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| == Regular temperaments == | | == Regular temperaments == |
| 16ED5/2 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[Subgroup temperaments|subgroup temperament]] which tempers out 256/255, 361/360, and 4624/4617, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintaleap'' temperament). This temperament is supported by {{Val list|12, 109, 121, 133, 145}}, and [[157edo|157]] EDOs.
| | {{Main| Quintaleap family }} |
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| Tempering out 400/399 (equating 20/19 and 21/20) leads ''[[Octagar temperaments #Quintupole|quintupole]]'' (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads ''[[Hemifamity temperaments #Quinticosiennic|quinticosiennic]]'' (12&145).
| | 16ed5/2 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[subgroup temperament]] which tempers out 256/255, 361/360, and 4624/4617, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintaleap'' temperament). This temperament is supported by {{Val list| 12-, 109-, 121-, 133-, 145- }}, and [[157edo]]. |
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| Another temperament related to 16ED5/2 is ''[[Marvel temperaments #Quintapole|quintapole]]'' (12&85). It is practically identical to the [[18/17s equal temperament #Related temperament|Galilei tuning]], which is generated by the ratios 2/1 and 18/17.
| | Tempering out 400/399 (equating 20/19 and 21/20) leads to ''[[quintupole]]'' (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads to ''[[quinticosiennic]]'' (12&145). |
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| | | Another temperament related to 16ed5/2 is ''[[quintapole]]'' (12&85). It is practically identical to the [[18/17s equal temperament #Related temperament|Galilei tuning]], which is generated by the ratios 2/1 and 18/17. |
| ; <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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| '''2.3.5.17.19 subgroup'''<br>
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| Comma list: 256/255, 361/360, 4624/4617<br>
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| Gencom: [2 18/17; 256/255 361/360 4624/4617]<br>
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| Gencom mapping: [{{val|1 2 1 5 4}}, {{val|0 -5 16 -11 3}}]<br>
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| POTE generator: ~18/17 = 99.276<br>
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| Vals: 12, 109, 121, 133<br>
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| RMS error: 0.3427 cents<br><br>
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| ; <font style="font-size: 1.15em">[[Octagar temperaments #Quintupole|Quintupole]] (12&121)</font>
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| {{See also|34ed7 #34ed7 as a generator}}
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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: ~35/33 = 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: ~35/33 = 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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| ; <font style="font-size: 1.15em">[[Hemifamity temperaments #Quinticosiennic|Quinticosiennic]] (12&145)</font>
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| '''7-limit'''<br>
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| Comma list: 5120/5103, 395136/390625<br>
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| Mapping: [{{val|1 2 1 -1}}, {{val|0 -5 16 46}}]<br>
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| POTE generator: ~135/128 = 99.345<br>
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| Vals: 12, 133, 145, 157, 302c, 459bcc<br>
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| Badness: 0.158041<br><br>
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| '''11-limit'''<br>
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| Comma list: 441/440, 896/891, 78408/78125<br>
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| Mapping: [{{val|1 2 1 -1 -2}}, {{val|0 -5 16 46 66}}]<br>
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| POTE generator: ~35/33 = 99.318<br>
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| Vals: 12, 133, 145<br>
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| Badness: 0.080674<br><br>
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| '''13-limit'''<br>
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| Comma list: 196/195, 352/351, 364/363, 78408/78125<br>
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| Mapping: [{{val|1 2 1 -1 -2 -3}}, {{val|0 -5 16 46 66 81}}]<br>
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| POTE generator: ~35/33 = 99.307<br>
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| Vals: 12f, 133, 145<br>
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| Badness: 0.052464<br><br>
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| '''17-limit'''<br>
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| Comma list: 196/195, 256/255, 352/351, 364/363, 3757/3750<br>
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| Mapping: [{{val|1 2 1 -1 -2 -3 5}}, {{val|0 -5 16 46 66 81 -11}}]<br>
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| POTE generator: ~18/17 = 99.308<br>
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| Vals: 12f, 133, 145<br>
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| Badness: 0.037108<br><br>
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| '''19-limit'''<br>
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| Comma list: 196/195, 256/255, 352/351, 361/360, 364/363, 476/475<br>
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| Mapping: [{{val|1 2 1 -1 -2 -3 5 4}}, {{val|0 -5 16 46 66 81 -11 3}}]<br>
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| POTE generator: ~18/17 = 99.303<br>
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| Vals: 12f, 133, 145<br>
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| Badness: 0.028440<br><br>
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| ; <font style="font-size: 1.15em">[[Marvel temperaments #Quintapole|Quintapole]] (12&85)</font>
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| {{See also|42ed11 #42ed11 as a generator}}
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| '''7-limit'''<br>
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| Comma list: 225/224, 7812500/7411887<br>
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| Mapping: [{{val|1 2 1 1}}, {{val|0 -5 16 22}}]<br>
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| POTE generator: ~21/20 = 98.994<br>
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| Vals: 12, 73c, 85, 97d<br>
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| Badness: 0.192498<br><br>
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| '''11-limit'''<br>
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| Comma list: 100/99, 225/224, 85184/84035<br>
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| Mapping: [{{val|1 2 1 1 0}}, {{val|0 -5 16 22 42}}]<br>
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| POTE generator: ~21/20 = 98.954<br>
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| Vals: 12, 73ce, 85, 97d<br>
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| Badness: 0.104353<br><br>
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| == See also == | | == See also == |