22/21 - Revision history

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:01:43Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:01, 3 November 2025
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	== Approximation ==		== Approximation ==
	10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s.		10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s.
	{{~~Interval_Edo_Approximation~~ \| 22/21}}		{{Interval edo approximation\|22/21}}

	== See also ==		== See also ==

Pailiaq: /* Approximation */

2025-11-03T06:34:41Z

Approximation

← Older revision		Revision as of 06:34, 3 November 2025
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	== Approximation ==		== Approximation ==
	10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s.		10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s.
			{{Interval_Edo_Approximation \| 22/21}}

	== See also ==		== See also ==

Fitzgerald Lee: Removed obvious fact, added two differences between two intervals

2025-04-09T11:13:11Z

Removed obvious fact, added two differences between two intervals

← Older revision		Revision as of 11:13, 9 April 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''22/21''' is a small [[superparticular]] [[semitone (interval region)\|semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It ~~makes~~ the difference between ~~the 21st~~ and ~~22nd~~ [[~~harmonic~~]]s.		'''22/21''' is a small [[superparticular]] [[semitone (interval region)\|semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It is the difference between [[12/11]] and [[8/7]], or between [[7/6]] and [[11/9]].

	In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the [[256/243\|Pythagorean minor second (256/243)]] by a [[896/891\|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.		In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the [[256/243\|Pythagorean minor second (256/243)]] by a [[896/891\|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.

	Furthermore, it is close in size to [[21/20]], a 7-limit superparticular interval most commonly treated as a minor second, differing from it by [[441/440]], about 3.9¢. The single degree of [[88cET]] can function as both 21/20 and 22/21, thus [[tempering out]] 441/440.		Furthermore, it is close in size to [[21/20]], a 7-limit superparticular interval most commonly treated as a minor second, differing from it by [[441/440]], about 3.9¢. The single degree of [[88cET]] can function as both 21/20 and 22/21, thus [[tempering out]] 441/440.

	== Approximation ==		== Approximation ==

FloraC: Update linking

2025-02-26T16:39:54Z

Update linking

← Older revision		Revision as of 16:39, 26 February 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
			'''22/21''' is a small [[superparticular]] [[semitone (interval region)\|semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It makes the difference between the 21st and 22nd [[harmonic]]s.
	'''22/21''' is a small [[superparticular]] [[semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It makes the difference between the 21st and 22nd [[harmonic]]s.

	In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the [[256/243\|Pythagorean minor second (256/243)]] by a [[896/891\|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.		In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the [[256/243\|Pythagorean minor second (256/243)]] by a [[896/891\|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.

FloraC: -typo; +link

2024-10-25T08:38:37Z

-typo; +link

← Older revision		Revision as of 08:38, 25 October 2024
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	In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the [[256/243\|Pythagorean minor second (256/243)]] by a [[896/891\|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.		In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the [[256/243\|Pythagorean minor second (256/243)]] by a [[896/891\|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.

	~~Further more~~, it is close in size to [[21/20]], a 7-limit superparticular interval most commonly treated as a minor second, differing from it by [[441/440]], about 3.9¢. The single degree of [[88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440.		Furthermore, it is close in size to [[21/20]], a 7-limit superparticular interval most commonly treated as a minor second, differing from it by [[441/440]], about 3.9¢. The single degree of [[88cET]] can function as both 21/20 and 22/21, thus [[tempering out]] 441/440.

	== Approximation ==		== Approximation ==

FloraC: Rework; +"undecimal minor semitone", +"pentacircle minor second" and reasons

2024-10-25T08:32:49Z

Rework; +"undecimal minor semitone", +"pentacircle minor second" and reasons

← Older revision		Revision as of 08:32, 25 October 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = small undecimal semitone		\| Name = small undecimal semitone, undecimal minor semitone, pentacircle minor second
	\| Color name = 1or1, loru unison		\| Color name = 1or1, loru unison
	\| Sound = jid_22_21_pluck_adu_dr220.mp3		\| Sound = jid_22_21_pluck_adu_dr220.mp3
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	}}		}}

	'''22/21''' is a small [[superparticular]] ~~'''~~semitone~~'''~~ of about 80.5¢ that appears in [[11-limit]] [[just intonation]]. It makes the difference between the 21st and 22nd [[harmonic]]s~~. It is close in size to [[21/20]], a 7-limit superparticular interval, differing from it by [[441/440]], about 3.9¢~~.		'''22/21''' is a small [[superparticular]] [[semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It makes the difference between the 21st and 22nd [[harmonic]]s.

	~~The single degree of~~ [[~~88cET~~]] ~~can function~~ as ~~both 21~~/20 and 22/21, ~~thus tempering out 441~~/~~440~~.		In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32\|undecimal quartertone (33/32)]] and a [[64/63\|septimal comma (64/63)]], neither of which changes the [[scale\|scale degree]] or [[interval quality\|quality]]. However, it is only flat of the [[256/243\|Pythagorean minor second (256/243)]] by a [[896/891\|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''.

			Further more, it is close in size to [[21/20]], a 7-limit superparticular interval most commonly treated as a minor second, differing from it by [[441/440]], about 3.9¢. The single degree of [[88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440.

			== Approximation ==
	10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s.		10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s.

BudjarnLambeth: Comma = yes (listed on medium commas page for a long time)

2024-10-14T04:57:36Z

Comma = yes (listed on medium commas page for a long time)

← Older revision		Revision as of 04:57, 14 October 2024
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	\| Color name = 1or1, loru unison		\| Color name = 1or1, loru unison
	\| Sound = jid_22_21_pluck_adu_dr220.mp3		\| Sound = jid_22_21_pluck_adu_dr220.mp3
			\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T12:38:14Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 12:38, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 22/21~~
	~~\| Monzo = 1 -1 0 -1 1~~
	~~\| Cents = 80.53704~~
	\| Name = small undecimal semitone		\| Name = small undecimal semitone
	\| Color name = 1or1, loru unison		\| Color name = 1or1, loru unison
	~~\| FJS name = P1<sup>11</sup><sub>7</sub>~~
	\| Sound = jid_22_21_pluck_adu_dr220.mp3		\| Sound = jid_22_21_pluck_adu_dr220.mp3
	}}		}}
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	~~[[Category:11-limit]]~~
	[[Category:Semitone]]		[[Category:Semitone]]
	~~[[Category:Superparticular]]~~

TallKite: corrected the color name from semitone to unison

2022-02-13T05:16:56Z

corrected the color name from semitone to unison

← Older revision		Revision as of 05:16, 13 February 2022
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	\| Cents = 80.53704		\| Cents = 80.53704
	\| Name = small undecimal semitone		\| Name = small undecimal semitone
	\| Color name = 1or1, loru ~~semitone~~		\| Color name = 1or1, loru unison
	\| FJS name = P1<sup>11</sup><sub>7</sub>		\| FJS name = P1<sup>11</sup><sub>7</sub>
	\| Sound = jid_22_21_pluck_adu_dr220.mp3		\| Sound = jid_22_21_pluck_adu_dr220.mp3

Fredg999: Order of categories

2021-12-15T18:29:55Z

Order of categories

← Older revision		Revision as of 18:29, 15 December 2021
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

			[[Category:11-limit]]
	[[Category:Semitone]]		[[Category:Semitone]]
	~~[[Category:11-limit]]~~
	[[Category:Superparticular]]		[[Category:Superparticular]]