12/11: Difference between revisions
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{{Wikipedia|Neutral second}} | {{Wikipedia|Neutral second}} | ||
'''12/11''', the | '''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. | ||
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". | Many Western listeners might describe 12/11 as sounding "exotic". | ||
== Approximation == | == 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 == | == See also == | ||
* [[11/6]] – its [[octave complement]] | * [[11/6]] – its [[octave complement]] | ||