Superpyth: Difference between revisions

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== Tunings ==

The fifth of superpyth is supposed to be tuned sharp of just for the accuracy of the overall temperament. Roughly speaking, it ranges from as flat as [[Pythagorean tuning|Pythagorean]] (where 3 is tuned just) to 1/2-comma (where 7 is tuned just, close to [[57edo|57b-edo]]), with 22edo and 27edo being typical endpoints of full 7-limit superpyth's optimal range.

The fifth of superpyth is accurately tuned sharp of just. Roughly speaking, it ranges from as flat as [[Pythagorean tuning|Pythagorean]] (where 3 is tuned just) to 1/2-comma (where 7 is tuned just, between [[52edo|52b-edo]] and [[57edo|57b-edo]]), with 22edo and 27edo being typical endpoints of full 7-limit superpyth's optimal range.

Despite being seen as the "counterpart" of meantone for sharp fifths, superpyth is actually of considerably higher damage than meantone, since the error accumulated to represent the 7th harmonic is split over only 2 generator steps, rather than 4 as in meantone, in addition to the tempered comma being slightly larger. Therefore, tuning superpyth can be a somewhat contentious matter, as some intervals have to be essentially sacrificed for the sake of optimizing for others. An additional consideration is the use of tertian triads in conventional diatonic harmony, whereby the interval 9/7 may also be more important than it looks from the bare math.

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 == Tunings ==
 The fifth of superpyth is supposed to be tuned sharp of just for the accuracy of the overall temperament. Roughly speaking, it ranges from as flat as [[Pythagorean tuning|Pythagorean]] (where 3 is tuned just) to 1/2-comma (where 7 is tuned just, close to [[57edo|57b-edo]]), with 22edo and 27edo being typical endpoints of full 7-limit superpyth's optimal range.
-The fifth of superpyth is accurately tuned sharp of just. Roughly speaking, it ranges from as flat as [[Pythagorean tuning|Pythagorean]] (where 3 is tuned just) to 1/2-comma (where 7 is tuned just, between [[52edo|52b-edo]] and [[57edo|57b-edo]]), with 22edo and 27edo being typical endpoints of full 7-limit superpyth's optimal range.
 Despite being seen as the "counterpart" of meantone for sharp fifths, superpyth is actually of considerably higher damage than meantone, since the error accumulated to represent the 7th harmonic is split over only 2 generator steps, rather than 4 as in meantone, in addition to the tempered comma being slightly larger. Therefore, tuning superpyth can be a somewhat contentious matter, as some intervals have to be essentially sacrificed for the sake of optimizing for others. An additional consideration is the use of tertian triads in conventional diatonic harmony, whereby the interval 9/7 may also be more important than it looks from the bare math.