101ed7: Difference between revisions

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== Theory ==

101ed7 is closely related to [[36edo]] (sixth-tone tuning), but with the 7th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.770 [[cent]]s. Like 36edo, 101ed7 is [[consistent]] to the [[integer limit|8-integer-limit]].

101ed7 is closely related to [[36edo]] (sixth-tone tuning), but with the 7th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.770 [[cent]]s (almost identical to [[93ed6]], where the octave is stretched by about 0.757 cents). Like 36edo, 101ed7 is [[consistent]] to the [[integer limit|8-integer-limit]].

Compared to 36edo, 101ed7 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1|3]], [[7/1|7]], [[13/1|13]] and [[17/1|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 101ed7 is better in the [[13-limit|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning.

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 == Theory ==
-ed7 is closely related to [[36edo]] (sixth-tone tuning), but with the 7th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.770 [[cent]]s. Like 36edo, 101ed7 is [[consistent]] to the [[integer limit|8-integer-limit]].
+ed7 is closely related to [[36edo]] (sixth-tone tuning), but with the 7th harmonic rather than the [[2/1|octave]] being just. The octave is stretched by about 0.770 [[cent]]s (almost identical to [[93ed6]], where the octave is stretched by about 0.757 cents). Like 36edo, 101ed7 is [[consistent]] to the [[integer limit|8-integer-limit]].
 Compared to 36edo, 101ed7 is pretty well optimized for the 2.3.7.13.17 [[subgroup]], with slightly better [[3/1|3]], [[7/1|7]], [[13/1|13]] and [[17/1|17]], and a slightly worse 2 versus 36edo. Using the [[patent val]], the [[5/1|5]] is also less accurate. Overall this means 36edo is still better in the [[5-limit]], but 101ed7 is better in the [[13-limit|13-]] and [[17-limit]], especially when treating it as a dual-5 dual-11 tuning.