22/21: Difference between revisions

(8 intermediate revisions by 5 users not shown)

Line 1:

{{Infobox Interval

~~| Icon =~~

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

~~| Ratio = 22/21~~

| Color name = 1or1, loru unison

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

~~| 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 overtone. 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.

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~~|relative cents~~]].

== 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.

== See also ==

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

* [[Gallery of ~~Just Intervals~~]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

[[Category:Semitone]]

~~[[Category:Interval]]~~

~~[[Category:Ratio]]~~

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

~~[[Category:Superparticular]]~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = small undecimal semitone, undecimal minor semitone, pentacircle minor second
-| Ratio = 22/21
+| Color name = 1or1, loru unison
-| Monzo = 1 -1 0 -1 1
-| 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 overtone. 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.
-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|relative cents]].
+== 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.
 == See also ==
 * [[21/11]] – its [[octave complement]]
-* [[Gallery of Just Intervals]]
+* [[Gallery of just intervals]]
 * [[List of superparticular intervals]]
 [[Category:Semitone]]
-[[Category:Interval]]
-[[Category:Ratio]]
-[[Category:11-limit]]
-[[Category:Superparticular]]