Marvel family: Difference between revisions
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The marvel comma can also be viewed as a comma of the 2.9.25.7 subgroup. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as [[11edo]] and [[17edo]] which are subsets of [[22edo]] and [[34edo]] which temper out the marvel comma. | The marvel comma can also be viewed as a comma of the 2.9.25.7 subgroup. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as [[11edo]] and [[17edo]] which are subsets of [[22edo]] and [[34edo]] which temper out the marvel comma. | ||
== Marvel | == Marvel == | ||
{{main| Marvel }} | {{main| Marvel }} | ||
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Scales: [[marvel9]], [[marvel10]], [[marvel11]], [[marvel12]], [[marvel19]], [[marvel22]], [[pump12_1]], [[pump12_2]], [[pump13]], [[pump14]], [[pump15]], [[pump16]], [[pump17]], [[pump18]] | Scales: [[marvel9]], [[marvel10]], [[marvel11]], [[marvel12]], [[marvel19]], [[marvel22]], [[pump12_1]], [[pump12_2]], [[pump13]], [[pump14]], [[pump15]], [[pump16]], [[pump17]], [[pump18]] | ||
{{Databox|[[Minkowski blocks]]| | |||
{2, 3, 5} subgroup | {2, 3, 5} subgroup | ||
* 8: 16/15, 250/243 | * 8: 16/15, 250/243 | ||
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* 31: 81/80, 34171875/33554432 | * 31: 81/80, 34171875/33554432 | ||
* 41: 34171875/33554432, 3125/3072 | * 41: 34171875/33554432, 3125/3072 | ||
}} | |||
=== Eleven-limit extensions === | === Eleven-limit extensions === | ||
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* 243/242 gives spectacle. | * 243/242 gives spectacle. | ||
== | == Undecimal marvel (unimarv) == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]] | Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]] | ||
{{Databox|Hobbit bases| | |||
{2, 3, 5} subgroup | {2, 3, 5} subgroup | ||
* 12: 128/125, 2048/2025 | * 12: 128/125, 2048/2025 | ||
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* 31: 2109375/2097152, 81/80 | * 31: 2109375/2097152, 81/80 | ||
* 41: 3125/3072, 34171875/33554432 | * 41: 3125/3072, 34171875/33554432 | ||
}} | |||
=== 13-limit === | |||
=== 13-limit | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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* 15-odd-limit eigenmonzo subgroup: 2.15/11.15/13 | * 15-odd-limit eigenmonzo subgroup: 2.15/11.15/13 | ||
{{Val list | Vals: {{Val list| 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff }} | ||
Badness: 0.690 × 10<sup>-3</sup> | Badness: 0.690 × 10<sup>-3</sup> | ||
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Complexity spectrum: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11 | Complexity spectrum: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11 | ||
=== Hecate | === Hecate === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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* 15-odd-limit eigenmonzo subgroup: 2.7.15/13 | * 15-odd-limit eigenmonzo subgroup: 2.7.15/13 | ||
{{Val list | Vals: {{Val list| 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf }} | ||
Badness: 0.721 × 10<sup>-3</sup> | Badness: 0.721 × 10<sup>-3</sup> | ||
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Complexity spectrum: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11 | Complexity spectrum: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11 | ||
==== 17-limit | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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POTE generators: ~3/2 = 700.9619, ~5/4 = 383.0310 | POTE generators: ~3/2 = 700.9619, ~5/4 = 383.0310 | ||
{{Val list | Vals: {{Val list| 19, 22f, 31fg, 41, 53g, 72, 166g, 238cfg, 404ccefgg }} | ||
Badness: 0.869 × 10<sup>-3</sup> | Badness: 0.869 × 10<sup>-3</sup> | ||
==== Enodia ==== | |||
==== Enodia | |||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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POTE generators: ~3/2 = 700.9658, ~5/4 = 383.3063 | POTE generators: ~3/2 = 700.9658, ~5/4 = 383.3063 | ||
{{Val list | Vals: {{Val list| 19g, 22f, 31f, 41g, 53, 72, 166g, 238cfg, 404ccefgg }} | ||
Badness: 0.917 × 10<sup>-3</sup> | Badness: 0.917 × 10<sup>-3</sup> | ||
=== Marvell | === Marvell === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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* 15-odd-limit eigenmonzo subgroup: 2.7.15/13 | * 15-odd-limit eigenmonzo subgroup: 2.7.15/13 | ||
{{Val list | Vals: {{Val list| 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff }} | ||
Badness: 0.862 × 10<sup>-3</sup> | Badness: 0.862 × 10<sup>-3</sup> | ||
=== Isis === | |||
=== Isis | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~3/2 = 701.9156, ~5/4 = 383.2445 | POTE generators: ~3/2 = 701.9156, ~5/4 = 383.2445 | ||
{{Val list | Vals: {{Val list| 10, 19f, 22, 31, 41, 53, 94 }} | ||
Badness: 0.866 × 10<sup>-3</sup> | Badness: 0.866 × 10<sup>-3</sup> | ||
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Projection pairs: 7 225/32 11 4096/375 13 131072/10125 | Projection pairs: 7 225/32 11 4096/375 13 131072/10125 | ||
=== Deecee | === Deecee === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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* 15-odd-limit eigenmonzo subgroup: 2.3.13/5 | * 15-odd-limit eigenmonzo subgroup: 2.3.13/5 | ||
{{Val list | Vals: {{Val list| 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff }} | ||
Badness: 0.920 × 10<sup>-3</sup> | Badness: 0.920 × 10<sup>-3</sup> | ||
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Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875 | Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875 | ||
=== Tripod | === Tripod === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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* 15-odd-limit eigenmonzo subgroup: 2.5/3.13/11 | * 15-odd-limit eigenmonzo subgroup: 2.5/3.13/11 | ||
{{Val list | Vals: {{Val list| 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df }} | ||
Badness: 0.745 × 10<sup>-3</sup> | Badness: 0.745 × 10<sup>-3</sup> | ||
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Projection pairs: 7 225/32 11 4096/375 13 3375/256 | Projection pairs: 7 225/32 11 4096/375 13 3375/256 | ||
=== Marvelcat | === Marvelcat === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~15/13 = 249.7138, ~5/4 = 383.5816 | POTE generators: ~15/13 = 249.7138, ~5/4 = 383.5816 | ||
{{Val list | Vals: {{Val list| 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff }} | ||
Badness: 0.9997 × 10<sup>-3</sup> | Badness: 0.9997 × 10<sup>-3</sup> | ||
== Minerva | == Minerva == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Associated temperament]]: [[Würschmidt family #Würschmidt|würschmidt]] | [[Associated temperament]]: [[Würschmidt family #Würschmidt|würschmidt]] | ||
=== Athene | === Athene === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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* 15-odd-limit eigenmonzo subgroup: 2.11/9.13/7 | * 15-odd-limit eigenmonzo subgroup: 2.11/9.13/7 | ||
{{Val list | Vals: {{Val list| 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def }} | ||
Badness: 0.818 × 10<sup>-3</sup> | Badness: 0.818 × 10<sup>-3</sup> | ||
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Projection pairs: 7 225/32 11 5625/512 13 625/48 | Projection pairs: 7 225/32 11 5625/512 13 625/48 | ||
== Apollo == | |||
== Apollo | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Associated temperament]]: [[Magic family #magic|magic]] | [[Associated temperament]]: [[Magic family #magic|magic]] | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Minimax tuning: 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9 | Minimax tuning: 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9 | ||
{{Val list | Vals: {{Val list| 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef }} | ||
Projection pairs: 7 225/32 11 100/9 13 3200/243 | Projection pairs: 7 225/32 11 100/9 13 3200/243 | ||
== Potassium | == Potassium == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Projection pair]]s: 7 225/32 11 45/4 | [[Projection pair]]s: 7 225/32 11 45/4 | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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* 15-odd-limit eigenmonzo subgroup: 2.9/7.13/9 | * 15-odd-limit eigenmonzo subgroup: 2.9/7.13/9 | ||
{{Val list | Vals: {{Val list| 9, 10, 12f, 19, 31e, 50e }} | ||
Badness: 0.733 × 10<sup>-3</sup> | Badness: 0.733 × 10<sup>-3</sup> | ||
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Projection pairs: 7 225/32 11 45/4 13 3375/256 | Projection pairs: 7 225/32 11 45/4 13 3375/256 | ||
== Malcolm | == Malcolm == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 1.250 × 10<sup>-3</sup> | [[Badness]]: 1.250 × 10<sup>-3</sup> | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~3/2 = 701.8913, ~5/4 = 382.4083 | POTE generators: ~3/2 = 701.8913, ~5/4 = 382.4083 | ||
{{Val list | Vals: {{Val list| 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef }} | ||
Badness: 1.075 × 10<sup>-3</sup> | Badness: 1.075 × 10<sup>-3</sup> | ||
== Prodigy | == Prodigy == | ||
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle. | Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle temperament]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle. | ||
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[[Associated temperament]]: [[Gamelismic clan #Miracle|miracle]] | [[Associated temperament]]: [[Gamelismic clan #Miracle|miracle]] | ||
{{Databox|Hobbit bases| | |||
{2, 3, 5} subgroup | {2, 3, 5} subgroup | ||
* 31: 81/80, 34171875/33554432 | * 31: 81/80, 34171875/33554432 | ||
* 41: 34171875/33554432, 32805/32768 | * 41: 34171875/33554432, 32805/32768 | ||
}} | |||
=== 13-limit === | |||
=== 13-limit | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~3/2 = 700.4006, ~5/4 = 381.4025 | POTE generators: ~3/2 = 700.4006, ~5/4 = 381.4025 | ||
{{Val list | Vals: {{Val list| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff }} | ||
Badness: 0.736 × 10<sup>-3</sup> | Badness: 0.736 × 10<sup>-3</sup> | ||
=== Prodigious | === Prodigious === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~3/2 = 700.3407, ~5/4 = 383.2592 | POTE generators: ~3/2 = 700.3407, ~5/4 = 383.2592 | ||
{{Val list | Vals: {{Val list| 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff }} | ||
Badness: 0.900 × 10<sup>-3</sup> | Badness: 0.900 × 10<sup>-3</sup> | ||
=== Prodigal | === Prodigal === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~3/2 = 699.4864, ~5/4 = 384.0998 | POTE generators: ~3/2 = 699.4864, ~5/4 = 384.0998 | ||
{{Val list | Vals: {{Val list| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }} | ||
Badness: 0.889 × 10<sup>-3</sup> | Badness: 0.889 × 10<sup>-3</sup> | ||
== Fantastic | == Fantastic == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 0.743 × 10<sup>-3</sup> | [[Badness]]: 0.743 × 10<sup>-3</sup> | ||
== Spectacle | == Spectacle == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 0.499 × 10<sup>-3</sup> | [[Badness]]: 0.499 × 10<sup>-3</sup> | ||
Projection | [[Projection pair]]s: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9 | ||
Scales (Scala files): [[spectacle31]] | Scales (Scala files): [[spectacle31]] | ||
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[[Associated temperament]]: [[Marvel temperaments #Marvo|marvo]] | [[Associated temperament]]: [[Marvel temperaments #Marvo|marvo]] | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~11/9 = 349.9247, ~5/4 = 384.3505 | POTE generators: ~11/9 = 349.9247, ~5/4 = 384.3505 | ||
{{Val list | Vals: {{Val list| 31, 72, 103, 175f }} <nowiki>*</nowiki> | ||
<nowiki>*</nowiki> optimal patent val: [[240edo|240]] | |||
Badness: 1.009 × 10<sup>-3</sup> | Badness: 1.009 × 10<sup>-3</sup> | ||
== Hestia | == Hestia == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 1.54 × 10<sup>-3</sup> | [[Badness]]: 1.54 × 10<sup>-3</sup> | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~15/13 = 249.7651, ~5/4 = 383.5558 | POTE generators: ~15/13 = 249.7651, ~5/4 = 383.5558 | ||
{{Val list | Vals: {{Val list| 19, 29, 43, 53, 72, 125f, 197ef, 269cef }} | ||
Badness: 1.062 × 10<sup>-3</sup> | Badness: 1.062 × 10<sup>-3</sup> | ||
== Artemis | == Artemis == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 630: | Line 587: | ||
{{Val list|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }} | {{Val list|legend=1| 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee }} | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~3/2 = 698.7090, ~11/10 = 158.7117 | POTE generators: ~3/2 = 698.7090, ~11/10 = 158.7117 | ||
{{Val list | Vals: {{Val list| 9, 20, 22f, 29, 31 }} | ||
=== Diana === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generators: ~3/2 = 700.9789, ~11/10 = 159.0048 | POTE generators: ~3/2 = 700.9789, ~11/10 = 159.0048 | ||
{{Val list | Vals: {{Val list| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }} | ||
== Catakleismoid == | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 1.275 × 10<sup>-3</sup> | [[Badness]]: 1.275 × 10<sup>-3</sup> | ||
=== 13-limit | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 686: | Line 639: | ||
POTE generators: ~6/5 = 316.7410, ~11/8 = 548.6028 | POTE generators: ~6/5 = 316.7410, ~11/8 = 548.6028 | ||
{{Val list | Vals: {{Val list| 19, 34d, 53, 72, 125f, 197ef, 269cef }} | ||
Badness: 0.916 × 10<sup>-3</sup> | Badness: 0.916 × 10<sup>-3</sup> | ||
== Mirage | == Mirage == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 225/224, 243/242, 385/384 | |||
Mapping: [{{val| 1 1 3 3 2 0 }}, {{val| 0 6 -7 -2 15 0 }}, {{val| 0 0 0 0 0 1 }}] | |||
Mapping generators: ~2, ~15/14, ~13 | Mapping generators: ~2, ~15/14, ~13 | ||
POTE generators: ~15/14 = 116.6327, ~13/8 = 837.7040 | |||
{{Val list | Vals: {{Val list| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }} | ||
Badness: 0.738 × 10<sup>-3</sup> | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||