Polaris - Revision history

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:27:31Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:27, 29 April 2025
Line 52:		Line 52:
	[[Category:Polaris\| ]] <!-- main article -->		[[Category:Polaris\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup temperaments]]~~		[[Category:Non-octave temperaments]]
	~~[[Category:Nonoctave]]~~
	~~[[Category:Tritave~~-~~equivalent~~ temperaments]]

FloraC: - parent category

2025-04-28T14:33:39Z

- parent category

← Older revision		Revision as of 14:33, 28 April 2025
Line 6:		Line 6:
	{\|class="wikitable"		{\|class="wikitable"
	\|-		\|-
	!Generators up		! Generators up
	!Cents		! Cents
	\|-		\|-
	\|0		\| 0
	\|0.0		\| 0.0
	\|-		\|-
	\|1		\| 1
	\|892.6		\| 892.6
	\|-		\|-
	\|2		\| 2
	\|1785.2		\| 1785.2
	\|-		\|-
	\|3		\| 3
	\|775.8		\| 775.8
	\|-		\|-
	\|4		\| 4
	\|1668.4		\| 1668.4
	\|-		\|-
	\|5		\| 5
	\|659.0		\| 659.0
	\|-		\|-
	\|6		\| 6
	\|1551.6		\| 1551.6
	\|-		\|-
	\|7		\| 7
	\|542.2		\| 542.2
	\|-		\|-
	\|8		\| 8
	\|1434.8		\| 1434.8
	\|-		\|-
	\|9		\| 9
	\|425.4		\| 425.4
	\|-		\|-
	\|10		\| 10
	\|1318.0		\| 1318.0
	\|}		\|}

	== Chords ==		== Chords ==
	Due to equating 7 5/3's with 15/11, Polaris contains an accurate tuning of the chord 33:45:55.		Due to equating 7 5/3's with 15/11, Polaris contains an accurate tuning of the chord 33:45:55.

	== Scales ==		== Scales ==
	* [[Polaris9]]		* [[Polaris9]]
	* [[Polaris11]]		* [[Polaris11]]

	[[Category:~~Temperaments~~]]		[[Category:Polaris\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
			[[Category:Subgroup temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	~~[[Category:Tritave]]~~
	~~[[Category:Rank-2 temperaments]]~~
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

Lériendil at 23:37, 19 April 2025

2025-04-19T23:37:11Z

← Older revision		Revision as of 23:37, 19 April 2025
Line 51:		Line 51:
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Tritave]]		[[Category:Tritave]]
			[[Category:Rank-2 temperaments]]
	[[Category:Tritave-equivalent temperaments]]		[[Category:Tritave-equivalent temperaments]]

BudjarnLambeth: Technical data link

2024-11-02T04:37:39Z

Technical data link

← Older revision		Revision as of 04:37, 2 November 2024
Line 1:		Line 1:
	'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. Good tunings for Polaris are [[15edt]] and [[32edt]].		'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. Good tunings for Polaris are [[15edt]] and [[32edt]].

			Technical data: [[No-twos subgroup temperaments#Polaris]]

	== Interval chain (CTE tuning) ==		== Interval chain (CTE tuning) ==
	{\|class="wikitable"		{\|class="wikitable"

Lériendil at 04:23, 22 August 2024

2024-08-22T04:23:18Z

← Older revision		Revision as of 04:23, 22 August 2024
Line 48:		Line 48:
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Tritave]]		[[Category:Tritave]]
			[[Category:Tritave-equivalent temperaments]]

CompactStar at 07:26, 23 May 2023

2023-05-23T07:26:43Z

← Older revision		Revision as of 07:26, 23 May 2023
Line 40:		Line 40:
	\|}		\|}
	== Chords ==		== Chords ==
	Due to equating 7 5/3's with 15/11, Polaris ~~enables~~ the ~~9:11:15 no-twos otonal~~ chord ~~and its "minor" utonal counterpart 99~~:~~135~~:~~165~~.		Due to equating 7 5/3's with 15/11, Polaris contains an accurate tuning of the chord 33:45:55.
	== Scales ==		== Scales ==
	* [[Polaris9]]		* [[Polaris9]]

CompactStar at 03:33, 1 April 2023

2023-04-01T03:33:55Z

← Older revision		Revision as of 03:33, 1 April 2023
Line 1:		Line 1:
	'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. ~~The smallest EDT that can seriously claim to support~~ Polaris ~~temperament is~~ [[15edt]]~~, with~~ [[32edt]] ~~also being a good option~~.		'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. Good tunings for Polaris are [[15edt]] and [[32edt]].
	== Interval chain (CTE tuning) ==		== Interval chain (CTE tuning) ==
	{\|class="wikitable"		{\|class="wikitable"

CompactStar at 02:46, 31 March 2023

2023-03-31T02:46:05Z

← Older revision		Revision as of 02:46, 31 March 2023
Line 1:		Line 1:
	'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11~~]]. Polaris temperament is to [[Trithagorean]] as [[meantone]] temperament is to [[Pythagorean tuning~~]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option.		'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option.
	== Interval chain (CTE tuning) ==		== Interval chain (CTE tuning) ==
	{\|class="wikitable"		{\|class="wikitable"

CompactStar at 02:37, 31 March 2023

2023-03-31T02:37:53Z

← Older revision		Revision as of 02:37, 31 March 2023
Line 1:		Line 1:
	'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. Polaris temperament is to ~~5/3-Pythagorean~~ [[~~Arcturus~~]] as [[meantone]] temperament is to [[Pythagorean tuning]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option.		'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. Polaris temperament is to [[Trithagorean]] as [[meantone]] temperament is to [[Pythagorean tuning]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option.
	== Interval chain (CTE tuning) ==		== Interval chain (CTE tuning) ==
	{\|class="wikitable"		{\|class="wikitable"

CompactStar at 18:13, 17 March 2023

2023-03-17T18:13:18Z

← Older revision		Revision as of 18:13, 17 March 2023
Line 1:		Line 1:
	'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. Polaris temperament is to [[Arcturus]] as [[meantone]] temperament is to [[Pythagorean tuning]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option.		'''Polaris''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 177147/171875 in the 3.5.11 subgroup, the amount by which 7 [[5/3]]'s fall short of [[15/11]]. Polaris temperament is to 5/3-Pythagorean [[Arcturus]] as [[meantone]] temperament is to [[Pythagorean tuning]]. It contains [[MOS scale]]s of the families [[2L 5s (tritave-equivalent)\|2L 5s<3/1>]], [[2L 7s (tritave-equivalent)\|2L 7s<3/1>]], and [[2L 9s (tritave-equivalent)\|2L 9s<3/1>]]. The hendecatonic scale is generally the most usable of these, with the heptatonic and nonatonic scales usually being lopsided. The smallest EDT that can seriously claim to support Polaris temperament is [[15edt]], with [[32edt]] also being a good option.
	== Interval chain (CTE tuning) ==		== Interval chain (CTE tuning) ==
	{\|class="wikitable"		{\|class="wikitable"