57edt: Difference between revisions
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== Theory == | == Theory == | ||
57edt is related to [[36edo]] (sixth-tone tuning), but with the 3/1 rather than the 2/1 being just. This stretches the octave by about 1.2347 [[cent]]s. It is consistent to the [[9-odd-limit|9-integer-limit]], whereas 36edo is only consistent up to the [[7-odd-limit|8-integer-limit]] due to a discrepancy with approximating 9/5. | 57edt is related to [[36edo]] (sixth-tone tuning), but with the 3/1 rather than the 2/1 being just. This stretches the octave by about 1.2347 [[cent]]s. It is consistent to the [[9-odd-limit|9-integer-limit]], whereas 36edo is only consistent up to the [[7-odd-limit|8-integer-limit]] due to a discrepancy with approximating 9/5, although 57edt barely manages to achieve this since it almost completely misses [[5/1]]. | ||
=== Harmonics === | === Harmonics === | ||
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* [[93ed6]] – relative ed6 | * [[93ed6]] – relative ed6 | ||
* [[101ed7]] – relative ed7 | * [[101ed7]] – relative ed7 | ||
* [[129ed12]] – relative ed12 | * [[129ed12]] – relative ed12, close to the zeta-optimized tuning for 36edo | ||
[[Category:36edo]] | [[Category:36edo]] | ||