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| === Overview to extensions === | | === Overview to extensions === |
| The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 11-limit family member we are looking at. | | The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 11-limit family member we are looking at. 4125/4096 gives unidecimal marvel; 91125/90112 gives prodigy; 5632/5625 gives minerva. These and many others considered below use the same generators as marvel. |
| * 4125/4096 gives unidecimal marvel,
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| * 91125/90112 gives prodigy,
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| * 5632/5625 gives minerva,
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| * 243/242 gives spectacle,
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| as well as others considered below. Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]).
| | Temperaments discussed elsewhere include |
| | * ''[[Supernatural]]'' (+245/243) → [[Keemic family #Supernatural|Keemic family]] |
| | * ''[[Artemis]]'' (+121/120) → [[Biyatismic clan #Artemis|Biyatismic clan]] |
| | * ''[[Spectacle]]'' (+243/242) → [[Rastmic rank three clan #Spectacle|Rastmic rank-3 clan]] |
| | * ''[[Mirage]]'' (+243/242, +385/384) → [[Rastmic rank three clan #Spectacle|Rastmic rank-3 clan]] |
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| == Undecimal marvel (unimarv) == | | == Undecimal marvel (unimarv) == |
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| [[Badness]]: 0.743 × 10<sup>-3</sup> | | [[Badness]]: 0.743 × 10<sup>-3</sup> |
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| == Spectacle ==
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| Spectacle, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_17700.html Yahoo! Tuning Group | ''Spectacle temperament?'']</ref>, can be described as the 31 & 34 & 41 temperament. It tempers out 243/242, making it a sort of marvel infested with neutral thirds.
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| [[Subgroup]]: 2.3.5.7.11
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| [[Comma list]]: 225/224, 243/242
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| {{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 4 5 | 0 0 1 2 0 }}
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| : mapping generators: ~2, ~11/9, ~5
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 350.0570, ~5/4 = 383.9323
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| [[Minimax tuning]]:
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| * [[11-odd-limit]]
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| : [{{monzo| 1 0 0 0 0 }}, {{monzo| 1/5 0 0 0 2/5 }}, {{monzo| 2/5 -2 1 0 4/5 }}, {{monzo| -19/5 -4 2 0 12/5 }}, {{monzo| 0 0 0 0 1 }}]
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| : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.11
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| {{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}
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| [[Badness]]: 0.499 × 10<sup>-3</sup>
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| [[Projection pair]]s: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9
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| Scales: [[spectacle31]]
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| [[Associated temperament]]: [[marvo]]
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 225/224, 243/242, 351/350
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| Mapping: {{mapping| 1 1 0 -3 2 -5 | 0 2 0 4 5 -2 | 0 0 1 2 0 4 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 349.9247, ~5/4 = 384.3505
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| {{Optimal ET sequence|legend=1| 31, 72, 103, 175f }} <nowiki>*</nowiki>
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| <nowiki>*</nowiki> optimal patent val: [[240edo|240]]
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| Badness: 1.009 × 10<sup>-3</sup>
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| == Hestia == | | == Hestia == |
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| Badness: 1.062 × 10<sup>-3</sup> | | Badness: 1.062 × 10<sup>-3</sup> |
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| == Artemis ==
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| [[Subgroup]]: 2.3.5.7.11
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| [[Comma list]]: 121/120, 225/224
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| {{Mapping|legend=1| 1 0 1 -3 2 | 0 1 1 4 1 | 0 0 -2 -4 -1 }}
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| : mapping generators: ~2, ~3, ~11/10
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 699.8719, ~11/10 = 158.3232
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| {{Optimal ET sequence|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }}
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 105/104, 121/120, 196/195
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| Mapping: {{mapping| 1 0 1 -3 2 -5 | 0 1 1 4 1 6 | 0 0 -2 -4 -1 -6 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.7090, ~11/10 = 158.7117
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| {{Optimal ET sequence|legend=1| 9, 20, 22f, 29, 31 }}
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| === Diana ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 121/120, 225/224, 275/273
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| Mapping: {{mapping| 1 0 1 -3 2 7 | 0 1 1 4 1 -2 | 0 0 -2 -4 -1 -1 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.9789, ~11/10 = 159.0048
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| {{Optimal ET sequence|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }}
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| == Morfil == | | == Morfil == |
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| Badness: 0.916 × 10<sup>-3</sup> | | Badness: 0.916 × 10<sup>-3</sup> |
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| == Mirage ==
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 225/224, 243/242, 385/384
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| Mapping: {{mapping| 1 1 3 3 2 0 | 0 6 -7 -2 15 0 | 0 0 0 0 0 1 }}
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| : mapping generators: ~2, ~15/14, ~13
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| Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.6327, ~13/8 = 837.7040
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| {{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
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| Badness: 0.738 × 10<sup>-3</sup>
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| [[Category:Temperament families]] | | [[Category:Temperament families]] |