111edo - 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"

2026-03-13T13:30:04Z

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 13:30, 13 March 2026
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	\| [[Rubidium]]		\| [[Rubidium]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|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

	== Scales ==		== Scales ==

FloraC: Was not wrong

2026-01-06T14:05:26Z

Was not wrong

← Older revision		Revision as of 14:05, 6 January 2026
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	\| [[Rubidium]]		\| [[Rubidium]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first ~~fractional~~ octave, and [[~~Normal~~ forms\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

Lucius Chiaraviglio: /* Rank-2 temperaments */ Fix fractional octave — half-octave was probably copied/pasted from something that actually has half-octaves

2026-01-05T16:43:01Z

Rank-2 temperaments: Fix fractional octave — half-octave was probably copied/pasted from something that actually has half-octaves

← Older revision		Revision as of 16:43, 5 January 2026
Line 528:		Line 528:
	\| [[Rubidium]]		\| [[Rubidium]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first ~~half-~~octave, and [[Normal forms\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first fractional octave, and [[Normal forms\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

FloraC: /* Approximation to JI */ - zeta table

2026-01-05T13:52:38Z

Approximation to JI: - zeta table

@@ Line 319: / Line 319: @@
 === Interval mappings ===
 {{Q-odd-limit intervals}}
 == Regular temperament properties ==

FloraC: /* Regular temperament properties */

2026-01-05T13:52:24Z

Regular temperament properties

← Older revision		Revision as of 13:52, 5 January 2026
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	\| 46\111<br>(1\111)		\| 46\111<br>(1\111)
	\| 497.30<br>(10.81)		\| 497.30<br>(10.81)
	\| 4/3<br>(~~161/160~~~169/168)		\| 4/3<br>(169/168)
	\| [[~~7th-octave temperaments#Rubidium\|~~Rubidium]]		\| [[Rubidium]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[Normal ~~lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

Lucius Chiaraviglio: /* Rank-2 temperaments */ Add Rubidium; also add 161/160 to ratios

2026-01-05T08:14:09Z

Rank-2 temperaments: Add Rubidium; also add 161/160 to ratios

← Older revision		Revision as of 08:14, 5 January 2026
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	\| 1		\| 1
	\| 10.8		\| 10.8
	\| [[121/120]], [[126/125]], [[144/143]], [[169/168]], [[196/195]], [[225/224]]		\| [[121/120]], [[126/125]], [[144/143]], [[161/160]], [[169/168]], [[196/195]], [[225/224]]
	\| {{UDnote\|step=1}}		\| {{UDnote\|step=1}}
	\|-		\|-
Line 535:		Line 535:
	\| 4/3<br>(18/17~19/18)		\| 4/3<br>(18/17~19/18)
	\| [[Misty]]		\| [[Misty]]
			\|-
			\| 37
			\| 46\111<br>(1\111)
			\| 497.30<br>(10.81)
			\| 4/3<br>(161/160~169/168)
			\| [[7th-octave temperaments#Rubidium\|Rubidium]]
	\|}		\|}
	<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 lists\|minimal form]] in parentheses if distinct

Lucius Chiaraviglio: /* Intervals */ 22/19 was in the wrong place

2025-11-06T05:05:39Z

Intervals: 22/19 was in the wrong place

← Older revision		Revision as of 05:05, 6 November 2025
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	\| 23		\| 23
	\| 248.6		\| 248.6
	\| [[15/13]]		\| [[15/13]], [[22/19]]
	\| {{UDnote\|step=23}}		\| {{UDnote\|step=23}}
	\|-		\|-
	\| 24		\| 24
	\| 259.5		\| 259.5
	\| ~~[[22/19]]~~		\|
	\| {{UDnote\|step=24}}		\| {{UDnote\|step=24}}
	\|-		\|-

BudjarnLambeth: Add instruments section

2025-08-02T00:04:35Z

Add instruments section

← Older revision		Revision as of 00:04, 2 August 2025
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	* Direct sunlight (subset of [[Sensi]][19]): 5 7 34 19 5 36 5 ((5, 12, 46, 65, 70, 106, 111)\111)		* Direct sunlight (subset of [[Sensi]][19]): 5 7 34 19 5 36 5 ((5, 12, 46, 65, 70, 106, 111)\111)
	* Hypersakura (subset of Sensi[19]): 5 41 19 5 41 ((5, 46, 65, 70, 111)\111)		* Hypersakura (subset of Sensi[19]): 5 41 19 5 41 ((5, 46, 65, 70, 111)\111)

			== Instruments ==
			* [[Lumatone mapping for 111edo]]

	== Music ==		== Music ==

FloraC: /* Intervals */ 28/23 isn't inconsistent. Note 45/34

2025-04-14T17:06:32Z

Intervals: 28/23 isn't inconsistent. Note 45/34

← Older revision		Revision as of 17:06, 14 April 2025
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	\| 32		\| 32
	\| 345.9		\| 345.9
	\| [[11/9]], ''[[28/23]]'', [[39/32]]		\| [[11/9]], [[28/23]], [[39/32]]
	\| {{UDnote\|step=32}}		\| {{UDnote\|step=32}}
	\|-		\|-
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	\| 45		\| 45
	\| 486.5		\| 486.5
	\| [[65/49]]		\| [[45/34]], [[65/49]]
	\| {{UDnote\|step=45}}		\| {{UDnote\|step=45}}
	\|-		\|-
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	\| …		\| …
	\|}		\|}
	<nowiki/>* As a 23-limit temperament		<nowiki/>* As a 23-limit temperament, inconsistently mapped intervals in ''italic''

	== Approximation to JI ==		== Approximation to JI ==

FloraC: /* Theory */ 23-limit notability

2025-04-14T16:59:34Z

Theory: 23-limit notability

← Older revision		Revision as of 16:59, 14 April 2025
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	== Theory ==		== Theory ==
	111edo is [[consistent]] through to the [[21-odd-limit]], and is the smallest edo [[distinctly consistent]] through the [[15-odd-limit]], marking it as an important higher limit tuning. It has a sharp tendency, with [[harmonic]]s 3 through 19 all tuned sharp. Since {{nowrap\| 111 {{=}} 3 × 37 }}, 111edo shares the mappings for [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] with [[37edo]].		111edo is [[consistent]] through to the [[21-odd-limit]], and is the smallest edo [[distinctly consistent]] through the [[15-odd-limit]], marking it as an important higher limit tuning. It has a sharp tendency, with [[prime harmonic\|primes]] 3 through 19 all tuned sharp. Since {{nowrap\| 111 {{=}} 3 × 37 }}, 111edo shares the mappings for [[5/1\|5]], [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] with [[37edo]].

	It is also significant for lower limits, especially in terms of what it [[tempering out\|tempers out]] in its [[patent val]]; for example, it tempers out [[176/175]] and gives an excellent [[optimal patent val]] for the corresponding [[11-limit]] [[rank-4 temperament]].		It is also significant for lower limits, especially in terms of what it [[tempering out\|tempers out]] in its [[patent val]]; for example, it tempers out [[176/175]] and gives an excellent [[optimal patent val]] for the corresponding [[11-limit]] [[rank-4 temperament]]. In fact in the [[7-limit]] it tempers out [[1728/1715]], [[3136/3125]], and [[5120/5103]], and in the 11-limit, 176/175, [[540/539]], [[1331/1323]], [[1375/1372]].

	~~In fact~~ in the [[~~7-limit~~]] ~~it tempers out~~ [[~~1728~~/~~1715~~]], [[~~3136~~/~~3125~~]], ~~and~~ [[~~5120~~/~~5103~~]], ~~and~~ in the 11-limit, ~~176~~/~~175,~~ [[~~540~~/~~539~~]], ~~1331~~/~~1323~~, [[~~1375~~/~~1372~~]], and ~~notably~~ the [[~~quartisma~~]].		It further tempers out among others [[351/350]], [[352/351]], [[640/637]], [[676/675]], [[847/845]], [[1001/1000]], [[1188/1183]], [[1573/1568]] in the 13-limit; [[256/255]], [[325/324]], [[442/441]] in the 17-limit; [[286/285]], [[400/399]], [[476/475]] in the 19-limit. It excels as a full [[23-limit]] temperament, tempering out [[253/252]] and [[276/275]]. The [[23/1\|23]] is tuned a little flat, unlike the lower primes. [[23/19]], [[23/21]] and their [[octave complement]]s are the only inconsistently mapped intervals in the [[23-odd-limit]].

	It is a particularly good tuning for the 11- or 13-limit versions of [[semisept]], the {{nowrap\| 31 & 80 }} temperament, and [[buzzard]], the {{nowrap\| 53 & 58 }} temperament. [[Gene Ward Smith]]'s trio in [[#Music]] section is in [[guanyin]] temperament, the [[rank-3 temperament]] [[tempering out]] 176/175 and 540/539, for which 111 also provides the optimal patent val.		It is a particularly good tuning for the 11- or 13-limit versions of [[semisept]], the {{nowrap\| 31 & 80 }} temperament, and [[buzzard]], the {{nowrap\| 53 & 58 }} temperament. [[Gene Ward Smith]]'s trio in [[#Music]] section is in [[guanyin]] temperament, the [[rank-3 temperament]] [[tempering out]] 176/175 and 540/539, for which 111 also provides the optimal patent val.