Undecimal octatonic comma: Difference between revisions

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


[[Category:Commas named for their regular temperament properties]]
[[Category:Commas named for their periods per equave]]

Revision as of 00:46, 4 November 2024

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, 214990848/214358881, is the amount by which a stack of eight 12/11 intervals exceeds 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.

Temperaments

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

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