22/21: Difference between revisions

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'''22/21'''

{{Infobox Interval

|1 -~~1 0 -1 1>~~

| Name = small undecimal semitone, undecimal minor semitone, pentacircle minor second

| Color name = 1or1, loru unison

| Sound = jid_22_21_pluck_adu_dr220.mp3

| 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 is the difference between [[12/11]] and [[8/7]], or between [[7/6]] and [[11/9]].

80.~~537 cents~~

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'''.

[[~~File:jid_22_21_pluck_adu_dr220~~.~~mp3~~]] [[~~:File:jid_22_21_pluck_adu_dr220.mp3|sound sample~~]]

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.

~~22/21 is a small [[superparticular|superparticular]] semitone~~ of ~~about 80.5¢ that appears in~~ [[~~11-limit|11-limit~~]] ~~[[Just_intonation|Just Intonation]]. It makes the difference between the 21st and 22nd overtone. It is close in size to [[21~~/~~20|~~21~~/20]],~~ a ~~7-limit [[superparticular|superparticular]] interval~~, ~~differing from it by~~ [[~~441/440|441/440~~]]~~, about 3.9¢~~.

== 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.

~~The single degree~~ of [[~~88cET|88cET~~]] ~~can function as both 21/20 and 22/21, thus tempering out 441/440.~~

== See also ==

* [[21/11]] – its [[octave complement]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

~~See:~~ [[~~Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[List_of_Superparticular_Intervals|List of Superparticular Intervals~~]]

[[Category:Semitone]]

@@ Line 1: / Line 1: @@
-'''22/21'''
+{{Infobox Interval
-|1 -1 0 -1 1&gt;
+| Name = small undecimal semitone, undecimal minor semitone, pentacircle minor second
+| Color name = 1or1, loru unison
+| Sound = jid_22_21_pluck_adu_dr220.mp3
+| 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 is the difference between [[12/11]] and [[8/7]], or between [[7/6]] and [[11/9]].
-.537 cents
+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'''.
-[[File:jid_22_21_pluck_adu_dr220.mp3]] [[:File:jid_22_21_pluck_adu_dr220.mp3|sound sample]]
+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.
-/21 is a small [[superparticular|superparticular]] semitone of about 80.5¢ that appears in [[11-limit|11-limit]] [[Just_intonation|Just Intonation]]. It makes the difference between the 21st and 22nd overtone. It is close in size to [[21/20|21/20]], a 7-limit [[superparticular|superparticular]] interval, differing from it by [[441/440|441/440]], about 3.9¢.
+== Approximation ==
+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.
-The single degree of [[88cET|88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440.
+== See also ==
+* [[21/11]] – its [[octave complement]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[List_of_Superparticular_Intervals|List of Superparticular Intervals]]
+[[Category:Semitone]]