Undecimal octatonic comma: Difference between revisions
Created page with "{{Infobox Interval |Ratio = 214990848/214358881 |Monzo = 15 8 0 0 -8 |Name = octatonic comma |Comma = yes }} '''Octatonic comma''', 214990848/214358881, is the difference bet..." |
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{{Infobox Interval | {{Infobox Interval | ||
|Ratio = 214990848/214358881 | | Ratio = 214990848/214358881 | ||
| | | Name = undecimal octatonic comma | ||
| | | 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. | |||
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 == | == Temperaments == | ||
[[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]] | |||