Bird's eye view of temperaments by accuracy: Difference between revisions

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m ~17-limit focus: add catakleismic
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Higher-limit focus: add sensible
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== Higher-limit focus ==
== Higher-limit focus ==
=== [[Sensible]] ===
{{ See also | Sensipent#Sensible interval table }}
Note counts:
* 26 for {3, 5, 11, 17, 23, 31, 33, 51, 55, 69, 85, 99(, 115)} ([[19L 8s]])
* 35 for adding {9, 15, 25, 93(, 155)} ([[19L 8s]] or 19L 27s)
Sensible is a fairly accurate (though quite complex) subgroup interpretation of sensi (or extension of [[#Sensipent]]) which is especially accurate in the [[CEE tuning]] (443.115{{cent}}) if avoiding composite odds and intervals of 23 so that under such restrictions it classifies as [[#Very high accuracy]], meaning it's one of the most accurate temperaments in this category, especially if you use error-cancellations of sharp harmonics to your advantage to construct complex harmonic series chords in order to justify the generally-higher errors of composite harmonics. [[46edo]] is a somewhat reasonable but trivial tuning of it, [[65edo]] is somewhat better, and [[111edo]] is even better, but it works especially well in a more optimized tuning, hence its significance as a rank 2 temperament. The 27-note MOS, though not achieving all of its odd harmonics from a single note, is sufficient, because the missing odds {9, 15, 25, 93(, 155)} also do reasonably occur within the span of the 27-note MOS. Therefore, sensible can be seen as a detempering of [[27edo]] to a more accurate rank 2 temperament on a mostly-unrelated subgroup.
=== [[Srutal]] ===
=== [[Srutal]] ===
Note count: 36 for {3, 5, 7, 9, 11, 13, 15, 17, 23, 33, 35, 51} (12L 22s)
Note count: 36 for {3, 5, 7, 9, 11, 13, 15, 17, 23, 33, 35, 51} (12L 22s)