135edo: Difference between revisions

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== Theory ==

135edo is [[consistent]] to the [[7-odd-limit]], but with large relative error for the [[5/1|5th]] and [[13/1|13th]] [[harmonic]]s. As every other step of the full [[13-limit]] monster – [[270edo|270et]], 135et ~~supports an easy but extremely accurate equal tuning of the~~ [[2.3.7.11 subgroup|2.3.7.11-]][[subgroup]] [[regular temperament|temperament]] ~~[[gary]]. As an equal temperament~~, it is characterized by [[tempering out]] the [[garischisma]], the [[~~symbiotic comma~~]] ~~and~~ the [[~~argyria~~]], ~~which indirectly also tempers out~~ the [[~~septiennealimma~~]], the [[~~olympia~~]] and the [[~~chrysia~~]]. On top of this, it also has fairly good approximations to primes [[17/1|17]], [[29/1|29]], and [[31/1|31]].

135edo is [[consistent]] to the [[7-odd-limit]], but with large relative error for the [[5/1|5th]] and [[13/1|13th]] [[harmonic]]s. As every other step of the full [[13-limit]] monster – [[270edo|270et]], 135et makes most sense to use as a [[2.3.7.11 subgroup|2.3.7.11-]][[subgroup]] [[regular temperament|temperament]], where it is characterized by [[tempering out]] the [[garischisma]], the [[septiennealimma]], the [[symbiotic comma]], the [[argyria]], the [[chrysia]], and the [[olympia]]. On top of this, it also has fairly good approximations to primes [[17/1|17]], [[29/1|29]], and [[31/1|31]].

If we consider the full 13-limit, the flat-tending {{val| 135 214 313 379 467 '''499''' }} (135f) and the sharp-tending {{val| 135 214 '''314''' 379 467 500 }} (135c) are reasonable choices.

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 == Theory ==
-edo is [[consistent]] to the [[7-odd-limit]], but with large relative error for the [[5/1|5th]] and [[13/1|13th]] [[harmonic]]s. As every other step of the full [[13-limit]] monster – [[270edo|270et]], 135et supports an easy but extremely accurate equal tuning of the [[2.3.7.11 subgroup|2.3.7.11-]][[subgroup]] [[regular temperament|temperament]] [[gary]]. As an equal temperament, it is characterized by [[tempering out]] the [[garischisma]], the [[symbiotic comma]] and the [[argyria]], which indirectly also tempers out the [[septiennealimma]], the [[olympia]] and the [[chrysia]]. On top of this, it also has fairly good approximations to primes [[17/1|17]], [[29/1|29]], and [[31/1|31]].
+edo is [[consistent]] to the [[7-odd-limit]], but with large relative error for the [[5/1|5th]] and [[13/1|13th]] [[harmonic]]s. As every other step of the full [[13-limit]] monster – [[270edo|270et]], 135et makes most sense to use as a [[2.3.7.11 subgroup|2.3.7.11-]][[subgroup]] [[regular temperament|temperament]], where it is characterized by [[tempering out]] the [[garischisma]], the [[septiennealimma]], the [[symbiotic comma]], the [[argyria]], the [[chrysia]], and the [[olympia]]. On top of this, it also has fairly good approximations to primes [[17/1|17]], [[29/1|29]], and [[31/1|31]].
 If we consider the full 13-limit, the flat-tending {{val| 135 214 313 379 467 '''499''' }} (135f) and the sharp-tending {{val| 135 214 '''314''' 379 467 500 }} (135c) are reasonable choices.