Septimal octatonic comma: Difference between revisions

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Tempering it out results in the 7-limit version of the '''octatonic''' temperament. For technical data see [[8th-octave temperaments#Octatonic]].
Tempering it out results in the 7-limit version of 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]]

Latest revision as of 00:49, 4 November 2024

Interval information
Ratio 2251875390625/2199023255552
Factorization 2-41 × 58 × 78
Monzo [-41 0 8 8⟩
Size in cents 41.11696¢
Name septimal octatonic comma
Color name lala-quadbizoyo 2nd, LLz8y82
FJS name [math]\displaystyle{ \text{AA2}^{5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 82.0343
Weil height (log2 max(n, d)) 82.0685
Wilson height (sopfr(nd)) 178
Comma size medium
Open this interval in xen-calc

The septimal octatonic comma, 2251875390625/2199023255552, is the difference between 8 35/32s 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.

Temperaments

Tempering it out results in the 7-limit version of the octatonic temperament. For technical data see 8th-octave temperaments#Octatonic.

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