Greenwoodmic temperaments: Difference between revisions

m Recategorize
Implement the change proposed in User: FloraC/Temperament extension issues, with explanation
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== Secund ==
== Secund ==
Secund tempers out the greendwoodma, the [[avicennma]], and the [[orwellisma]]. It may be described as the {{nowrap| 9 & 26 }} temperament, with a [[ploidacot]] signature of pentacot. It divides the [[3/2|perfect fifth]] into five [[~]][[16/15]] generators, two for [[7/6]] and three for [[9/7]].  
Secund tempers out the greendwoodma, the [[avicennma]], and the [[orwellisma]]. It may be described as the {{nowrap| 9 & 26 }} temperament, with a [[ploidacot]] signature of pentacot. It divides the [[3/2|perfect fifth]] into five [[~]][[16/15]] generators, two for [[7/6]] and three for [[9/7]]. Related temperaments include [[progression]] and [[jerome]], which only differ by the mapping of 5.
 
The fourth generator step (representing [[45/32]]~[[49/36]]) comes close to [[11/8]]. This allows a simple [[11-limit]] extension in which the generator doubles as [[12/11]], tempering out [[45/44]] and [[99/98]] as is natural for greenwoodmic temperaments. From here, it only makes sense to let the generator take on the additional role of [[13/12]]~[[14/13]], resulting in a full [[13-limit]] temperament.
 
Possible tunings include [[26edo]], [[35edo]] in the 35f val, or anything in between.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 45/44, 99/98, 385/384
Mapping: {{mapping| 1 1 3 2 3 2 | 0 5 -6 7 4 15 }}
Optimal tunings:
* WE: ~2 = 1202.4465{{c}}, ~12/11 = 137.2165{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 137.0309{{c}}
{{Optimal ET sequence|legend=0| 9, 35 }}
Badness (Sintel): 2.05
==== Secundly ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13