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.

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 [[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.

=== 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.

[[Category:Rank 2]]

[[Category:Quartismic]]

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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.
-edo 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 [[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.
+=== 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.
 [[Category:Rank 2]]
 [[Category:Quartismic]]