No-threes subgroup temperaments: Difference between revisions

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 * Mercy ([[823543/819200]]) → [[Quince clan #Mercy|Quince clan]]
 * Llywelyn a.k.a. shoe ([[4194304/4117715]]) → [[Llywelynsmic clan #Llywelyn a.k.a. shoe|Llywelynsmic clan]]
+* Sidewalk ([[823543/800000]]) → [[2023/2000#Sidewalk]]
 === Frostburn ===
-{{See also| Magic family #Quadrimage }}
+{{See also| Magic family #Quadrimage | Subgroup temperaments #Baldy }}
-{{See also| Subgroup temperaments #Baldy }}
 [[Subgroup]]: 2.5.7
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 {{Main| Bastille }}
-Described as the 2.5.7 subgroup 1407 & 1789 temperament, and named after an eponymous historical event which took place on July 14, 1789 (14/07/1789). Extensions discussed elsewhere include [[The Jacobins#Double bastille|double bastille]].
+Described as the 2.5.7 subgroup 1407 & 1789 temperament, and named after an [[wikipedia:Storming of the Bastille|eponymous historical event]] which took place on July 14, 1789 (14/07/1789). Extensions discussed elsewhere include [[The Jacobins#Double bastille|double bastille]].
 Subgroup: 2.5.7
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 === No-threes naiad ===
-{{See also| Wizardharry clan #Naiad }}
+{{See also| Wizardharry clan #Naiad | Werckismic temperaments #Seminaiad }}
+This temperament can be described as the 21 & 29 & 37 temperament in no-threes subgroups. It expands [[Subgroup temperaments #Tridec|tridec]] and [[Subgroup temperaments #Naiadec|naiadec]].
 [[Subgroup]]: 2.5.7.11
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 [[Badness]] (Sintel): 1.862
+==== 2.5.7.11.13 subgroup ====
+Subgroup: 2.5.7.11.13
+Comma list: 847/845, 1001/1000
+Sval mapping: {{Mapping| 1 0 2 0 1 | 0 1 1 1 1 | 0 0 -4 3 1 }}
+Optimal tunings:
+* WE: ~2 = 1200.034¢, ~5 = 2786.678¢, ~13/10 = 454.569¢
+* CWE: ~2 = 1200.000¢, ~5 = 2786.646¢, ~13/10 = 454.557¢
+{{Optimal ET sequence|legend=0| 16, 21, 29, 37, 50, 58, 66, 87, 103, 124 }}
+Badness (Sintel): 0.179
+==== 2.5.7.11.13.17 subgroup ====
+Subgroup: 2.5.7.11.13.17
+Comma list: 170/169, 221/220, 847/845
+Sval mapping: {{Mapping| 1 0 2 0 1 1 | 0 1 1 1 1 1 | 0 0 -4 3 1 2 }}
+Optimal tunings:
+* WE: ~2 = 1200.407¢, ~5 = 2787.484¢, ~13/10 = 455.036¢
+* CWE: ~2 = 1200.000¢, ~5 = 2787.107¢, ~13/10 = 454.906¢
+{{Optimal ET sequence|legend=0| 16, 21, 29g, 37, 50, 58, 66g, 87g }}
+Badness (Sintel): 0.438
 == Higher 2.5 temperaments ==
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 {{Optimal ET sequence|legend=1|8, 13, 21, 34, 81, 115}}
-=== Vengeance ===
-{{Main| Vengeance }}
-Another lower-error replica of mavila, with the fifth being ~[[25/17]] instead of ~[[3/2]].
-[[Subgroup]]: 2.5.17
-[[Comma list]]: 78608/78125
-{{Mapping|legend=2|1 1 1|0 3 7}}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~[[34/25]] = 529.095
-{{Optimal ET sequence|legend=1|7g, 9, 25, 34, 93, 127, 288, 415}}
 == No-threes-or-fives subgroup temperaments ==