Auk - Revision history

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:19:57Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:19, 29 April 2025
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	[[Category:Auk\| ]] <!-- main article -->		[[Category:Auk\| ]] <!-- main article -->
	~~[[Category:Subgroup temperaments]]~~
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
			[[Category:Non-octave temperaments]]

FloraC: - parent category

2025-04-28T13:46:43Z

- parent category

← Older revision		Revision as of 13:46, 28 April 2025
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	'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. It contains tempered versions of the chords 1-832/729-112/81 (fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81 (fifth-reduction of 1/(13:17:1)).		'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. It contains tempered versions of the chords 1-832/729-112/81 (fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81 (fifth-reduction of 1/(13:17:1)).

	For more technical data, see [[Subgroup temperaments#Auk]].		For more technical data, see [[Subgroup temperaments #Auk]].

	== Interval chain ==		== Interval chain ==
	{\|class="wikitable"		{\|class="wikitable"
	\|-		\|-
	!#		! #
	!Cents		! Cents
	!Approximate ratios		! Approximate ratios
	\|-		\|-
	\|0		\| 0
	\|0.00		\| 0.00
	\|[[1/1]]		\| [[1/1]]
	\|-		\|-
	\|1		\| 1
	\|546.95		\| 546.95
	\|112/81		\| 112/81
	\|-		\|-
	\|2		\| 2
	\|392.94		\| 392.94
	\|[[26/21]], 25088/19683		\| [[26/21]], 25088/19683
	\|-		\|-
	\|3		\| 3
	\|236.93		\| 236.93
	\|832/729		\| 832/729
	\|-		\|-
	\|4		\| 4
	\|81.92		\| 81.92
	\|1352/1323		\| 1352/1323
	\|-		\|-
	\|5		\| 5
	\|628.87		\| 628.87
	\|		\|
	\|-		\|-
	\|6		\| 6
	\|473.86		\| 473.86
	\|		\|
	\|}		\|}

	[[Category:~~Temperaments~~]]		[[Category:Auk\| ]] <!-- main article -->
			[[Category:Subgroup temperaments]]
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]

Lériendil at 22:59, 19 April 2025

2025-04-19T22:59:13Z

← Older revision		Revision as of 22:59, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]

CompactStar at 08:34, 11 May 2023

2023-05-11T08:34:15Z

← Older revision		Revision as of 08:34, 11 May 2023
Line 1:		Line 1:
	'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. ~~For more technical data, see [[Subgroup temperaments#Auk]].~~ It contains tempered versions of the chords 1-832/729-112/81		'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. It contains tempered versions of the chords 1-832/729-112/81 (fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81 (fifth-reduction of 1/(13:17:1)).
	(fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81 (fifth-reduction of 1/(13:17:1)).

			For more technical data, see [[Subgroup temperaments#Auk]].
	== Interval chain ==		== Interval chain ==
	{\|class="wikitable"		{\|class="wikitable"

CompactStar at 08:34, 11 May 2023

2023-05-11T08:34:00Z

← Older revision		Revision as of 08:34, 11 May 2023
Line 1:		Line 1:
	'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]]. It contains tempered versions of the chords 1-832/729-112/81		'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]]. It contains tempered versions of the chords 1-832/729-112/81
	(fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81 (fifth-reduction of 1/(1:7:13)).		(fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81 (fifth-reduction of 1/(13:17:1)).

	== Interval chain ==		== Interval chain ==

CompactStar at 08:33, 11 May 2023

2023-05-11T08:33:54Z

← Older revision		Revision as of 08:33, 11 May 2023
Line 1:		Line 1:
	'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]]. It contains tempered versions of the chords 1-832/729-112/81		'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]]. It contains tempered versions of the chords 1-832/729-112/81
	(fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81.		(fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81 (fifth-reduction of 1/(1:7:13)).

	== Interval chain ==		== Interval chain ==

CompactStar at 08:33, 11 May 2023

2023-05-11T08:33:34Z

← Older revision		Revision as of 08:33, 11 May 2023
Line 1:		Line 1:
	'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]]. It contains a tempered ~~version~~ of the ~~chord~~ 1-832/729-112/81		'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]]. It contains tempered versions of the chords 1-832/729-112/81
	(fifth-reduction of 1:7:13).		(fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81.

	== Interval chain ==		== Interval chain ==

CompactStar at 08:33, 11 May 2023

2023-05-11T08:33:23Z

← Older revision		Revision as of 08:33, 11 May 2023
Line 1:		Line 1:
	'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]].		'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]]. It contains a tempered version of the chord 1-832/729-112/81
			(fifth-reduction of 1:7:13).

	== Interval chain ==		== Interval chain ==

CompactStar at 08:30, 11 May 2023

2023-05-11T08:30:51Z

← Older revision		Revision as of 08:30, 11 May 2023
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	\|		\|
	\|}		\|}

			[[Category:Temperaments]]

CompactStar at 08:30, 11 May 2023

2023-05-11T08:30:39Z

← Older revision		Revision as of 08:30, 11 May 2023
Line 1:		Line 1:
	'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it.		'''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)\|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. For more technical data, see [[Subgroup temperaments#Auk]].

	== Interval chain ==		== Interval chain ==
	{\|class="wikitable"		{\|class="wikitable"