12/11: Difference between revisions

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~~'''12/11'''~~

{{Infobox Interval

|~~2 1 0 0 -1>~~

| Name = undecimal neutral second, Alpharabian tendoneutral second

| Color name = 1u2, lu 2nd

| Sound = jid_12_11_pluck_adu_dr220.mp3

}}

150.~~63706 cents~~

'''12/11''', conventionally the '''(lesser) undecimal neutral second''', is an interval found between the 11th and 12th partials of the [[harmonic series]]. In [[just intonation]] it is represented by the [[superparticular ratio]] 12/11, and is about 150.6 [[cent]]s large.

[[~~File:jid_12_11_pluck_adu_dr220.mp3~~]] [[~~:File:jid_12_11_pluck_adu_dr220.mp3|sound sample~~]]

In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second''', which contrasts [[88/81]], the other undecimal neutral second.

The (lesser) neutral second is ~~a strangely exotic interval found between~~ the ~~11th and 12th partials of the harmonic series. In Just Intonation~~ it ~~is represented~~ by the [[~~superparticular|superparticular~~]] ~~ratio 12~~/11, ~~and is about 150.6~~ [[~~cent|cents~~]] ~~large. One step of~~ [[~~8edo|8edo~~]] ~~is an excellent approximation of the just neutral second~~, and ~~eight of them exceed the octave by the comma (12/11)^8/2 = |15 8 0 0 -8>. It follows that EDOs which are multiples of 8~~, ~~such as~~ [[~~16edo|16edo~~]] ~~and~~ [[~~24edo|24edo~~]], ~~will also represent this interval well~~.

The name ''lesser undecimal neutral second'' is said as opposed to [[11/10]], the larger undecimal neutral second or undecimal submajor second (~165 cents), from which it differs by [[121/120]] (~14.4 cents). [[Regular temperament|Temperaments]] which conflate the two (thus [[tempering out]] 121/120) include [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], and their [[support]]ing [[edo]]s: [[15edo]], [[22edo]], [[31edo]], etc.

12/11 ~~differs from~~ the ~~larger undecimal~~ neutral second 11/~~10 (~165 cents) by 121~~/~~120~~ (~~~14.4 cents~~). ~~Temperaments~~ which ~~conflate the two (thus tempering out 121/120) include~~ [[~~15edo|15edo~~]], [[~~22edo|22edo~~]], [[~~31edo|31edo~~]], [[~~Orwell|orwell~~]], [[~~Porcupine|porcupine~~]], [[~~Mohajira|mohajira~~]] ~~and~~ [[~~Valentine|valentine~~]].

Many Western listeners might describe 12/11 as sounding "exotic".

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

[[~~Category:interval~~]]

== Approximation ==

[[~~Category:just_interval~~]]

One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the [[octave]] by the comma [[undecimal octatonic comma|(12/11)<sup>8</sup>/2]] ({{monzo| 15 8 0 0 -8 }}). It follows that edos which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well.

[[Category:~~neutral_2nd~~]]

[[Category:~~ratio~~]]

[[Category:~~second~~]]

== See also ==

* [[11/6]] – its [[octave complement]]

* [[11/8]] – its [[fifth complement]]

* [[11/9]] – its [[fourth complement]]

* [[Iceface Tuning]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

[[Category:Second]]

[[Category:Neutral second]]

[[Category:Over-11 intervals]]

@@ Line 1: / Line 1: @@
-'''12/11'''
+{{Infobox Interval
-|2 1 0 0 -1&gt;
+| Name = undecimal neutral second, Alpharabian tendoneutral second
+| Color name = 1u2, lu 2nd
+| Sound = jid_12_11_pluck_adu_dr220.mp3
+}}
+{{Wikipedia|Neutral second}}
-.63706 cents
+'''12/11''', conventionally the '''(lesser) undecimal neutral second''', is an interval found between the 11th and 12th partials of the [[harmonic series]]. In [[just intonation]] it is represented by the [[superparticular ratio]] 12/11, and is about 150.6 [[cent]]s large.
-[[File:jid_12_11_pluck_adu_dr220.mp3]] [[:File:jid_12_11_pluck_adu_dr220.mp3|sound sample]]
+In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second''', which contrasts [[88/81]], the other undecimal neutral second.
-The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the [[superparticular|superparticular]] ratio 12/11, and is about 150.6 [[cent|cents]] large. One step of [[8edo|8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = |15 8 0 0 -8&gt;. It follows that EDOs which are multiples of 8, such as [[16edo|16edo]] and [[24edo|24edo]], will also represent this interval well.
+The name ''lesser undecimal neutral second'' is said as opposed to [[11/10]], the larger undecimal neutral second or undecimal submajor second (~165 cents), from which it differs by [[121/120]] (~14.4 cents). [[Regular temperament|Temperaments]] which conflate the two (thus [[tempering out]] 121/120) include [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], and their [[support]]ing [[edo]]s: [[15edo]], [[22edo]], [[31edo]], etc.
-/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo|15edo]], [[22edo|22edo]], [[31edo|31edo]], [[Orwell|orwell]], [[Porcupine|porcupine]], [[Mohajira|mohajira]] and [[Valentine|valentine]].
+Many Western listeners might describe 12/11 as sounding "exotic".
-[[Category:11-limit]]
-[[Category:interval]]
+== Approximation ==
-[[Category:just_interval]]
+One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the [[octave]] by the comma [[undecimal octatonic comma|(12/11)<sup>8</sup>/2]] ({{monzo| 15 8 0 0 -8 }}). It follows that edos which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well.
-[[Category:neutral_2nd]]
-[[Category:ratio]]
+{{Interval edo approximation|12/11}}
-[[Category:second]]
+== See also ==
+* [[11/6]] – its [[octave complement]]
+* [[11/8]] – its [[fifth complement]]
+* [[11/9]] – its [[fourth complement]]
+* [[Iceface Tuning]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+[[Category:Second]]
+[[Category:Neutral second]]
+[[Category:Over-11 intervals]]