Shibboleth family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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== Shibboleth ==
== Shibboleth ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 1953125/1889568
[[Comma list]]: 1953125/1889568


[[Mapping]]: [{{val| 1 4 5 }}, {{val| 0 -9 -10 }}]
{{Mapping|legend=1| 1 4 5 | 0 -9 -10 }}


[[POTE generator]]: ~6/5 = 321.852
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.852


{{Optimal ET sequence|legend=1| 15, 26, 41, 179c, 220c, 261cc, 302cc }}
{{Optimal ET sequence|legend=1| 15, 26, 41, 179c, 220c, 261cc, 302cc }}
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== Superkleismic ==
== Superkleismic ==
{{main| Superkleismic }}
{{Main| Superkleismic }}
{{see also| Gamelismic clan #Superkleismic }}
{{See also| Gamelismic clan #Superkleismic }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 875/864, 1029/1024
[[Comma list]]: 875/864, 1029/1024


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


{{Multival|legend=1| 9 10 -3 -5 -30 -35 }}
{{Multival|legend=1| 9 10 -3 -5 -30 -35 }}


[[POTE generator]]: ~6/5 = 321.930
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.930


{{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}
{{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}
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Comma list: 100/99, 245/242, 385/384
Comma list: 100/99, 245/242, 385/384


Mapping: [{{val| 1 4 5 2 4 }}, {{val| 0 -9 -10 3 -2 }}]
Mapping: {{mapping| 1 4 5 2 4 | 0 -9 -10 3 -2 }}


POTE generator: ~6/5 = 321.847
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.847


{{Optimal ET sequence|legend=1| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
{{Optimal ET sequence|legend=1| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
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Comma list: 100/99, 105/104, 144/143, 245/243
Comma list: 100/99, 105/104, 144/143, 245/243


Mapping: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}]
Mapping: {{mapping| 1 4 5 2 4 8 | 0 -9 -10 3 -2 -16 }}


POTE generator: ~6/5 = 321.994
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.994


{{Optimal ET sequence|legend=1| 11cf, 15, 26, 41 }}
{{Optimal ET sequence|legend=1| 11cf, 15, 26, 41 }}
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== Gilead ==
== Gilead ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 343/324
[[Comma list]]: 126/125, 343/324


[[Mapping]]: [{{val| 1 4 5 6 }}, {{val| 0 -9 -10 -12 }}]
{{Mapping|legend=1| 1 4 5 6 | 0 -9 -10 -12 }}


{{Multival|legend=1| 9 10 12 -5 -6 0 }}
{{Multival|legend=1| 9 10 12 -5 -6 0 }}


[[POTE generator]]: ~6/5 = 321.423
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.423


{{Optimal ET sequence|legend=1| 11cd, 15, 41dd, 56dd }}
{{Optimal ET sequence|legend=1| 11cd, 15, 41dd, 56dd }}

Revision as of 12:28, 26 August 2023

The shibboleth family tempers out the shibboleth comma, 1953125/1889568.

Temperaments discussed elsewhere include:

Shibboleth

Subgroup: 2.3.5

Comma list: 1953125/1889568

Mapping[1 4 5], 0 -9 -10]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.852

Optimal ET sequence15, 26, 41, 179c, 220c, 261cc, 302cc

Badness: 0.227553

Superkleismic

Subgroup: 2.3.5.7

Comma list: 875/864, 1029/1024

Mapping[1 4 5 2], 0 -9 -10 3]]

Wedgie⟨⟨ 9 10 -3 -5 -30 -35 ]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.930

Optimal ET sequence11c, 15, 26, 41

Badness: 0.047932

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 385/384

Mapping: [1 4 5 2 4], 0 -9 -10 3 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.847

Optimal ET sequence11c, 15, 26, 41, 179cde, 220cde, 261ccdee

Badness: 0.025659

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 144/143, 245/243

Mapping: [1 4 5 2 4 8], 0 -9 -10 3 -2 -16]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.994

Optimal ET sequence11cf, 15, 26, 41

Badness: 0.021478

Gilead

Subgroup: 2.3.5.7

Comma list: 126/125, 343/324

Mapping[1 4 5 6], 0 -9 -10 -12]]

Wedgie⟨⟨ 9 10 12 -5 -6 0 ]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.423

Optimal ET sequence11cd, 15, 41dd, 56dd

Badness: 0.115292