212edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:41:20Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:41, 13 March 2026
Line 156:		Line 156:
	\| [[Schismerc]] / [[cartography]]		\| [[Schismerc]] / [[cartography]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

Overthink: /* Theory */

2025-10-19T03:53:27Z

Theory

← Older revision		Revision as of 03:53, 19 October 2025
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	It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.		It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.

	To the 13-limit we may add the [[prime harmonic\|prime]] [[23/1\|23]] without introducing too much extra error, tempering out [[484/483]] and [[507/506]]. The 212gh val shows some potential if the full [[23-limit]] is desired, where it ~~notably~~ tempers out [[289/288]] and [[361/360]]. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone. This is related to the fact that 212edo splits steps of 53edo, which are mapped to a syntonic comma, in four.		To the 13-limit we may add the [[prime harmonic\|prime]] [[23/1\|23]] without introducing too much extra error, tempering out [[484/483]] and [[507/506]]. The 212gh val shows some potential if the full [[23-limit]] is desired, where due to the flatness of harmonics 17 and 19, it tempers out the square superparticulars for both of them, being [[289/288]] and [[361/360]] respectively. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone. This is related to the fact that 212edo splits steps of 53edo, which are mapped to a syntonic comma, in four.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Cleanup

2025-08-27T13:28:41Z

Cleanup

← Older revision		Revision as of 13:28, 27 August 2025
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	It [[tempering out\|tempers out]] the same commas ([[15625/15552]], [[32805/32768]], [[amity comma\|1600000/1594323]], etc.) as 53edo in the [[5-limit]]. In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]). In the [[11-limit]], [[385/384]], [[1375/1372]], [[6250/6237]], [[9801/9800]], and [[14641/14580]]; in the [[13-limit]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], and [[10648/10647]].		It [[tempering out\|tempers out]] the same commas ([[15625/15552]], [[32805/32768]], [[amity comma\|1600000/1594323]], etc.) as 53edo in the [[5-limit]]. In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]). In the [[11-limit]], [[385/384]], [[1375/1372]], [[6250/6237]], [[9801/9800]], and [[14641/14580]]; in the [[13-limit]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], and [[10648/10647]].

	It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[~~Kleismic rank three family #Rank-3 kleismic\|~~rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.		It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.

	To the 13-limit we may add the [[prime harmonic\|prime]] [[23/1\|23]] without introducing too much extra error, tempering out [[484/483]] and [[507/506]]. The 212gh val shows some potential if the full [[23-limit]] is desired, where it notably tempers out [[289/288]] and [[361/360]]. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone. This is related to the fact that 212edo splits steps of 53edo, which are mapped to a syntonic comma, in four.		To the 13-limit we may add the [[prime harmonic\|prime]] [[23/1\|23]] without introducing too much extra error, tempering out [[484/483]] and [[507/506]]. The 212gh val shows some potential if the full [[23-limit]] is desired, where it notably tempers out [[289/288]] and [[361/360]]. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone. This is related to the fact that 212edo splits steps of 53edo, which are mapped to a syntonic comma, in four.
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	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
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	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 133:		Line 133:
	\|-		\|-
	\| 2		\| 2
	\| 97\212<br />(9\212)		\| 97\212<br>(9\212)
	\| 549.06<br />(50.94)		\| 549.06<br>(50.94)
	\| 11/8<br />(36/35)		\| 11/8<br>(36/35)
	\| [[Kleischismic]]		\| [[Kleischismic]]
	\|-		\|-
	\| 4		\| 4
	\| 56\212<br />(3\212)		\| 56\212<br>(3\212)
	\| 316.98<br />(16.98)		\| 316.98<br>(16.98)
	\| 6/5<br />(126/125)		\| 6/5<br>(126/125)
	\| [[Quadritikleismic]]		\| [[Quadritikleismic]]
	\|-		\|-
	\| 4		\| 4
	\| 88\212<br />(18\212)		\| 88\212<br>(18\212)
	\| 498.11<br />(101.89)		\| 498.11<br>(101.89)
	\| 4/3<br />(35/33)		\| 4/3<br>(35/33)
	\| [[Quadrant]]		\| [[Quadrant]]
	\|-		\|-
	\| 53		\| 53
	\| 41\212<br />(1\212)		\| 41\212<br>(1\212)
	\| 232.08<br />(5.66)		\| 232.08<br>(5.66)
	\| 8/7<br />(225/224)		\| 8/7<br>(225/224)
	\| [[Schismerc]] / [[cartography]]		\| [[Schismerc]] / [[cartography]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

FloraC: /* Regular temperament properties */ + 23-limit

2025-08-12T20:25:14Z

Regular temperament properties: + 23-limit

← Older revision		Revision as of 20:25, 12 August 2025
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	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 15625/15552, 32805/32768		\| 2401/2400, 15625/15552, 32805/32768
	\| {{~~mapping~~\| 212 336 492 595 }}		\| {{Mapping\| 212 336 492 595 }}
	\| +0.243		\| +0.243
	\| 0.244		\| 0.244
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 385/384, 1375/1372, 6250/6237, 14641/14580		\| 385/384, 1375/1372, 6250/6237, 14641/14580
	\| {{~~mapping~~\| 212 336 492 595 733 }}		\| {{Mapping\| 212 336 492 595 733 }}
	\| +0.325		\| +0.325
	\| 0.273		\| 0.273
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 325/324, 385/384, 625/624, 1375/1372, 10648/10647		\| 325/324, 385/384, 625/624, 1375/1372, 10648/10647
	\| {{~~mapping~~\| 212 336 492 595 733 784 }}		\| {{Mapping\| 212 336 492 595 733 784 }}
	\| +0.396		\| +0.396
	\| 0.296		\| 0.296
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	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 289/288, 325/324, 385/384, 442/441, 625/624, 10648/10647		\| 289/288, 325/324, 385/384, 442/441, 625/624, 10648/10647
	\| {{~~mapping~~\| 212 336 492 595 733 784 866 }} (212g)		\| {{Mapping\| 212 336 492 595 733 784 866 }} (212g)
	\| +0.447		\| +0.447
	\| 0.301		\| 0.301
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	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 289/288, 325/324, 361/360, 385/384, 442/441, 513/512, 625/624		\| 289/288, 325/324, 361/360, 385/384, 442/441, 513/512, 625/624
	\| {{~~mapping~~\| 212 336 492 595 733 784 866 900 }} (212gh)		\| {{Mapping\| 212 336 492 595 733 784 866 900 }} (212gh)
	\| +0.485		\| +0.485
	\| 0.299		\| 0.299
	\| 5.27		\| 5.27
			\|-
			\| 2.3.5.7.11.13.17.19.23
			\| 289/288, 323/322, 325/324, 361/360, 385/384, 442/441, 484/483, 507/506
			\| {{Mapping\| 212 336 492 595 733 784 866 900 959 }} (212gh)
			\| +0.430
			\| 0.321
			\| 5.67
	\|}		\|}
	* 212et (212gh val) has a lower absolute error in the 19-limit than any previous equal temperaments, past [[193edo\|193]] and followed by [[217edo\|217]].		* 212et (212gh val) has a lower absolute error in the 19-limit than any previous equal temperaments, past [[193edo\|193]] and followed by [[217edo\|217]].

FloraC: /* Theory */ full 23-limit isn't too much of a stretch

2025-08-12T20:21:17Z

Theory: full 23-limit isn't too much of a stretch

← Older revision		Revision as of 20:21, 12 August 2025
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	It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[Kleismic rank three family #Rank-3 kleismic\|rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.		It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[Kleismic rank three family #Rank-3 kleismic\|rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.

	The 212gh val shows some potential ~~beyond 15-odd~~-limit. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone. This is related to the fact that 212edo splits steps of 53edo, which are mapped to a syntonic comma, in four.		To the 13-limit we may add the [[prime harmonic\|prime]] [[23/1\|23]] without introducing too much extra error, tempering out [[484/483]] and [[507/506]]. The 212gh val shows some potential if the full [[23-limit]] is desired, where it notably tempers out [[289/288]] and [[361/360]]. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone. This is related to the fact that 212edo splits steps of 53edo, which are mapped to a syntonic comma, in four.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 212 factors into {{~~factorisation~~\|~~212~~}}, 212edo has subset edos {{EDOs\| 2, 4, 53, and 106 }}. As such, it can be used to tune the 53rd-octave [[cartography]] temperament and the 106th-octave [[boiler]] temperment.		Since 212 factors into primes as {{nowrap\| 2<sup>2</sup> × 53 }}, 212edo has subset edos {{EDOs\| 2, 4, 53, and 106 }}. As such, it can be used to tune the 53rd-octave [[cartography]] temperament and the 106th-octave [[boiler]] temperment.

	A step of 212edo is exactly 50 [[türk sent]]s.		A step of 212edo is exactly 50 [[türk sent]]s.

FloraC: /* Theory */ +octave stretch

2025-04-18T14:55:26Z

Theory: +octave stretch

← Older revision		Revision as of 14:55, 18 April 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|212}}		{{Harmonics in equal\|212}}

			=== Octave stretch ===
			212edo can benefit from slightly [[stretched and compressed tuning\|stretching the octave]], using tunings such as [[124edf]] or [[336edt]]. This improves the approximated harmonics 5, 7, 11, 13 and brings the flat mappings of 17 and 19 closer; only the 23 becomes less accurate as it is tuned sharp already.

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 212 factors into {{factorisation\|212}}, 212edo has subset edos {{EDOs\| 2, 4, 53, and 106 }}. As such, it can be used to tune the ~~period~~-53 [[cartography]] temperament and the ~~period~~-~~106~~ [[boiler]] temperment.		Since 212 factors into {{factorisation\|212}}, 212edo has subset edos {{EDOs\| 2, 4, 53, and 106 }}. As such, it can be used to tune the 53rd-octave [[cartography]] temperament and the 106th-octave [[boiler]] temperment.

	A step of 212edo is exactly 50 [[türk sent]]s.		A step of 212edo is exactly 50 [[türk sent]]s.

ArrowHead294 at 14:16, 20 February 2025

2025-02-20T14:16:47Z

← Older revision		Revision as of 14:16, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|212~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T15:31:44Z

Theory: cleanup

← Older revision		Revision as of 15:31, 17 January 2025
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	212edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]] with [[harmonic]]s of 3 through 13 all tuned flat. It shares the [[3/1\|3rd]], [[5/1\|5th]], and [[13/1\|13th]] [[harmonic]]s with [[53edo]], but the mapping differs for [[7/1\|7]] and [[11/1\|11]].		212edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]] with [[harmonic]]s of 3 through 13 all tuned flat. It shares the [[3/1\|3rd]], [[5/1\|5th]], and [[13/1\|13th]] [[harmonic]]s with [[53edo]], but the mapping differs for [[7/1\|7]] and [[11/1\|11]].

	It [[tempers out]] the same commas ([[15625/15552]], [[32805/32768]], [[amity comma\|1600000/1594323]], etc.) as 53edo in the [[5-limit]]. In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]). In the [[11-limit]], [[385/384]], [[1375/1372]], [[6250/6237]], [[9801/9800]], and [[14641/14580]]; in the [[13-limit]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], and [[10648/10647]].		It [[tempering out\|tempers out]] the same commas ([[15625/15552]], [[32805/32768]], [[amity comma\|1600000/1594323]], etc.) as 53edo in the [[5-limit]]. In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]). In the [[11-limit]], [[385/384]], [[1375/1372]], [[6250/6237]], [[9801/9800]], and [[14641/14580]]; in the [[13-limit]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], and [[10648/10647]].

	It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[Kleismic rank three family #Rank-3 kleismic\|rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.		It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[Kleismic rank three family #Rank-3 kleismic\|rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|212~~\|columns=11~~}}		{{Harmonics in equal\|212}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294 at 14:49, 16 January 2025

2025-01-16T14:49:11Z

← Older revision		Revision as of 14:49, 16 January 2025
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	== Theory ==		== Theory ==
	212edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]] with [[harmonic]]s of 3 through 13 all tuned flat. ~~212 = 4 × 53, and it~~ shares the [[3/1\|3rd]], [[5/1\|5th]], and [[13/1\|13th]] [[harmonic]]s with [[53edo]], but the mapping differs for [[7/1\|7]] and [[11/1\|11]].		212edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]] with [[harmonic]]s of 3 through 13 all tuned flat. It shares the [[3/1\|3rd]], [[5/1\|5th]], and [[13/1\|13th]] [[harmonic]]s with [[53edo]], but the mapping differs for [[7/1\|7]] and [[11/1\|11]].

	~~The equal temperament~~ [[~~tempering out\|~~tempers out]] the same commas ([[15625/15552]], [[32805/32768]], [[amity comma\|1600000/1594323]], etc.) as 53edo in the [[5-limit]]. In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]). In the [[11-limit]], [[385/384]], [[1375/1372]], [[6250/6237]], [[9801/9800]] and [[14641/14580]]; in the [[13-limit]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]] and [[10648/10647]].		It [[tempers out]] the same commas ([[15625/15552]], [[32805/32768]], [[amity comma\|1600000/1594323]], etc.) as 53edo in the [[5-limit]]. In the [[7-limit]], it tempers out 2401/2400 ([[breedsma]]), 390625/388962 ([[dimcomp comma]]), and 4802000/4782969 ([[canousma]]). In the [[11-limit]], [[385/384]], [[1375/1372]], [[6250/6237]], [[9801/9800]], and [[14641/14580]]; in the [[13-limit]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], and [[10648/10647]].

	It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[Kleismic rank three family #Rank-3 kleismic\|rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.		It is the [[optimal patent val]] for 7- and 13-limit [[quadritikleismic]] temperament, the 7-limit [[Kleismic rank three family #Rank-3 kleismic\|rank-3 kleismic]] temperament, and the 13-limit rank-3 [[agni]] temperament. It enables [[marveltwin chords]], [[keenanismic chords]], [[sinbadmic chords]], and [[lambeth chords]] in the 13-odd-limit in addition to [[island chords]] in the 15-odd-limit.
Line 15:		Line 15:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 212 factors into ~~2<sup>2</sup> × 53~~, 212edo has subset edos {{EDOs\| 2, 4, 53, and 106 }}. As such, it can be used to tune the period-53 [[cartography]] temperament and the period-106 [[boiler]] temperment.		Since 212 factors into {{factorisation\|212}}, 212edo has subset edos {{EDOs\| 2, 4, 53, and 106 }}. As such, it can be used to tune the period-53 [[cartography]] temperament and the period-106 [[boiler]] temperment.

	A step of 212edo is exactly 50 [[türk sent]]s.		A step of 212edo is exactly 50 [[türk sent]]s.
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	\| [[Schismerc]] / [[cartography]]		\| [[Schismerc]] / [[cartography]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

ArrowHead294 at 12:03, 16 November 2024

2024-11-16T12:03:24Z

← Older revision		Revision as of 12:03, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
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	\| 0.299		\| 0.299
	\| 5.27		\| 5.27
	~~{{comma basis end}~~}		\|}
	* 212et (212gh val) has a lower absolute error in the 19-limit than any previous equal temperaments, past [[193edo\|193]] and followed by [[217edo\|217]].		* 212et (212gh val) has a lower absolute error in the 19-limit than any previous equal temperaments, past [[193edo\|193]] and followed by [[217edo\|217]].

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	Note: temperaments supported by 53et are not included.		Note: temperaments supported by 53et are not included.

	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 8/7<br />(225/224)		\| 8/7<br />(225/224)
	\| [[Schismerc]] / [[cartography]]		\| [[Schismerc]] / [[cartography]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==