Equivalence continuum: Difference between revisions
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An '''equivalence continuum''' is the space of all rank-''k'' temperaments on a specified [[JI subgroup]] that are supported by a specified temperament of a lower rank on the same subgroup (such as an [[edo]] viewed as a temperament on said subgroup). This term was first used by [[ | An '''equivalence continuum''' is the space of all rank-''k'' temperaments on a specified [[JI subgroup]] that are supported by a specified temperament of a lower rank on the same subgroup (such as an [[edo]] viewed as a temperament on said subgroup). This term was first used by [[Mike Battaglia]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_99315.html Yahoo! Tuning Group | ''Some new 5-limit microtemperaments'']</ref><ref>[https://en.xen.wiki/index.php?title=Temperament_orphanage&oldid=27177 Xenharmonic Wiki | ''Temperament orphanage''] – first occurrence on this wiki, same date as the thread above. </ref>. | ||
Examples: | Examples: | ||
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* [[hemithirds]] tempers out 1029/1024 = '''u'''<sub>''z''</sub> = (0, 0, 1) and 3136/3125 = 2'''u'''<sub>''x''</sub> + '''u'''<sub>''y''</sub> = (2, 1, 0). This corresponds to '''v''' = (1, −2, 0). | * [[hemithirds]] tempers out 1029/1024 = '''u'''<sub>''z''</sub> = (0, 0, 1) and 3136/3125 = 2'''u'''<sub>''x''</sub> + '''u'''<sub>''y''</sub> = (2, 1, 0). This corresponds to '''v''' = (1, −2, 0). | ||
* [[miracle]] tempers out 1029/1024 = '''u'''<sub>''z''</sub> = (0, 0, 1) and 225/224 = '''u'''<sub>''x''</sub> − '''u'''<sub>''y''</sub> = (1, −1, 0). This corresponds to '''v''' = (1, 1, 0). | * [[miracle]] tempers out 1029/1024 = '''u'''<sub>''z''</sub> = (0, 0, 1) and 225/224 = '''u'''<sub>''x''</sub> − '''u'''<sub>''y''</sub> = (1, −1, 0). This corresponds to '''v''' = (1, 1, 0). | ||
== Notes == | |||
[[Category:Math]] | [[Category:Math]] | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Equivalence continua| ]] <!-- main article --> | [[Category:Equivalence continua| ]] <!-- main article --> | ||