262144/177147

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Interval information
Ratio 262144/177147
Factorization 218 × 3-11
Monzo [18 -11
Size in cents 678.49499¢
Name Pythagorean diminished sixth
Color name sasawa 6th, ssw6
FJS name [math]\text{d6}[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 35.4346
Weil height (log2 max(n, d)) 36
Wilson height (sopfr(nd)) 69
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.26864 bits
open this interval in xen-calc

262144/177147, the Pythagorean diminished sixth, is a 3-limit interval. It is called a wolf fifth due to appearing in the circle of fifths in Pythagorean 12-note tuning. It is separated from the classical wolf fifth 40/27 by a schisma.

Temperaments

In compton temperament, this interval and 3/2 are tempered together, because the pythagorean comma 531441/524288 is tempered out.

If this interval itself is taken as a comma to be tempered out, it leads to the malicious temperament, and the interval can be called the malicious comma (the origin of the "malicious compliance" pun from that page).

See also