Septimal octatonic comma
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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]\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]\sqrt{nd}[/math])
~4.5165 bits
Comma size
medium
open this interval in xen-calc
| Interval information |
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
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.