4L 5s (3/1-equivalent): Difference between revisions

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Below is a list of equal temperaments which contain a 4L 5s scale using generators between 422.7 cents and 475.5 cents.

{{Scale tree|depth=7|Comments=13/6:BPS is in this region|Comments=22/13:Essentially just 7/3}}

Analogously to how the diatonic scale equalizes approaching [[7edo]] and its small steps collapse to 0 in [[5edo]], this scale equalizes approaching [[9edt]] and its small steps collapse in [[4edt]]; therefore, temperaments setting the 7/3 generator to precisely 7\9edt and to precisely 3\4edt are analogs of [[whitewood]] and [[blackwood]] respectively; however, unlike for the diatonic scale, the just point is not close to the center of the tuning range, but approximately 1/4 of the way between 9edt and 4edt, being closely approximated by 37\[[48edt]] and extremely closely approximated by 118\[[153edt]].

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 Below is a list of equal temperaments which contain a 4L 5s scale using generators between 422.7 cents and 475.5 cents.
-{{Scale tree|depth=7|Comments=9/4:BPS is in this region}}
+{{Scale tree|depth=7|Comments=13/6:BPS is in this region|Comments=22/13:Essentially just 7/3}}
 Analogously to how the diatonic scale equalizes approaching [[7edo]] and its small steps collapse to 0 in [[5edo]], this scale equalizes approaching [[9edt]] and its small steps collapse in [[4edt]]; therefore, temperaments setting the 7/3 generator to precisely 7\9edt and to precisely 3\4edt are analogs of [[whitewood]] and [[blackwood]] respectively; however, unlike for the diatonic scale, the just point is not close to the center of the tuning range, but approximately 1/4 of the way between 9edt and 4edt, being closely approximated by 37\[[48edt]] and extremely closely approximated by 118\[[153edt]].