Semaphoresmic clan: Difference between revisions

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Negri tempers out the [[negri comma]] in the 5-limit, [[49/48]] and [[225/224]] in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.  
Negri tempers out the [[negri comma]] in the 5-limit, [[49/48]] and [[225/224]] in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.  


Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 16875/16384
[[Comma list]]: 16875/16384


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
: mapping generators: ~2, ~16/15


{{Multival|legend=1| 4 -3 -14 }}
{{Multival|legend=1| 4 -3 -14 }}


[[POTE generator]]: ~16/15 = 125.7549
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 125.7549


{{Optimal ET sequence|legend=1| 9, 10, 19, 67c, 86c, 105c }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 67c, 86c, 105c }}
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=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 225/224
[[Comma list]]: 49/48, 225/224
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{{Multival|legend=1| 4 -3 2 -14 -8 13 }}
{{Multival|legend=1| 4 -3 2 -14 -8 13 }}


[[POTE generator]]: ~15/14 = 125.608
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 125.608


{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
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[[Badness]]: 0.026483
[[Badness]]: 0.026483


==== Negra ====
==== 2.3.5.7.13 subgroup (negra) ====
This is the 2.3.5.7.13 extension of negri.
 
Subgroup: 2.3.5.7.13
Subgroup: 2.3.5.7.13


[[Comma list]]: 49/48, 65/64, 91/90
Comma list: 49/48, 65/64, 91/90


[[Sval]] [[mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]
Sval mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]


[[Gencom]] [[mapping]]: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]
Gencom mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]


[[Gencom]]: [2 14/13; 49/48 65/64 91/90]
: gencom: [2 14/13; 49/48 65/64 91/90]


[[POTE generator]]: ~14/13 = 125.567
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 125.567


{{Optimal ET sequence|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
{{Optimal ET sequence|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
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Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]


POTE generator: ~15/14 = 126.474
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 126.474


{{Optimal ET sequence|legend=1| 9, 10, 19 }}
{{Optimal ET sequence|legend=1| 9, 10, 19 }}
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Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]
Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]


POTE generator: ~14/13 = 126.431
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.431


{{Optimal ET sequence|legend=1| 9, 10, 19 }}
{{Optimal ET sequence|legend=1| 9, 10, 19 }}
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Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]


POTE generator: ~15/14 = 124.767
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.767


{{Optimal ET sequence|legend=1| 19, 29, 48d, 77cdd }}
{{Optimal ET sequence|legend=1| 19, 29, 48d, 77cdd }}
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Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]


POTE generator: ~14/13 = 124.716
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.716


{{Optimal ET sequence|legend=1| 19, 29, 48df, 77cddf }}
{{Optimal ET sequence|legend=1| 19, 29, 48df, 77cddf }}
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Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]


POTE generator: ~15/14 = 127.039
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 127.039


{{Optimal ET sequence|legend=1| 9, 19e }}
{{Optimal ET sequence|legend=1| 9, 19e }}
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Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]


POTE generator: ~14/13 = 127.039
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 127.039


{{Optimal ET sequence|legend=1| 9, 19e }}
{{Optimal ET sequence|legend=1| 9, 19e }}
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Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]


POTE generator: ~15/14 = 124.539
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.539


{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddee }}
{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddee }}
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Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]


POTE generator: ~14/13 = 124.545
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.545


{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddeef }}
{{Optimal ET sequence|legend=1| 10, 19e, 29, 77cddeef }}
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Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]
Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]


POTE generator: ~11/8 = 537.186
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.186


{{Optimal ET sequence|legend=1| 9, 20, 29, 38d, 67cdde }}
{{Optimal ET sequence|legend=1| 9, 20, 29, 38d, 67cdde }}
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Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]
Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]


POTE generator: ~11/8 = 537.208
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.208


{{Optimal ET sequence|legend=1| 9, 20, 29, 38df, 67cddef }}
{{Optimal ET sequence|legend=1| 9, 20, 29, 38df, 67cddef }}
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Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]
Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]


POTE generator: ~11/8 = 537.230
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.230


{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
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Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]
Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]


POTE generator: ~11/8 = 537.214
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.214


{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}
{{Optimal ET sequence|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}

Revision as of 06:57, 15 May 2023

The slendro 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, 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]

Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 949.615

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

Scales: semaphore5, semaphore9, semaphore14

Negri

Main article: Negri

Negri tempers out the negri comma in the 5-limit, 49/48 and 225/224 in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 to the comma list; this will be discussed below under the title of negra.

Subgroup: 2.3.5

Comma list: 16875/16384

Mapping: [⟨1 2 2], ⟨0 -4 3]]

mapping generators: ~2, ~16/15

Wedgie: ⟨⟨ 4 -3 -14 ]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 125.7549

Optimal ET sequence: 9, 10, 19, 67c, 86c, 105c

Badness: 0.086856

7-limit

Subgroup: 2.3.5.7

Comma list: 49/48, 225/224

Mapping: [⟨1 2 2 3], ⟨0 -4 3 -2]]

Wedgie: ⟨⟨ 4 -3 2 -14 -8 13 ]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 125.608

Optimal ET sequence: 9, 10, 19, 48d, 67cdd, 86cdd

Badness: 0.026483

2.3.5.7.13 subgroup (negra)

Subgroup: 2.3.5.7.13

Comma list: 49/48, 65/64, 91/90

Sval mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -3]]

Gencom mapping: [⟨1 2 2 3 0 4], ⟨0 -4 3 -2 0 -3]]

gencom: [2 14/13; 49/48 65/64 91/90]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 125.567

Optimal ET sequence: 9, 10, 19, 48df, 67cddf, 86cddff

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 49/48, 56/55

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

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 126.474

Optimal ET sequence: 9, 10, 19

Badness: 0.026190

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 49/48, 56/55, 78/77

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

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.431

Optimal ET sequence: 9, 10, 19

Badness: 0.017833

Negril

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 225/224

Mapping: [⟨1 2 2 3 2], ⟨0 -4 3 -2 14]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.767

Optimal ET sequence: 19, 29, 48d, 77cdd

Badness: 0.038679

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90, 875/858

Mapping: [⟨1 2 2 3 2 4], ⟨0 -4 3 -2 14 -3]]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.716

Optimal ET sequence: 19, 29, 48df, 77cddf

Badness: 0.024383

Negric

Subgroup: 2.3.5.7.11

Comma list: 33/32, 49/48, 77/75

Mapping: [⟨1 2 2 3 3], ⟨0 -4 3 -2 4]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 127.039

Optimal ET sequence: 9, 19e

Badness: 0.030617

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 33/32, 49/48, 65/64, 91/90

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

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 127.039

Optimal ET sequence: 9, 19e

Badness: 0.020205

Negroni

Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 225/224

Mapping: [⟨1 2 2 3 5], ⟨0 -4 3 -2 -15]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 124.539

Optimal ET sequence: 10, 19e, 29, 77cddee

Badness: 0.035296

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 65/64, 91/90

Mapping: [⟨1 2 2 3 5 4], ⟨0 -4 3 -2 -15 -3]]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 124.545

Optimal ET sequence: 10, 19e, 29, 77cddeef

Badness: 0.021559

Wilsec

Subgroup: 2.3.5.7.11

Comma list: 49/48, 121/120, 225/224

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

Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.186

Optimal ET sequence: 9, 20, 29, 38d, 67cdde

Badness: 0.041886

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90, 121/120

Mapping: [⟨1 6 -1 5 4 7], ⟨0 -8 6 -4 -1 -6]]

Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.208

Optimal ET sequence: 9, 20, 29, 38df, 67cddef

Badness: 0.025192

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 49/48, 65/64, 91/90, 121/120, 154/153

Mapping: [⟨1 6 -1 5 4 7 -2], ⟨0 -8 6 -4 -1 -6 11]]

Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.230

Optimal ET sequence: 9, 20g, 29g, 38df, 67cddefg

Badness: 0.021778

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153

Mapping: [⟨1 6 -1 5 4 7 -2 7], ⟨0 -8 6 -4 -1 -6 11 -5]]

Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 537.214

Optimal ET sequence: 9, 20g, 29g, 38df, 67cddefgh

Badness: 0.016828

Nuke

Subgroup: 2.3.5.7

Comma list: 49/48, 3584/3375

Mapping: [⟨1 2 2 3], ⟨0 -6 5 -3]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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 ]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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 ]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~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]]

Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.635

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

Badness: 0.046588

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