12/11: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 12/11

| Monzo = 2 1 0 0 -1

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| 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)<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''', 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 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.

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[[Category:11-limit]]

[[Category:~~Interval ratio]]~~

[[Category:Second]]

~~[[Category:Just interval~~]]

[[Category:Neutral second]]

~~[[Category:Second]]~~

[[Category:Superparticular]]

[[Category:Over-11]]

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 {{Infobox Interval
-| Icon =
 | Ratio = 12/11
 | Monzo = 2 1 0 0 -1
@@ Line 9: / Line 8: @@
 | 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''', 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.
 /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.
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 [[Category:11-limit]]
-[[Category:Interval ratio]]
+[[Category:Second]]
-[[Category:Just interval]]
 [[Category:Neutral second]]
-[[Category:Second]]
 [[Category:Superparticular]]
 [[Category:Over-11]]