Rhodium: Difference between revisions
This relationship to Ben Johnston's notation is sloppy bs as Ben Johnston's notation is never intended to be used for tempered systems. Modulation is a composing technique that has nothing to do with notation. |
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'''Rhodium''' is a [[rank-2]] [[regular temperament|temperament]] which splits the [[octave]] into 45 parts and has a generator that is mapped to [[55/32]]. It is named after the 45th element by [[Eliora]] in 2023. | '''Rhodium''' is a [[rank-2]] [[regular temperament|temperament]] which splits the [[octave]] into 45 parts and has a generator that is mapped to [[55/32]]. It is named after the 45th element by [[Eliora]] in 2023. | ||
As a [[weak extension]] of the [[ennealimmal]] temperament, rhodium has the same mapping as ennealimmal in the 7-limit – [[27/25]] for 1\9, [[7/6]] for 2\9, [[63/50]] for third-octave and [[49/36]] for 4\9. However, it also provides a mapping of the Alpharabian quarter-tone [[33/32]] to 2\45 and thereby also tempers out the [[quartisma]]. Since rhodium tempers out [[4225/4224]], a single period is mapped to an interval that stands both for ~[[66/65]] and ~[[65/64]] and two of them make 33/32, and ten thus make 7/6. | |||
[[1665edo]] is the optimal patent val for rhodium both in the 11-limit and in the 13-limit. Other notable equal temperaments which support rhodium include [[270edo]] and [[1395edo]], which are [[The Riemann zeta function and tuning|zeta edos]], and [[1125edo]], which while is not zeta, is still a multiple of 45 consistent in the 15-odd-limit. | |||
For technical data see [[Ragismic microtemperaments #Rhodium]]. | |||
[[Category:Rhodium| ]] <!-- main article --> | [[Category:Rhodium| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank-2 temperaments]] | ||
[[Category: | [[Category:Ennealimmal]] | ||