Rastmic rank-3 clan: Difference between revisions

Move 7-limit parents to a dedicated collection page
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== Mirwomo ==
== Mirwomo ==
: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Mirwomo]].''
Mirwomo tempers out 385/384 and may be described as the {{nowrap| 24 & 31 & 41 }} temperament, equating the undecimal quartertone ~33/32 with the septimal quartertone ~36/35.  
Mirwomo tempers out 385/384 and may be described as the {{nowrap| 24 & 31 & 41 }} temperament, equating the undecimal quartertone ~33/32 with the septimal quartertone ~36/35.  


=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 33075/32768
{{Mapping|legend=1| 1 1 0 6 | 0 2 0 -3 | 0 0 1 -1 }}
: mapping generators: ~2, ~128/105, ~5
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.8046{{c}}, ~11/9 = 350.3723{{c}}, ~5/4 = 384.1239{{c}}
: [[error map]]: {{val| +0.805 -0.406 -0.581 -0.848 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.1448{{c}}, ~5/4 = 383.8961{{c}}
: error map: {{val| 0.000 -1.665 -2.418 -3.157 }}
{{Optimal ET sequence|legend=1| 17, 21, 24, 31, 41, 72, 281d, 322cd, 353cd, 425bcdd, 497bcdd }}
[[Badness]] (Sintel): 3.40
=== 11-limit ===
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


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== Parahemif ==
== Parahemif ==
: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Parahemif]].''
Parahemif tempers out 896/891 and may be described as the {{nowrap| 24 & 34d & 41 }} temperament. It is related to [[hemif]], the no-5 rank-2 temperament that tempers out the same list of commas. As such, it finds the interval class of 7 at +13 generator steps, as a semi-augmented sixth (C–At). In the 13-limit, it tempers out 144/143, 352/351, 364/363 among others, and finds ~16/13 at the same neutral third as ~11/9.  
Parahemif tempers out 896/891 and may be described as the {{nowrap| 24 & 34d & 41 }} temperament. It is related to [[hemif]], the no-5 rank-2 temperament that tempers out the same list of commas. As such, it finds the interval class of 7 at +13 generator steps, as a semi-augmented sixth (C–At). In the 13-limit, it tempers out 144/143, 352/351, 364/363 among others, and finds ~16/13 at the same neutral third as ~11/9.  


=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 1605632/1594323
{{Mapping|legend=1| 1 1 0 -1 | 0 2 0 13 | 0 0 1 0 }}
: mapping generators: ~2, ~896/729, ~5
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7303{{c}}, ~896/729 = 351.4056{{c}}, ~5/4 = 386.8527{{c}}
: [[error map]]: {{val| -0.270 +0.586 -0.000 -0.284 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~896/729 = 351.4569{{c}}, ~5/4 = 386.6884{{c}}
: error map: {{val| 0.000 +0.959 +0.375 +0.114 }}
{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }}
[[Badness]] (Sintel): 8.77
=== 11-limit ===
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11