Luna family: Difference between revisions

+Semiluna temperament
Hemithirds: update
Line 13: Line 13:


= Hemithirds =
= Hemithirds =
{{main|Hemithirds}}
{{main| Hemithirds }}
{{see also|Gamelismic clan #Hemithirds}}
{{see also| Hemimean clan #Hemithirds }}


Commas: 1029/1024, 3136/3125
Subgroup: 2.3.5.7


POTE generator: ~28/25 = 193.244
[[Comma list]]: 1029/1024, 3136/3125


Map: [<1 4 2 2|, <0 -15 2 5|]
[[Mapping]]: [{{val| 1 4 2 2 }}, {{val| 0 -15 2 5 }}]


Wedgie: <<15 -2 -5 -38 -50 -6||
{{Multival|legend=1| 15 -2 -5 -38 -50 -6 }}


EDOs: {{EDOs|31, 87, 118}}
[[POTE generator]]: ~28/25 = 193.244
 
[[Minimax tuning]]:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 11/5 -1/10 0 1/10 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [[Eigenmonzo]]s: 2, 7/6
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 82/35 -4/35 0 2/35 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 7/6
 
{{Val list|legend=1| 31, 87, 118 }}


Badness: 0.0443
Badness: 0.0443


== 11-limit ==
== 11-limit ==
Commas: 385/384, 441/440, 3136/3125
 
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 3136/3125
 
Mapping: [{{val| 1 4 2 2 7 }}, {{val| 0 -15 2 5 -22 }}]


POTE generator: ~28/25 = 193.227
POTE generator: ~28/25 = 193.227


Map: [<1 4 2 2 7|, <0 -15 2 5 -22|]
Minimax tuning:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}]
: Eigenmonzos: 2, 11/7


EDOs: {{EDOs|31, 87, 118}}
{{Val list|legend=1| 31, 87, 118 }}


Badness: 0.0190
Badness: 0.0190


== 13-limit ==
== 13-limit ==
Commas: 196/195, 352/351, 1001/1000, 1029/1024
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 385/384, 625/624
 
Mapping: [{{val| 1 4 2 2 7 0 }}, {{val| 0 -15 2 5 -22 23 }}]


POTE generator: ~28/25 = 193.166
POTE generator: ~28/25 = 193.166


Map: [<1 4 2 2 7 0|, <0 -15 2 5 -22 23|]
{{Val list|legend=1| 31, 56, 87, 118, 205d }}
 
EDOs: {{EDOs|31, 56, 87, 118, 205d}}


Badness: 0.0217
Badness: 0.0217