Marveltwin: Difference between revisions
Cleanup (3/) |
m Fix linking |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Todo|inline=1| intro }} | |||
== Marveltwin and marvel == | == 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. | 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. | ||
| Line 39: | Line 40: | ||
|} | |} | ||
: 3 pure; 5, 7, 11 and 13 all flat by (325/324)<sup>1/3</sup>, which is 1.778 cents. | : 3 pure; 5, 7, 11 and 13 all flat by (325/324)<sup>1/3</sup>, which is 1.778 cents. | ||
: [[eigenmonzo basis| | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5.11/5.13/5 | ||
[[Complexity spectrum]]: 4/3, 6/5, 10/9, 5/4, 9/8, 8/7, 16/15, 18/13, 13/12, 7/6, 16/13, 7/5, 11/8, 9/7, 12/11, 15/14, 11/10, 11/9, 13/10, 14/13, 15/13, 14/11, 15/11, 13/11 | [[Complexity spectrum]]: 4/3, 6/5, 10/9, 5/4, 9/8, 8/7, 16/15, 18/13, 13/12, 7/6, 16/13, 7/5, 11/8, 9/7, 12/11, 15/14, 11/10, 11/9, 13/10, 14/13, 15/13, 14/11, 15/11, 13/11 | ||
| Line 54: | Line 55: | ||
[[Minimax tuning]]s: | [[Minimax tuning]]s: | ||
* 13-limit | * 13-limit unchanged-interval (eigenmonzo) basis: 2.7.11/5.13/5 | ||
* 15-limit | * 15-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11.15/13 | ||
{{Optimal ET sequence|legend=1| 12, 19, 41, 53, 72, 166 }} | {{Optimal ET sequence|legend=1| 12, 19, 41, 53, 72, 166 }} | ||
| Line 64: | Line 65: | ||
=== 385/384 === | === 385/384 === | ||
[[ | See [[Keenanismic family #Martwin]]. | ||
=== 364/363 === | === 364/363 === | ||
| Line 141: | Line 134: | ||
== Rank-3 temperaments == | == Rank-3 temperaments == | ||
Notable rank-3 temperaments of marveltwin include: | |||
* [[Portent|Portending]] → [[Gamelismic family #Portending|Gamelismic family]] | |||
: +385/384, 441/440 | |||
* [[Marvel|Marvel (hecate)]] → [[Marvel family #Hecate|Marvel family]] | |||
: +225/224, 385/384 | |||
* [[Enlil|Enlil a.k.a. sumatra]] → [[Kleismic rank-3 family #Enlil|Kleismic rank-3 family]] | |||
: +385/384, 625/624 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Commatic realms]] | [[Category:Commatic realms]] | ||
[[Category:Marveltwin]] | [[Category:Marveltwin]] | ||