Rhodium: Difference between revisions

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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.

[[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 [[zeta edo]]s, and [[1125edo]], which while is not zeta, is still a multiple of 45 consistent in the 15-odd-limit.

For technical data see [[Septiennealimmal clan #Rhodium]].

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 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.
+[[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 [[zeta edo]]s, and [[1125edo]], which while is not zeta, is still a multiple of 45 consistent in the 15-odd-limit.
 For technical data see [[Septiennealimmal clan #Rhodium]].