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Quintaleap family: Difference between revisions

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{{Main| Quintupole }}
{{Main| Quintupole }}


The ''quintupole'' temperament tempers out the octagar comma (4000/3969) and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth|polypyth]] fourth (~4/3, about 495.8 cents). [[User:Xenllium|Xenllium]] proposes the pronunciation of the word "quintupole" as /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". ''Not to be confused with [[#Quintapole|quint<u>'''a'''</u>pole]] temperament (12&amp;85).''
The ''quintupole'' temperament tempers out the octagar comma (4000/3969) and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means ''five poles'', but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the [[Porwell temperaments #Polypyth|polypyth]] fourth (~4/3, about 495.8 cents).  


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
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Badness (Sintel): 1.449
Badness (Sintel): 1.449
== 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


== Quinticosiennic ==
== Quinticosiennic ==
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