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. |
This doesn't warrant a section |
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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:Temperaments]] | [[Category:Temperaments]] | ||
Revision as of 09:27, 21 July 2024
Rhodium is a rank-2 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 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.