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|~~11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[~~13-limit|~~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.

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.

=Rank five=

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10^5 * Badness: 68.005

[[Category:~~list~~]]

[[Category:~~marvel~~]]

[[Category:List]]

[[Category:Temperament]]

[[Category:Marvel]]

[[Category:Marveltwin]]

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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|11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit|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.
+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.
 =Rank five=
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 ^5 * Badness: 68.005
-[[Category:list]]
-[[Category:marvel]]
+[[Category:List]]
+[[Category:Temperament]]
+[[Category:Marvel]]
+[[Category:Marveltwin]]