Greenwoodmic temperaments: Difference between revisions
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Temperaments discussed elsewhere are | Temperaments discussed elsewhere are | ||
* ''[[ | * ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism|Archytas clan]] | ||
* ''[[Superpelog]]'' (+49/48) → [[Semaphoresmic clan #Superpelog|Semaphoresmic clan]] | * ''[[Superpelog]]'' (+49/48) → [[Semaphoresmic clan #Superpelog|Semaphoresmic clan]] | ||
* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]] | * ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]] | ||
* ''[[ | * ''[[August]]'' (+36/35) → [[Augmented family #August|Augmented family]] | ||
* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi|Dicot family]] | |||
* ''[[Ripple]]'' (+126/125) → [[Ripple family #Septimal ripple|Ripple family]] | |||
* ''[[Wesley]]'' (+875/864) → [[Wesley family #Septimal wesley|Wesley family]] | |||
* ''[[Greenwood]]'' (+1323/1280) → [[Whitewood family #Greenwood|Whitewood family]] | * ''[[Greenwood]]'' (+1323/1280) → [[Whitewood family #Greenwood|Whitewood family]] | ||
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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]]. 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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Badness (Sintel): 1.41 | Badness (Sintel): 1.41 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness (Sintel): 4.38 | Badness (Sintel): 4.38 | ||
[[Category:Greenwoodmic temperaments| ]] <!-- main article --> | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category: | [[Category:Catalogs of rank-2 temperaments]] | ||