Rhodium - Revision history

Overthink: fix link

2026-03-22T03:25:14Z

fix link

← Older revision		Revision as of 03:25, 22 March 2026
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	[[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.

	For technical data see [[~~Ragismic microtemperaments~~ #Rhodium]].		For technical data see [[Septiennealimmal clan #Rhodium]].

	[[Category:Rhodium\| ]] <!-- main article -->		[[Category:Rhodium\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]

FloraC: - parent category

2025-04-28T14:38:12Z

- parent category

← Older revision		Revision as of 14:38, 28 April 2025
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	For technical data see [[Ragismic microtemperaments #Rhodium]].		For technical data see [[Ragismic microtemperaments #Rhodium]].

	~~[[Category:Temperaments]]~~
	[[Category:Rhodium\| ]] <!-- main article -->		[[Category:Rhodium\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Quartismic~~]]		[[Category:Ennealimmal]]

Lériendil at 23:41, 19 April 2025

2025-04-19T23:41:34Z

← Older revision		Revision as of 23:41, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Rhodium\| ]] <!-- main article -->		[[Category:Rhodium\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank-2 temperaments]]
	[[Category:Quartismic]]		[[Category:Quartismic]]

FloraC: This doesn't warrant a section

2024-07-21T09:27:14Z

This doesn't warrant a section

← Older revision		Revision as of 09:27, 21 July 2024
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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.

	~~For technical data see~~ [[~~Ragismic microtemperaments #Rhodium~~]].		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.

	~~== Theory ==~~		[[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.
	~~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.		For technical data see [[Ragismic microtemperaments #Rhodium]].

	[[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:Temperaments]]		[[Category:Temperaments]]

FloraC: 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.

2024-07-21T09:11:40Z

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.

← Older revision		Revision as of 09:11, 21 July 2024
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	[[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:Temperaments]]		[[Category:Temperaments]]

FloraC: Rework on intro

2024-07-21T09:08:26Z

Rework on intro

← Older revision		Revision as of 09:08, 21 July 2024
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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: [[Ragismic microtemperaments#Rhodium]]		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]]

Eliora: /* Theory */

2023-07-31T00:06:04Z

Theory

← Older revision		Revision as of 00:06, 31 July 2023
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	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.

	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.		[[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.

Eliora: /* Theory */ figured this is notable

2023-07-31T00:05:46Z

Theory: figured this is notable

← Older revision		Revision as of 00:05, 31 July 2023
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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.		[[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:Rank 2]]
	[[Category:Quartismic]]		[[Category:Quartismic]]

Eliora at 20:08, 28 February 2023

2023-02-28T20:08:41Z

← Older revision		Revision as of 20:08, 28 February 2023
Line 6:		Line 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.		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]]

Eliora at 19:56, 28 February 2023

2023-02-28T19:56:43Z

← Older revision		Revision as of 19:56, 28 February 2023
Line 1:		Line 1:
	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 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==		==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.