Rhodium: Difference between revisions
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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. | 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. | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Quartismic]] | [[Category:Quartismic]] | ||
Revision as of 20:08, 28 February 2023
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.
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.