22/21: Difference between revisions

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{{Infobox Interval

~~| Ratio = 22/21~~

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

~~| Monzo = 1 -1 0 -1 1~~

| Color name = 1or1, loru unison

~~| Cents = 80.53704~~

| Name = small undecimal semitone

| Color name = 1or1, loru ~~semitone~~

~~| FJS name = P1<sup>11</sup><sub>7</sub>~~

| 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]].

~~'''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¢.

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'''.

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 ==

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.

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[[Category:Semitone]]

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

~~[[Category:Superparticular]]~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 22/21
+| Name = small undecimal semitone, undecimal minor semitone, pentacircle minor second
-| Monzo = 1 -1 0 -1 1
+| Color name = 1or1, loru unison
-| Cents = 80.53704
-| Name = small undecimal semitone
-| Color name = 1or1, loru semitone
-| FJS name = P1<sup>11</sup><sub>7</sub>
 | 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]].
-'''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¢.
+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'''.
-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 ==
 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.
@@ Line 21: / Line 20: @@
 [[Category:Semitone]]
-[[Category:11-limit]]
-[[Category:Superparticular]]