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 1.23 [[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. Like 36edo, 101ed7 is [[consistent]] to the [[integer limit|8-integer-limit]].

Compared to 36edo, 101ed7's harmonics are almost exactly the same, but it has a slightly better [[3/1]], [[7/1]], and [[13/1]], and a slightly worse 2/1 and [[5/1]] versus 36edo. Overall this means 36edo is still better in the [[5-limit]], but 101ed7 is better in the [[13-limit]]. (The [[7-limit]] and [[11-limit]] could go either way.)

Compared to 36edo, 101ed7's harmonics are almost exactly the same, but it has a slightly better [[3/1|3]], [[7/1|7]], and [[13/1|13]], and a slightly worse 2 and [[5/1|5]] versus 36edo. Overall this means 36edo is still better in the [[5-limit]], but 101ed7 is better in the [[13-limit]]. (The [[7-limit]] and [[11-limit]] could go either way.)

36edo's 5-limit dominance flips on its head, though, if one approaches it as a [[dual-n|dual-5]] tuning. In that case, the fact that 101ed7's 5/1 is closer to 50% relative error is actually a ''good'' thing, because it means the error on the worse of the two 5/1's is less. So as a single-5 5-limit tuning, 36edo is better. But as a dual-5 5-limit tuning, 101ed7 is better, and as a dual-5, dual-11 [[31-limit]] tuning, 101ed7 is exceptional for its size. It is very accurate.

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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 1.23 [[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. Like 36edo, 101ed7 is [[consistent]] to the [[integer limit|8-integer-limit]].
-Compared to 36edo, 101ed7's harmonics are almost exactly the same, but it has a slightly better [[3/1]], [[7/1]], and [[13/1]], and a slightly worse 2/1 and [[5/1]] versus 36edo. Overall this means 36edo is still better in the [[5-limit]], but 101ed7 is better in the [[13-limit]]. (The [[7-limit]] and [[11-limit]] could go either way.)
+Compared to 36edo, 101ed7's harmonics are almost exactly the same, but it has a slightly better [[3/1|3]], [[7/1|7]], and [[13/1|13]], and a slightly worse 2 and [[5/1|5]] versus 36edo. Overall this means 36edo is still better in the [[5-limit]], but 101ed7 is better in the [[13-limit]]. (The [[7-limit]] and [[11-limit]] could go either way.)
 edo's 5-limit dominance flips on its head, though, if one approaches it as a [[dual-n|dual-5]] tuning. In that case, the fact that 101ed7's 5/1 is closer to 50% relative error is actually a ''good'' thing, because it means the error on the worse of the two 5/1's is less. So as a single-5 5-limit tuning, 36edo is better. But as a dual-5 5-limit tuning, 101ed7 is better, and as a dual-5, dual-11 [[31-limit]] tuning, 101ed7 is exceptional for its size. It is very accurate.