Rastmic rank three clan: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
Move spectacle, mirage and cuckoo here as strong extensions |
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* ''[[Urania]]'', {81/80, 121/120} → [[Didymus rank three family #Urania|Didymus rank-3 family]] | * ''[[Urania]]'', {81/80, 121/120} → [[Didymus rank three family #Urania|Didymus rank-3 family]] | ||
* ''[[Mandos]]'', {176/175, 243/242} → [[Valinorsmic temperaments #Mandos|Valinorsmic temperaments]] | * ''[[Mandos]]'', {176/175, 243/242} → [[Valinorsmic temperaments #Mandos|Valinorsmic temperaments]] | ||
* [[Jove]], {243/242, 441/440} → [[Breed family #Jove|Breed family]] | * [[Jove]], {243/242, 441/440} → [[Breed family #Jove|Breed family]] | ||
* ''[[Hagrid]]'', {243/242, 9801/9800} → [[Cataharry family #Hagrid|Cataharry family]] | * ''[[Hagrid]]'', {243/242, 9801/9800} → [[Cataharry family #Hagrid|Cataharry family]] | ||
* ''[[Betarabian]]'', {243/242, 131769/131072} → [[Alpharabian rank three clan #Betarabian|Alpharabian rank-3 clan]] | * ''[[Betarabian]]'', {243/242, 131769/131072} → [[Alpharabian rank three clan #Betarabian|Alpharabian rank-3 clan]] | ||
== Spectacle == | |||
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 225/224, making it a sort of marvel infested with neutral thirds. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 225/224, 243/242 | |||
{{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 4 5 | 0 0 1 2 0 }} | |||
: mapping generators: ~2, ~11/9, ~5 | |||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 350.0570, ~5/4 = 383.9323 | |||
[[Minimax tuning]]: | |||
* [[11-odd-limit]] | |||
: [{{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 }}] | |||
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.11 | |||
{{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }} | |||
[[Badness]]: 0.499 × 10<sup>-3</sup> | |||
[[Projection pair]]s: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9 | |||
Scales: [[spectacle31]] | |||
[[Associated temperament]]: [[marvo]] | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 225/224, 243/242, 351/350 | |||
Mapping: {{mapping| 1 1 0 -3 2 -5 | 0 2 0 4 5 -2 | 0 0 1 2 0 4 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 349.9247, ~5/4 = 384.3505 | |||
{{Optimal ET sequence|legend=1| 31, 72, 103, 175f }} <nowiki>*</nowiki> | |||
<nowiki>*</nowiki> optimal patent val: [[240edo|240]] | |||
Badness: 1.009 × 10<sup>-3</sup> | |||
== Cuckoo == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 126/125, 243/242 | |||
{{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 -4 5 | 0 0 1 3 0 }} | |||
: mapping generators: ~2, ~11/9, ~5 | |||
{{Optimal ET sequence|legend=1| 24d, 27e, 31, 58, 89, 154, 185 }} | |||
[[Badness]]: 0.933 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 126/125, 196/195, 243/242 | |||
Mapping: {{mapping| 1 1 0 -3 2 -5 | 0 2 0 -4 5 -10 | 0 0 1 3 0 5 }} | |||
{{Optimal ET sequence|legend=1| 27e, 31, 58, 96d, 154 }} | |||
== Mirwomo == | == Mirwomo == | ||
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[[Badness]]: 0.641 × 10<sup>-3</sup> | [[Badness]]: 0.641 × 10<sup>-3</sup> | ||
== Mirage == | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 225/224, 243/242, 385/384 | |||
Mapping: {{mapping| 1 1 3 3 2 0 | 0 6 -7 -2 15 0 | 0 0 0 0 0 1 }} | |||
: mapping generators: ~2, ~15/14, ~13 | |||
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.6327, ~13/8 = 837.7040 | |||
{{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }} | |||
Badness: 0.738 × 10<sup>-3</sup> | |||
== Parahemif == | == Parahemif == | ||