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| Octagar temperaments temper out the octagar comma, {{monzo|5 -4 3 -2}} = 4000/3969.
| | This is a collection of temperaments tempering out the octagar comma, {{monzo| 5 -4 3 -2 }} = [[4000/3969]]. |
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| Temperaments discussed elsewhere include [[Garibaldi temperament|garibaldi]], [[Augmented family #Augene|augene]], [[Tetracot family #Octacot|octacot]], [[Orwellismic temperaments #Quartonic|quartonic]], [[superkleismic]], [[Meantone family #Injera|injera]], [[Diaschismic family #Bidia|bidia]], [[Kleismic family #Hemikleismic|hemikleismic]], [[Mirkwai clan #Pluto|pluto]], [[Porcupine family #Nautilus|nautilus]], [[Avicennmic temperaments #Roman|roman]], [[Ripple family|ripple]], and [[Amity family #Hamity|hamity]]. | | Temperaments discussed elsewhere include: |
| | * ''[[Ripple]]'', {36/35, 2560/2401} → [[Ripple family #Septimal ripple|Ripple family]] |
| | * ''[[Nautilus]]'', {49/48, 250/243} → [[Porcupine family #Nautilus|Porcupine family]] |
| | * ''[[Injera]]'', {50/49, 81/80} → [[Meantone family #Injera|Meantone family]] |
| | * ''[[Augene]]'', {64/63, 126/125} → [[Augmented family #Augene|Augmented family]] |
| | * [[Garibaldi temperament|Garibaldi]], {225/224, 3125/3087} → [[Schismatic family #Garibaldi|Schismatic family]] |
| | * ''[[Octacot]]'', {245/243, 2401/2400} → [[Tetracot family #Octacot|Tetracot family]] |
| | * ''[[Roman]]'', {525/512, 3125/3024} → [[Wesley family #Roman|Wesley family]] and [[Avicennmic temperaments #Roman|Avicennmic temperaments]] |
| | * ''[[Superkleismic]]'', {875/864, 1029/1024} → [[Shibboleth family #Superkleismic|Shibboleth family]] and [[Gamelismic clan #Superkleismic|Gamelismic clan]] |
| | * ''[[Quartonic]]'', {1728/1715, 4000/3969} → [[Orwellismic temperaments #Quartonic|Orwellismic temperaments]] |
| | * ''[[Bidia]]'', {2048/2025, 3136/3125} → [[Diaschismic family #Bidia|Diaschismic family]] |
| | * ''[[Hamity]]'', {2430/2401, 4000/3969} → [[Amity family #Hamity|Amity family]] |
| | * ''[[Hemikleismic]]'', {4000/3969, 6144/6125} → [[Kleismic family #Hemikleismic|Kleismic family]] |
| | * ''[[Pluto]]'', {4000/3969, 10976/10935} → [[Mirkwai clan #Pluto|Mirkwai clan]] |
| | * ''[[Quintupole]]'', {4000/3969, 458752/455625} → [[Quintaleap family #Quintupole|Quintaleap family]] |
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| | Considered below are slendi and slithy. |
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| == Slendi == | | == Slendi == |
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| Badness: 0.028492 | | Badness: 0.028492 |
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| == Quintupole ==
| | [[Category:Regular temperament theory]] |
| : ''See also: [[16ed5/2 #Regular temperaments]] or [[34ed7 #Regular temperaments]]''
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| The ''quintupole'' temperament tempers out the octagar comma 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). Proper pronunciation of the word "quintupole" is /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". ''Not to be confused with [[Marvel temperaments #Quintapole|quint<u>'''a'''</u>pole]] temperament (12&85).''
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 4000/3969, 458752/455625
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| [[Mapping]]: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]
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| {{Multival|legend=1| 5 -16 -34 -37 -68 -34 }}
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| [[POTE generator]]: ~135/128 = 99.175
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| {{Vals|legend=1| 12, 97, 109, 121 }}
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| [[Badness]]: 0.111620
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 896/891, 1375/1372, 4375/4356
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| Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]
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| POTE generator: ~35/33 = 99.156
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| Vals: {{Val list| 12, 109, 121, 351bde, 472bdee }}
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| Badness: 0.056501
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 352/351, 364/363, 625/624, 2704/2695
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| Mapping: [{{val|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69}}]
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| POTE generator: ~35/33 = 99.165
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| Vals: {{Val list| 12f, 109, 121 }}
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| Badness: 0.038431
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 256/255, 352/351, 364/363, 375/374, 442/441
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| Mapping: [{{val|1 2 1 0 -1 -2 5}}, {{val|0 -5 16 34 54 69 -11}}]
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| POTE generator: ~18/17 = 99.172
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| Vals: {{Val list| 12f, 109, 121 }}
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| Badness: 0.028721
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| === 19-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374
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| Mapping: [{{val|1 2 1 0 -1 -2 5 4}}, {{val|0 -5 16 34 54 69 -11 3}}]
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| POTE generator: ~18/17 = 99.164
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| Vals: {{Val list| 12f, 109, 121 }}
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| Badness: 0.023818
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| [[Category:Temperament collection]] | | [[Category:Temperament collection]] |
| [[Category:Octagar]] | | [[Category:Octagar temperaments| ]] <!-- main article --> |
| [[Category:Rank 2]] | | [[Category:Rank 2]] |