Undecimal octatonic comma: Difference between revisions

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{{Infobox Interval

|Ratio = 214990848/214358881

| Ratio = 214990848/214358881

~~|Monzo = 15 8 0 0 -8~~

| Name = undecimal octatonic comma

|Name = undecimal octatonic comma

| Color name = 1u82, quadbilu 2nd

|Color name = 1u82, quadbilu 2nd

| Comma = yes

|Comma = yes

}}

The '''undecimal octatonic comma''' ({{monzo|legend=1| 15 8 0 0 -8 }}, [[ratio]]: 214 990 848 / 214 358 881) is a [[small comma]] in the [[11-limit]] (specifically the [[2.3.11 subgroup]]), measuring about 5.10 [[cent]]s. It is the amount by which a stack of eight [[12/11]] intervals exceeds the octave.

~~The '''Octatonic comma''', 214990848/214358881~~, is the difference between 8 [[~~12/11~~]]s ~~and~~ the ~~octave. Since equates eight of one interval with an octave~~, it ~~is tempered out if and only if~~ the ~~number of notes in~~ the ~~octave is a multiple of 8~~.

In terms of other commas, it is the difference between the [[Pythagorean comma]] and a stack of two [[Alpharabian comma]]s. In the full 11-limit, it factors into simpler commas as ([[46656/46585]])⋅([[161280/161051]]), the latter being the difference between 46656/46585 and [[9801/9800]]; thus it can be expressed as (46656/46585)2/(9801/9800) as well.

== Temperaments ==

Tempering it out results in the octatonic temperament. For technical data see [[8th-octave temperaments#Octatonic]].

[[Tempering out]] this comma in the 2.3.11 subgroup results in the octatonic temperament. For technical data see [[8th-octave temperaments #Octatonic]]. Since it equates eight of one interval with an octave, it is tempered out if and only if the number of notes in the octave is a multiple of 8.

[[Category:Commas named for their periods per equave]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-|Ratio = 214990848/214358881
+| Ratio = 214990848/214358881
-|Monzo = 15 8 0 0 -8
+| Name = undecimal octatonic comma
-|Name = undecimal octatonic comma
+| Color name = 1u<sup>8</sup>2, quadbilu 2nd
-|Color name = 1u<sup>8</sup>2, quadbilu 2nd
+| Comma = yes
-|Comma = yes
 }}
+The '''undecimal octatonic comma''' ({{monzo|legend=1| 15 8 0 0 -8 }}, [[ratio]]: 214 990 848 / 214 358 881) is a [[small comma]] in the [[11-limit]] (specifically the [[2.3.11 subgroup]]), measuring about 5.10 [[cent]]s. It is the amount by which a stack of eight [[12/11]] intervals exceeds the octave.
-The '''Octatonic comma''', 214990848/214358881, is the difference between 8 [[12/11]]s and the octave. Since equates eight of one interval with an octave, it is tempered out if and only if the number of notes in the octave is a multiple of 8.
+In terms of other commas, it is the difference between the [[Pythagorean comma]] and a stack of two [[Alpharabian comma]]s. In the full 11-limit, it factors into simpler commas as ([[46656/46585]])⋅([[161280/161051]]), the latter being the difference between 46656/46585 and [[9801/9800]]; thus it can be expressed as (46656/46585)<sup>2</sup>/(9801/9800) as well.
 == Temperaments ==
-Tempering it out results in the octatonic temperament. For technical data see [[8th-octave temperaments#Octatonic]].
+[[Tempering out]] this comma in the 2.3.11 subgroup results in the octatonic temperament. For technical data see [[8th-octave temperaments #Octatonic]]. Since it equates eight of one interval with an octave, it is tempered out if and only if the number of notes in the octave is a multiple of 8.
+[[Category:Commas named for their periods per equave]]