Werckismic temperaments: Difference between revisions

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 * ''[[Tiberius]]'' (+2048/2025) → [[Diaschismic rank-3 family #Tiberius|Diaschismic rank-3 family]]
 * ''[[Belobog]]'' (+3136/3125) → [[Hemimean family #Belobog|Hemimean family]]
+* ''[[Landy]]'' (+4375/4356) → [[Landscape family #Landy|Landscape family]]
 * ''[[Turan]]'' (+10976/10935) → [[Hemimage family #Turan|Hemimage family]]
 * ''[[Snape]]'' (+19683/19600) → [[Cataharry family #Snape|Cataharry family]]
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 : ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #History]].''
-History splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].
+History, named by [[Graham Breed]] some time before 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96550.html#96556 Yahoo! Tuning Group | ''Madagascar<nowiki>[</nowiki>19<nowiki>]</nowiki>'']</ref>, splits the perfect fourth into six, each for [[21/20]][[~]][[22/21]]. A recommendable tuning is given by [[289edo]].
 [[Subgroup]]: 2.3.5.7.11
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 Badness (Sintel): 1.38
+== Seminaiad ==
+: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Seminaiad]].''
+Named by [[User:Xenllium|Xenllium]] in 2026, seminaiad is a weak extension of [[No-threes subgroup temperaments #No-threes naiad|no-threes naiad]]. It splits ~13/5 in two to represent ~21/13.
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 441/440, 1127357/1125000
+{{Mapping|legend=1| 1 5 0 -2 3 | 0 -11 0 8 -6 | 0 0 1 1 1 }}
+: mapping generators: ~2, ~150/121, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.203{{c}}, ~150/121 = 372.665{{c}}, ~5/4 = 386.499{{c}}
+: [[error map]]: {{val| +0.203 -0.257 +0.592 -1.004 +0.206 }}
+* [[CWE]]: ~2 = 1200.000{{c}}, ~150/121 = 372.591{{c}}, ~5/4 = 386.702{{c}}
+: error map: {{val| 0.000 -0.453 +0.388 -1.399 -0.161 }}
+{{Optimal ET sequence|legend=1| 16, 29, 45e, 58, 87, 103, 145, 161, 190 }}
+[[Badness]] (Sintel): 2.582
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 441/440, 847/845, 1001/1000
+Mapping: {{mapping| 1 5 0 -2 3 2 | 0 -11 0 8 -6 -2 | 0 0 1 1 1 1 }}
+Optimal tunings:
+* WE: ~2 = 1200.161{{c}}, ~26/21 = 372.652{{c}}, ~5/4 = 386.381{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~26/21 = 372.593{{c}}, ~5/4 = 386.546{{c}}
+{{Optimal ET sequence|legend=0| 16, 29, 45ef, 58, 87, 103, 145, 161, 190 }}
+Badness (Sintel): 0.944
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 170/169, 221/220, 441/440, 847/845
+Mapping: {{mapping| 1 5 0 -2 3 2 3 | 0 -11 0 8 -6 -2 -4 | 0 0 1 1 1 1 1 }}
+Optimal tunings:
+* WE: ~2 = 1200.375{{c}}, ~21/17 = 372.711{{c}}, ~5/4 = 386.747{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~21/17 = 372.573{{c}}, ~5/4 = 387.138{{c}}
+{{Optimal ET sequence|legend=0| 16, 29g, 45efg, 58, 87g }}
+Badness (Sintel): 1.748
+==== Seminaiadia ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 441/440, 833/832, 847/845, 1001/1000
+Mapping: {{mapping| 1 5 0 -2 3 2 12 | 0 -11 0 8 -6 -2 -18 | 0 0 1 1 1 1 -1 }}
+Optimal tunings:
+* WE: ~2 = 1199.925{{c}}, ~26/21 = 372.566{{c}}, ~5/4 = 387.117{{c}}
+* CWE: ~2 = 1200.000{{c}}, ~26/21 = 372.594{{c}}, ~5/4 = 387.080{{c}}
+{{Optimal ET sequence|legend=0| 16, 29, 45ef, 58, 87, 103, 145, 161, 190 }}
+Badness (Sintel): 1.284
+== References ==
+[[Category:Werckismic temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Werckismic temperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]
-[[Category:Varuna]]
-[[Category:Trimyna]]