12/11: Difference between revisions

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

{{Infobox Interval

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

| Icon =

| Ratio = 12/11

| Monzo = 2 1 0 0 -1

| Cents = 150.63706

| Name = undecimal neutral second

| Sound = jid_12_11_pluck_adu_dr220.mp3

}}

150.~~63706~~ cents

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.

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

'''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]].

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.

[[Category:11-limit]]

[[Category:interval]]

@@ Line 1: / Line 1: @@
-'''12/11'''
+{{Infobox Interval
-|2 1 0 0 -1&gt;
+| Icon =
+| Ratio = 12/11
+| Monzo = 2 1 0 0 -1
+| Cents = 150.63706
+| Name = undecimal neutral second
+| Sound = jid_12_11_pluck_adu_dr220.mp3
+}}
-.63706 cents
+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.
-[[File:jid_12_11_pluck_adu_dr220.mp3]] [[:File:jid_12_11_pluck_adu_dr220.mp3|sound sample]]
+'''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]].
-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.
-/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]].
 [[Category:11-limit]]
 [[Category:interval]]