262144/177147: Difference between revisions
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Note that it's inconsistently mapped in 23edo and note how to consistently approximate it. +categories |
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'''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]]. | '''262144/177147''', the '''Pythagorean diminished sixth''', is a [[3-limit]] interval. It is often 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]]. | ||
== Approximation == | |||
Like any 3-limit intervals, this interval is well approximated by any equal tuning with accurate octaves and fifths. It is very closely, though inconsistently approximated by [[23edo]]'s flat fifth of 13\23. The first superset of 23edo that consistently approximates it is {{nowrap| 23 × 11 {{=}} [[253edo]] }}. | |||
== Temperaments == | == 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 com''pliance" pun from that page). | |||
== See also == | == See also == | ||
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[[Category:Fifth]] | [[Category:Fifth]] | ||
[[Category:Subfifth]] | |||
[[Category:Sixth]] | |||
[[Category:Diminished sixth]] | |||