Greenwoodmic temperaments: Difference between revisions
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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. | 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 [[mint temperaments #Progression|progression]] and [[meantone family #Jerome|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. | 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. | ||
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[[Category:Greenwoodmic temperaments| ]] <!-- main article --> | [[Category:Greenwoodmic temperaments| ]] <!-- main article --> | ||
[[Category:Greenwoodmic| ]] <!-- key article --> | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Catalogs of rank-2 temperaments]] | [[Category:Catalogs of rank-2 temperaments]] | ||