Undecimal octatonic comma

Interval information

Ratio	214990848/214358881
Factorization	215 × 38 × 11-8
Monzo	[15 8 0 0 -8⟩
Size in cents	5.096468¢
Name	undecimal octatonic comma
Color name	1u82, quadbilu 2nd
FJS name	[math]\displaystyle{ \text{AA2}_{11,11,11,11,11,11,11,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	55.3552
Weil norm (log2 max(n, d))	55.3594
Wilson norm (sopfr(nd))	142
Comma size	small
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The undecimal octatonic comma (monzo: [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 cents. 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 commas. 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 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.