12/11: Difference between revisions

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'''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 [[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''', 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)<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.

== See also ==

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 {{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 [[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''', 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 ==