Diminished (temperament): Difference between revisions

Line 7:

It can be extended to the 2.3.5.7.19-[[subgroup]] where the 1/4-octave period stands in for both ~6/5 and ~19/16 since this ~19/16 is more accurate, though its mos structure of 4L 4s is very flexible, so one could use 3\4 minus ~8/7 as a ~670{{cent}} fifth for a 2.7.19 subgroup version of diminished, for example.

[[12edo]] is an obvious tuning. ~~Other~~ possible ~~tunings include~~ [[16edo]] ~~and [[28edo]], both of~~ which ~~having~~ the interesting feature of being good in the 2.7.19 subgroup, so that the fifth is approximately [[28/19]]. [[28edo]] is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[strongly consistent circle]] of them.

[[12edo]] is an obvious tuning. Another possible tuning is [[16edo]] which has the interesting feature of being relatively good in the 2.7.19 subgroup so that the fifth is approximately [[28/19]], or [[28edo]], which uses something like [[~]][[95/64]] = [[~]][[19/16]] * [[~]][[5/4]] as its fifth, of which the latter is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[strongly consistent circle]] of them.

See [[Dimipent family #Diminished]] for technical data.

@@ Line 7: / Line 7: @@
 It can be extended to the 2.3.5.7.19-[[subgroup]] where the 1/4-octave period stands in for both ~6/5 and ~19/16 since this ~19/16 is more accurate, though its mos structure of 4L 4s is very flexible, so one could use 3\4 minus ~8/7 as a ~670{{cent}} fifth for a 2.7.19 subgroup version of diminished, for example.
-[[12edo]] is an obvious tuning. Other possible tunings include [[16edo]] and [[28edo]], both of which having the interesting feature of being good in the 2.7.19 subgroup, so that the fifth is approximately [[28/19]]. [[28edo]] is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[strongly consistent circle]] of them.
+[[12edo]] is an obvious tuning. Another possible tuning is [[16edo]] which has the interesting feature of being relatively good in the 2.7.19 subgroup so that the fifth is approximately [[28/19]], or [[28edo]], which uses something like [[~]][[95/64]] = [[~]][[19/16]] * [[~]][[5/4]] as its fifth, of which the latter is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[strongly consistent circle]] of them.
 See [[Dimipent family #Diminished]] for technical data.