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| == Regular temperaments == | | == Regular temperaments == |
| {{See also|16ed5/2 #Regular temperaments}} | | {{See also| Quintaleap family }} |
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| 34ED7 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintupole'' temperament). This temperament is supported by [[12edo|12EDO]], [[109edo|109EDO]], and [[121edo|121EDO]] among others. | | 34ED7 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 896/891, 1375/1372, and 4375/4356, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''[[Quintaleap family #Quintupole|quintupole]]'' temperament). This temperament is supported by [[12edo|12EDO]], [[109edo|109EDO]], and [[121edo|121EDO]] among others. |
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| ; <font style="font-size: 1.15em">[[High badness temperaments #Quintaleap|Quintaleap]] (12&121)</font>
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| '''5-limit'''<br>
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| Comma: {{monzo|37 -16 -5}} = 137438953472/134521003125<br>
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| Mapping: [{{val|1 2 1}}, {{val|0 -5 16}}]<br>
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| POTE generator: ~135/128 = 99.267<br>
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| Vals: 12, 85, 97, 109, 121, 133, 278c, 411bc, 544bc<br>
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| Badness: 0.444506<br><br>
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| ; <font style="font-size: 1.15em">[[Octagar temperaments #Quintupole|Quintupole]] (12&121)</font>
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| '''7-limit'''<br>
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| Comma list: 4000/3969, 458752/455625<br>
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| Mapping: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]<br>
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| POTE generator: ~135/128 = 99.175<br>
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| Vals: 12, 97, 109, 121<br>
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| Badness: 0.111620<br><br>
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| '''11-limit'''<br>
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| Comma list: 896/891, 1375/1372, 4375/4356<br>
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| Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]<br>
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| POTE generator: ~132/125 = 99.156<br>
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| Vals: 12, 109, 121, 351bde, 472bdee<br>
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| Badness: 0.056501<br><br>
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| '''13-limit'''<br>
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| Comma list: 352/351, 364/363, 625/624, 2704/2695<br>
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| Mapping: [{{val|1 2 1 0 -1 -2}}, {{val|0 -5 16 34 54 69}}]<br>
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| POTE generator: ~55/52 = 99.165<br>
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| Vals: 12f, 109, 121<br>
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| Badness: 0.038431<br><br>
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| '''17-limit'''<br>
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| Comma list: 256/255, 352/351, 364/363, 375/374, 442/441<br>
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| Mapping: [{{val|1 2 1 0 -1 -2 5}}, {{val|0 -5 16 34 54 69 -11}}]<br>
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| POTE generator: ~18/17 = 99.172<br>
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| Vals: 12f, 109, 121<br>
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| Badness: 0.028721<br><br>
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| '''19-limit'''<br>
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| Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374<br>
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| Mapping: [{{val|1 2 1 0 -1 -2 5 4}}, {{val|0 -5 16 34 54 69 -11 3}}]<br>
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| POTE generator: ~18/17 = 99.164<br>
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| Vals: 12f, 109, 121<br>
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| Badness: 0.023818<br><br>
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| == See also == | | == See also == |