Marveltwin: Difference between revisions

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== Marveltwin and marvel ==

The marveltwin comma, [[325/324]], bears a curiously close analogy to the marvel comma, [[225/224]]. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.

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=== 385/384 ===

[[~~Subgroup~~]]~~: 2~~.~~3.5.7.11.13~~

See [[Keenanismic family #Martwin]].

~~[[Comma list]]: 325/324, 385/384~~

~~[[Complexity spectrum]]: 4/3, 6/5, 10/9, 5/4, 9/8, 8/7, 11/8, 7/6, 12/11, 16/15, 18/13, 13/12, 9/7, 7/5, 16/13, 11/9, 11/10, 13/11, 14/13, 15/14, 15/11, 13/10, 15/13, 14/11~~

~~{{Optimal ET sequence|legend=1| 7, 15, 19, 26, 34, 41, 46, 53, 72, 87, 140, 159, 212, 299 }}~~

~~[[Badness]]: 2.206 × 10<sup>-6</sup>~~

=== 364/363 ===

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[[Category:Commatic realms]]

[[Category:Marveltwin]]

~~{{Todo| cleanup }}~~

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+{{Todo|inline=1| intro }}
 == Marveltwin and marvel ==
 The marveltwin comma, [[325/324]], bears a curiously close analogy to the marvel comma, [[225/224]]. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel, aka hecate. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.
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 === 385/384 ===
-[[Subgroup]]: 2.3.5.7.11.13
+See [[Keenanismic family #Martwin]].
-[[Comma list]]: 325/324, 385/384
-[[Complexity spectrum]]: 4/3, 6/5, 10/9, 5/4, 9/8, 8/7, 11/8, 7/6, 12/11, 16/15, 18/13, 13/12, 9/7, 7/5, 16/13, 11/9, 11/10, 13/11, 14/13, 15/14, 15/11, 13/10, 15/13, 14/11
-{{Optimal ET sequence|legend=1| 7, 15, 19, 26, 34, 41, 46, 53, 72, 87, 140, 159, 212, 299 }}
-[[Badness]]: 2.206 × 10<sup>-6</sup>
 === 364/363 ===
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 [[Category:Commatic realms]]
 [[Category:Marveltwin]]
-{{Todo| cleanup }}