Septimal octatonic comma

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
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.5165 bits
Comma size	medium
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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.