Undecimal octatonic comma: Difference between revisions

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{{Infobox Interval
{{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]]: 214990848/214358881) 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 '''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.  


== Temperaments ==
== Temperaments ==

Revision as of 10:48, 4 July 2026

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
Open this interval in xen-calc

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.

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.