Didacus: Difference between revisions

Line 8:

| Mapping = 1; 2 5 9

| Odd limit 1 = 7 | Mistuning 1 = 1.22 | Complexity 1 = 13

| Odd limit 2 = 11 | Mistuning 2 = ~~???~~ | Complexity 2 = 19

| Odd limit 2 = 11 | Mistuning 2 = 4.13 | Complexity 2 = 19

}}

'''Didacus''' is an temperament of the [[2.5.7 subgroup]], tempering out [[3136/3125]], the hemimean comma, such that two intervals of [[7/5]] reach three intervals of [[5/4]]; the generator is therefore (7/5)/(5/4) = [[28/25]], two of which stack to 5/4 and three of which stack to 7/5, notable for being one of the most efficient traversals of the no-threes subgroup. [[31edo]] is a very good tuning of didacus, with its generator 5\31 (which is the "mean tone" of 31edo); but [[25edo]], [[37edo]], and [[68edo]] among others are good tunings as well. As this generator tends to be slightly less than 1/6 of the octave, [[MOS scale]]s of didacus tend to consist of 6 long intervals interspersed by sequences of diesis-sized steps (representing [[50/49]]~[[128/125]]), therefore bearing similar properties to those of [[slendric]].

@@ Line 8: / Line 8: @@
 | Mapping = 1; 2 5 9
 | Odd limit 1 = 7 | Mistuning 1 = 1.22 | Complexity 1 = 13
-| Odd limit 2 = 11 | Mistuning 2 = ??? | Complexity 2 = 19
+| Odd limit 2 = 11 | Mistuning 2 = 4.13 | Complexity 2 = 19
 }}
 '''Didacus''' is an temperament of the [[2.5.7 subgroup]], tempering out [[3136/3125]], the hemimean comma, such that two intervals of [[7/5]] reach three intervals of [[5/4]]; the generator is therefore (7/5)/(5/4) = [[28/25]], two of which stack to 5/4 and three of which stack to 7/5, notable for being one of the most efficient traversals of the no-threes subgroup. [[31edo]] is a very good tuning of didacus, with its generator 5\31 (which is the "mean tone" of 31edo); but [[25edo]], [[37edo]], and [[68edo]] among others are good tunings as well. As this generator tends to be slightly less than 1/6 of the octave, [[MOS scale]]s of didacus tend to consist of 6 long intervals interspersed by sequences of diesis-sized steps (representing [[50/49]]~[[128/125]]), therefore bearing similar properties to those of [[slendric]].