Semaphoresmic clan: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
m Cleanup
Line 1: Line 1:
This clan tempers out the slendro diesis, [[49/48]], a triprime comma with factors of 2, 3 and 7.  
The '''slendro clan''' tempers out the slendro diesis, [[49/48]], a triprime comma with factors of 2, 3 and 7.  


Discussed elsewhere are [[Father family #Baba|baba]], [[Dicot family #Decimal|decimal]], [[Bug family #Beep|beep]], [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Godzilla|godzilla]], [[Kleismic family #Keemun|keemun]], [[Augmented family #Triforce|triforce]], [[Pelogic family #Superpelog|superpelog]], [[Marvel temperaments #Negri|negri]], [[Porcupine family #Nautilus|nautilus]], [[Magic family #Spell|spell]] and [[Immunity family #Immunity|immunity]].  
Discussed elsewhere are [[Father family #Baba|baba]], [[Dicot family #Decimal|decimal]], [[Bug family #Beep|beep]], [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Godzilla|godzilla]], [[Kleismic family #Keemun|keemun]], [[Augmented family #Triforce|triforce]], [[Pelogic family #Superpelog|superpelog]], [[Marvel temperaments #Negri|negri]], [[Porcupine family #Nautilus|nautilus]], [[Magic family #Spell|spell]] and [[Immunity family #Immunity|immunity]].  


== Semaphore ==
== Semaphore ==
{{main| Semaphore and Godzilla }}
{{Main| Semaphore and godzilla }}


Subgroup: 2.3.7
[[Subgroup]]: 2.3.7


[[Comma list]]: 49/48
[[Comma list]]: 49/48


[[Sval]] [[Mapping]]: [{{val| 1 0 2 }}, {{val| 0 2 1 }}]
[[Sval]] [[mapping]]: [{{val| 1 0 2 }}, {{val| 0 2 1 }}]


Sval mapping generators: ~2, ~7/4
: sval mapping generators: ~2, ~7/4


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


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


[[POTE generator]]: ~7/6 = 250.385
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 949.615


{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67dd, 91dd }}
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67dd, 91dd }}
Line 25: Line 25:


== Nuke ==
== Nuke ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 3584/3375
[[Comma list]]: 49/48, 3584/3375
Line 31: Line 31:
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -6 5 -3 }}]
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -6 5 -3 }}]


[[POTE generator]]: ~16/15 = 80.9538
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 80.9538


{{Optimal ET sequence|legend=1| 14, 15, 44cd }}
{{Optimal ET sequence|legend=1| 14, 15, 44cd }}
Line 44: Line 44:
Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -6 5 -3 7 }}]
Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -6 5 -3 7 }}]


POTE generator: ~16/15 = 80.8171
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 80.8171


{{Optimal ET sequence|legend=1| 14e, 15 }}
{{Optimal ET sequence|legend=1| 14e, 15 }}
Line 57: Line 57:
Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -6 5 -3 7 -4 }}]
Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -6 5 -3 7 -4 }}]


POTE generator: ~16/15 = 81.0243
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 81.0243


{{Optimal ET sequence|legend=1| 14e, 15, 44cdeff }}
{{Optimal ET sequence|legend=1| 14e, 15, 44cdeff }}
Line 64: Line 64:


== Mabila ==
== Mabila ==
{{see also| Mabila family }}
{{See also| Mabila family }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 28672/28125
[[Comma list]]: 49/48, 28672/28125
Line 74: Line 74:
{{Multival|legend=1| 10 -3 5 -28 -20 20 }}
{{Multival|legend=1| 10 -3 5 -28 -20 20 }}


[[POTE generator]]: ~75/56 = 529.667
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/56 = 529.667


{{Optimal ET sequence|legend=1| 9, 25, 34 }}
{{Optimal ET sequence|legend=1| 9, 25, 34 }}
Line 87: Line 87:
Mapping: [{{val| 1 6 1 5 7 }}, {{val| 0 -10 3 -5 -8 }}]
Mapping: [{{val| 1 6 1 5 7 }}, {{val| 0 -10 3 -5 -8 }}]


POTE generator: ~15/11 = 529.729
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.729


{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
Line 100: Line 100:
Mapping: [{{val| 1 6 1 5 7 9 }}, {{val| 0 -10 3 -5 -8 -12 }}]
Mapping: [{{val| 1 6 1 5 7 9 }}, {{val| 0 -10 3 -5 -8 -12 }}]


POTE generator: ~15/11 = 529.763
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.763


{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
Line 113: Line 113:
Mapping: [{{val| 1 6 1 5 7 9 1 }}, {{val| 0 -10 3 -5 -8 -12 7 }}]
Mapping: [{{val| 1 6 1 5 7 9 1 }}, {{val| 0 -10 3 -5 -8 -12 7 }}]


POTE generator: ~15/11 = 529.695
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.695


{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
Line 126: Line 126:
Mapping: [{{val| 1 6 1 5 7 9 1 6 }}, {{val| 0 -10 3 -5 -8 -12 7 -4 }}]
Mapping: [{{val| 1 6 1 5 7 9 1 6 }}, {{val| 0 -10 3 -5 -8 -12 7 -4 }}]


POTE generator: ~15/11 = 529.736
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 529.736


{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
{{Optimal ET sequence|legend=1| 9, 25e, 34 }}
Line 133: Line 133:


== Hemiripple ==
== Hemiripple ==
{{see also| Ripple family #Hemiripple }}
{{See also| Ripple family #Hemiripple }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 6561/6250
[[Comma list]]: 49/48, 6561/6250
Line 143: Line 143:
{{Multival|legend=1| 10 16 5 2 -20 -33 }}
{{Multival|legend=1| 10 16 5 2 -20 -33 }}


[[POTE generator]]: ~36/35 = 50.826
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 50.826


{{Optimal ET sequence|legend=1| 23d, 24, 47d, 71bdd }}
{{Optimal ET sequence|legend=1| 23d, 24, 47d, 71bdd }}
Line 156: Line 156:
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -10 -16 -5 -13 }}]
Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -10 -16 -5 -13 }}]


POTE generator: ~36/35 = 50.826
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.826


{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
Line 169: Line 169:
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -10 -16 -5 -13 -7 }}]
Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -10 -16 -5 -13 -7 }}]


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


{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
Line 176: Line 176:


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Slendro]]
[[Category:Slendro clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 09:32, 8 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, 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]

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

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]]

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

Retrieved from "https://en.xen.wiki/index.php?title=Semaphoresmic_clan&oldid=112820"