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 }} | ||
| Line 73: | Line 73: | ||
</div></div> | </div></div> | ||
== Eleven-limit extensions == | === Eleven-limit 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, | * 4125/4096 gives unidecimal marvel, | ||
| Line 80: | Line 80: | ||
* 243/242 gives spectacle. | * 243/242 gives spectacle. | ||
= 11-limit (unimarv) = | == 11-limit (unimarv) == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 127: | Line 127: | ||
</div></div> | </div></div> | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 147: | Line 147: | ||
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 | ||
| Line 169: | Line 169: | ||
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 | ||
| Line 185: | Line 185: | ||
</div></div> | </div></div> | ||
=== Enodia === | ==== Enodia ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 199: | Line 199: | ||
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 | ||
| Line 219: | Line 219: | ||
</div></div> | </div></div> | ||
== Isis == | === Isis === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 235: | Line 235: | ||
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 | ||
| Line 255: | Line 255: | ||
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 | ||
| Line 275: | Line 275: | ||
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 | ||
| Line 291: | Line 291: | ||
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 | ||
| Line 319: | Line 319: | ||
[[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 | ||
| Line 341: | Line 341: | ||
</div></div> | </div></div> | ||
= Apollo = | == Apollo == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 359: | Line 359: | ||
[[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 | ||
| Line 375: | Line 375: | ||
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 | ||
| Line 393: | Line 393: | ||
[[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 | ||
| Line 413: | Line 413: | ||
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 | ||
| Line 427: | Line 427: | ||
[[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 | ||
| Line 441: | Line 441: | ||
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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</div></div> | </div></div> | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 497: | Line 497: | ||
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 | ||
| Line 511: | Line 511: | ||
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 | ||
| Line 525: | Line 525: | ||
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 | ||
| Line 541: | Line 541: | ||
[[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 | ||
| Line 568: | Line 568: | ||
[[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 | ||
| Line 584: | Line 584: | ||
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 | ||
| Line 600: | Line 600: | ||
[[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 | ||
| Line 616: | Line 616: | ||
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 630: | ||
{{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 | ||
| Line 644: | Line 644: | ||
{{Val list|legend=1| 9, 20, 22f, 29, 31 }} | {{Val list|legend=1| 9, 20, 22f, 29, 31 }} | ||
== Diana == | === Diana === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 658: | Line 658: | ||
{{Val list|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }} | {{Val list|legend=1| 22, 29, 31, 53, 82e, 84e, 113e, 166ee }} | ||
= Catakleismoid = | == Catakleismoid == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 674: | Line 674: | ||
[[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 690: | Line 690: | ||
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 | ||