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Xenharmonic Wiki:Deleted temperament entries: Difference between revisions

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Created page with "These temperament names are no longer in use, although older material may still reference them. If one must refer to these temperaments, it is recommended to do so with an ET join (e. g. "11-limit 12 & 85") or as a restriction of a different temperament (e. g. "no-7s cassandra") == Maqamschismic (2.3.5.11) == Proposed by Eufalesio in 2026, maqamschismic is equivalent to the no-7 cassandra. The 2.3.5.11.13 subgroup adds 352/351 to the comma list and tempers 1..."
 
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Badness (Sintel): 0.862
Badness (Sintel): 0.862
== Quintapole ==
The ''quintapole'' temperament (12&amp;85) tempers out the marvel comma (225/224) and 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the [[Marvel family #Apollo|apollo temperament]], and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). [[User:Xenllium|Xenllium]] proposes the pronunciation of the word "quintapole" as /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". ''Not to be confused with [[#Quintupole|quint<u>'''u'''</u>pole]] temperament (12&amp;121).''
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 7812500/7411887
[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -5 16 22 }}]
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.959¢, ~21/20 = 98.908¢
* [[CWE]]: ~2 = 1200.000¢, ~21/20 = 98.968¢
{{Optimal ET sequence|legend=1| 12, 73c, 85, 97d }}
[[Badness]] (Sintel): 4.872
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 85184/84035
Mapping: [{{val| 1 2 1 1 0 }}, {{val| 0 -5 16 22 42 }}]
Optimal tunings:
* WE: ~2 = 1198.982¢, ~21/20 = 98.870¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.931¢
Optimal ET sequence: {{Optimal ET sequence| 12, 73ce, 85, 97d }}
Badness (Sintel): 3.450
==== Galileic ====
The name ''galileic'' comes from "{{w|Vincenzo Galilei}}", because this temperament is strongly related to [[Galilei's tuning]].
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 225/224, 275/273, 12168/12005
Mapping: [{{val| 1 2 1 1 0 -1 }}, {{val| 0 -5 16 22 42 57 }}]
Optimal tunings:
* WE: ~2 = 1198.912¢, ~21/20 = 98.902¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.970¢
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceff, 85f, 97d }}
Badness (Sintel): 3.231
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 120/119, 225/224, 275/273, 2431/2401
Mapping: [{{val| 1 2 1 1 0 -1 5 }}, {{val| 0 -5 16 22 42 57 -11 }}]
Optimal tunings:
* WE: ~2 = 1198.798¢, ~18/17 = 98.903¢
* CWE: ~2 = 1200.000¢, ~18/17 = 98.986¢
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceffg, 85fg, 97dg }}
Badness (Sintel): 2.997
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 120/119, 225/224, 247/245, 275/273, 361/357
Mapping: [{{val| 1 2 1 1 0 -1 5 4 }}, {{val| 0 -5 16 22 42 57 -11 3 }}]
Optimal tunings:
* WE: ~2 = 1199.031¢, ~18/17 = 98.907¢
* CWE: ~2 = 1200.000¢, ~18/17 = 98.976¢
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceffg, 85fg, 97dg }}
Badness (Sintel): 2.765
==== Catagali ====
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 225/224, 847/845, 1040/1029
Mapping: [{{val| 1 2 1 1 0 0 }}, {{val| 0 -5 16 22 42 45 }}]
Optimal tunings:
* WE: ~2 = 1199.021¢, ~21/20 = 98.801¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.860¢
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ce, 85 }}
Badness (Sintel): 3.065
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 120/119, 225/224, 442/441, 847/845
Mapping: [{{val| 1 2 1 1 0 0 5 }}, {{val| 0 -5 16 22 42 45 -11 }}]
Optimal tunings:
* WE: ~2 = 1198.792¢, ~18/17 = 98.805¢
* CWE: ~2 = 1200.000¢, ~18/17 = 98.887¢
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceg, 85g }}
Badness (Sintel): 2.951
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 120/119, 209/208, 225/224, 361/357, 442/441
Mapping: [{{val| 1 2 1 1 0 0 5 4 }}, {{val| 0 -5 16 22 42 45 -11 3 }}]
Optimal tunings:
* WE: ~2 = 1199.037¢, ~18/17 = 98.808¢
* CWE: ~2 = 1200.000¢, ~18/17 = 98.875¢
Optimal ET sequence: {{Optimal ET sequence| 12f, 73ceg, 85g }}
Badness (Sintel): 2.720
=== Quintain ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/242, 5000/4851
Mapping: [{{val| 1 2 1 1 1 }}, {{val| 0 -5 16 22 30 }}]
Optimal tunings:
* WE: ~2 = 1198.804¢, ~21/20 = 98.718¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.784¢
Optimal ET sequence: {{Optimal ET sequence| 12, 61c, 73c, 85e }}
Badness (Sintel): 3.730
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 245/242, 275/273, 1040/1029
Mapping: [{{val| 1 2 1 1 1 0 }}, {{val| 0 -5 16 22 30 45 }}]
Optimal tunings:
* WE: ~2 = 1198.830¢, ~21/20 = 98.700¢
* CWE: ~2 = 1200.000¢, ~21/20 = 98.768¢
Optimal ET sequence: {{Optimal ET sequence| 12f, 61cf, 73c, 85e }}
Badness (Sintel): 3.302
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