12/11: Difference between revisions

(15 intermediate revisions by 10 users not shown)

Line 1:

{{Infobox Interval

~~| Icon =~~

| Name = undecimal neutral second, Alpharabian tendoneutral second

~~| Ratio = 12/11~~

| Color name = 1u2, lu 2nd

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

~~| Cents = 150.63706~~

| Name = undecimal neutral second

| Sound = jid_12_11_pluck_adu_dr220.mp3

}}

~~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]] 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 = {{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''', the '''undecimal neutral second''' or '''(lesser) 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. 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. In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second'''.

~~'''~~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]] ~~and~~ [[valentine]].

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.

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

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

[[~~Category:interval~~]]

[[~~Category:just_interval~~]]

== See also ==

[[Category:~~neutral_2nd~~]]

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

[[Category:~~ratio~~]]

* [[11/8]] – its [[fifth complement]]

[[Category:~~second~~]]

* [[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: @@
 {{Infobox Interval
-| Icon =
+| Name = undecimal neutral second, Alpharabian tendoneutral second
-| Ratio = 12/11
+| Color name = 1u2, lu 2nd
-| Monzo = 2 1 0 0 -1
-| Cents = 150.63706
-| Name = undecimal neutral second
 | Sound = jid_12_11_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|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]] 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 = {{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''', the '''undecimal neutral second''' or '''(lesser) 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. 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.  In [[Alpharabian tuning]] it is known as the '''Alpharabian tendoneutral second'''.
-'''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]] and [[valentine]].
+/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.
-[[Category:11-limit]]
+Many Western listeners might describe 12/11 as sounding "exotic".
-[[Category:interval]]
-[[Category:just_interval]]
+== See also ==
-[[Category:neutral_2nd]]
+* [[11/6]] – its [[octave complement]]
-[[Category:ratio]]
+* [[11/8]] – its [[fifth complement]]
-[[Category:second]]
+* [[11/9]] – its [[fourth complement]]
+* [[Iceface Tuning]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
+[[Category:Second]]
+[[Category:Neutral second]]
+[[Category:Over-11 intervals]]