Würschmidt family: Difference between revisions
No edit summary |
→2.3.5.23 subgroup: note further extensions |
||
| (3 intermediate revisions by 3 users not shown) | |||
| Line 39: | Line 39: | ||
=== 2.3.5.23 subgroup === | === 2.3.5.23 subgroup === | ||
Extensions to harmonics [[47/1|47]] and [[49/1|49]] are also available at +11 and +5 generator steps respectively, equalizing the 45::50 [[harmonic series segment|segment]] of the [[harmonic series]]. If we derive a mapping of prime [[7/1|7]] from this mapping of 49, then we get the weak extension [[hemiwürschmidt]]. | |||
Subgroup: 2.3.5.23 | Subgroup: 2.3.5.23 | ||
| Line 69: | Line 71: | ||
== Septimal würschmidt == | == Septimal würschmidt == | ||
Würschmidt, aside from the commas listed above, also tempers out [[225/224]]. [[31edo]] or [[127edo]] can be used as tunings. It extends naturally to an 11-limit version | Würschmidt, aside from the commas listed above, also tempers out [[225/224]]. [[31edo]] or [[127edo]] can be used as tunings. It extends naturally to an 11-limit version which also tempers out [[99/98]], [[176/175]] and 243/242. 127edo is again an excellent tuning for 11-limit würschmidt, as well as for [[minerva]], the 11-limit rank-3 temperament tempering out 99/98 and 176/175. | ||
2-würschmidt, the temperament with all the same commas as würschmidt but a generator of twice the size, is equivalent to [[skwares]] as a 2.3.7.11 subgroup temperament. | 2-würschmidt, the temperament with all the same commas as würschmidt but a generator of twice the size, is equivalent to [[skwares]] as a 2.3.7.11 subgroup temperament. | ||