma list: 49/48, 6561/6250

Mapping: [⟨1 2 3 3], ⟨0 -10 -16 -5]]

Wedgie: ⟨⟨ 10 16 5 2 -20 -33 ]]

POTE generator: ~36/35 = 50.826

Optimal ET sequence: 23d, 24, 47d, 71bdd

Badness: 0.175113

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 121/120, 567/550

Mapping: [⟨1 2 3 3 4], ⟨0 -10 -16 -5 -13]]

POTE generator: ~36/35 = 50.826

Optimal ET sequence: 23de, 24, 47de, 71bdde

Badness: 0.066834

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 66/65, 121/120, 351/350

Mapping: [⟨1 2 3 3 4 4], ⟨0 -10 -16 -5 -13 -7]]

POTE generator: ~36/35 = 50.635

Optimal ET sequence: 23de, 24, 47de, 71bdde

Badness: 0.046588

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