Rhodium: Difference between revisions
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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. | '''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. | ||
For technical data see | For technical data see [[Ragismic microtemperaments #Rhodium]]. | ||
==Theory== | |||
== Theory == | |||
From a classical regular temperament theory perspective, rhodium is just an extension of the [[ennealimmal temperament]], and respectively has the same mappings for the 9edo subset - [[27/25]] for 1\9, [[7/6]] for 2\9, [[63/50]] for third-octave and [[49/36]] for 4\9. | From a classical regular temperament theory perspective, rhodium is just an extension of the [[ennealimmal temperament]], and respectively has the same mappings for the 9edo subset - [[27/25]] for 1\9, [[7/6]] for 2\9, [[63/50]] for third-octave and [[49/36]] for 4\9. | ||
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=== Relationship to Ben Johnston's notation === | === Relationship to Ben Johnston's notation === | ||
Rhodium tempers 65/64 to 1\45 and 33/32 to 2\45. These intervals are used in Ben Johnston notation to translate a nearby simple interval into a usually more complex tridecimal (65/64) or undecimal (33/32) version. As such, using symbols 11 and 13 while playing in rhodium enables modulation by various steps of 45edo. | Rhodium tempers 65/64 to 1\45 and 33/32 to 2\45. These intervals are used in Ben Johnston notation to translate a nearby simple interval into a usually more complex tridecimal (65/64) or undecimal (33/32) version. As such, using symbols 11 and 13 while playing in rhodium enables modulation by various steps of 45edo. | ||
[[Category:Temperaments]] | |||
[[Category:Rhodium| ]] <!-- main article --> | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Quartismic]] | [[Category:Quartismic]] | ||
Revision as of 09:08, 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.
For technical data see Ragismic microtemperaments #Rhodium.
Theory
From a classical regular temperament theory perspective, rhodium is just an extension of the ennealimmal temperament, and respectively has the same mappings for the 9edo subset - 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.
Relationship to Ben Johnston's notation
Rhodium tempers 65/64 to 1\45 and 33/32 to 2\45. These intervals are used in Ben Johnston notation to translate a nearby simple interval into a usually more complex tridecimal (65/64) or undecimal (33/32) version. As such, using symbols 11 and 13 while playing in rhodium enables modulation by various steps of 45edo.