12/11: Difference between revisions

(8 intermediate revisions by 6 users not shown)

Line 1:

{{Infobox Interval

~~| Ratio = 12/11~~

| Name = undecimal neutral second, Alpharabian tendoneutral second

~~| Monzo = 2 1 0 0 -1~~

~~| Cents = 150.63706~~

| Name = undecimal neutral second

| Color name = 1u2, lu 2nd

~~| FJS name = M211~~

| Sound = jid_12_11_pluck_adu_dr220.mp3

}}

'''12/11''', the ~~'''undecimal neutral second''' or~~ '''(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]] ~~ratio~~ 12/11, and is about 150.6 [[cent]]s large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)8/2 = {{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.

'''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.

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]], [[22edo]], [[31edo]], [[~~orwell~~]], [[~~porcupine~~]], [[~~mohajira~~]], [[~~valentine~~]], ~~etc~~.

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

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.

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

== Approximation ==

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)8/2]] ({{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.

== See also ==

Line 22:

Line 27:

* [[List of superparticular intervals]]

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

[[Category:Second]]

[[Category:Neutral second]]

~~[[Category:Superparticular]]~~

[[Category:Over-11 intervals]]

[[Category:Over-11]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 12/11
+| Name = undecimal neutral second, Alpharabian tendoneutral second
-| Monzo = 2 1 0 0 -1
-| Cents = 150.63706
-| Name = undecimal neutral second
 | Color name = 1u2, lu 2nd
-| FJS name = M2<sub>11</sub>
 | Sound = jid_12_11_pluck_adu_dr220.mp3
 }}
 {{Wikipedia|Neutral second}}
-'''12/11''', the '''undecimal neutral second''' or '''(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]] ratio 12/11, and is about 150.6 [[cent]]s large. One step of [[8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the 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.
+'''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.
-/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]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]], [[valentine]], etc.
+In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second''', which contrasts [[88/81]], the other undecimal neutral second.
+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.
+Many Western listeners might describe 12/11 as sounding "exotic".
+== Approximation ==
+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.
+{{Interval edo approximation|12/11}}
 == See also ==
@@ Line 22: / Line 27: @@
 * [[List of superparticular intervals]]
-[[Category:11-limit]]
 [[Category:Second]]
 [[Category:Neutral second]]
-[[Category:Superparticular]]
+[[Category:Over-11 intervals]]
-[[Category:Over-11]]