270edo: Difference between revisions

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== Theory ==

270edo is an extremely strong [[13-limit]] system, [[distinctly consistent]] through the [[15-odd-limit]] with all intervals in the 15-odd-limit being approximated with less than 25% relative error ~~with only the exception of~~ [[15/13]] which barely ~~misses~~ (corresponding to the ~~fact of~~ tempering out [[676/675]]). This results in it being a record edo for [[Pepper ambiguity]] in the 11-, 13- and 15-odd-limit. It is [[The Riemann zeta function and tuning #Zeta EDO lists|the 11th zeta gap edo, the 13th zeta integral edo, the 23rd zeta peak edo, and the 18th zeta peak integer edo]], making it a strict zeta edo, and is the first [[Trivial temperament|non-trivial]] edo to be consistent in the 16-[[Odd prime sum limit|odd-prime-sum-limit]].

270edo is an extremely strong [[13-limit]] system, [[distinctly consistent]] through the [[15-odd-limit]] with all intervals in the 15-odd-limit being approximated with less than 25% relative error except [[15/13]] and [[26/15]] which barely miss (corresponding to the [[tempering out]] of [[676/675]]). This results in it being a record edo for [[Pepper ambiguity]] in the 11-, 13- and 15-odd-limit. It is [[The Riemann zeta function and tuning #Zeta EDO lists|the 11th zeta gap edo, the 13th zeta integral edo, the 23rd zeta peak edo, and the 18th zeta peak integer edo]], making it a strict zeta edo, and is the first [[Trivial temperament|non-trivial]] edo to be consistent in the 16-[[Odd prime sum limit|odd-prime-sum-limit]].

In the [[5-limit]] it tempers out the [[ennealimma]], {{monzo| 1 -27 18 }}, the [[vulture comma]], {{monzo| 24 -21 4 }}, and the [[vishnuzma]] (a.k.a. semisuper comma), {{monzo| 23 6 -14 }}.

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 == Theory ==
-edo is an extremely strong [[13-limit]] system, [[distinctly consistent]] through the [[15-odd-limit]] with all intervals in the 15-odd-limit being approximated with less than 25% relative error with only the exception of [[15/13]] which barely misses (corresponding to the fact of tempering out [[676/675]]). This results in it being a record edo for [[Pepper ambiguity]] in the 11-, 13- and 15-odd-limit. It is [[The Riemann zeta function and tuning #Zeta EDO lists|the 11th zeta gap edo, the 13th zeta integral edo, the 23rd zeta peak edo, and the 18th zeta peak integer edo]], making it a strict zeta edo, and is the first [[Trivial temperament|non-trivial]] edo to be consistent in the 16-[[Odd prime sum limit|odd-prime-sum-limit]].
+edo is an extremely strong [[13-limit]] system, [[distinctly consistent]] through the [[15-odd-limit]] with all intervals in the 15-odd-limit being approximated with less than 25% relative error except [[15/13]] and [[26/15]] which barely miss (corresponding to the [[tempering out]] of [[676/675]]). This results in it being a record edo for [[Pepper ambiguity]] in the 11-, 13- and 15-odd-limit. It is [[The Riemann zeta function and tuning #Zeta EDO lists|the 11th zeta gap edo, the 13th zeta integral edo, the 23rd zeta peak edo, and the 18th zeta peak integer edo]], making it a strict zeta edo, and is the first [[Trivial temperament|non-trivial]] edo to be consistent in the 16-[[Odd prime sum limit|odd-prime-sum-limit]].
 In the [[5-limit]] it tempers out the [[ennealimma]], {{monzo| 1 -27 18 }}, the [[vulture comma]], {{monzo| 24 -21 4 }}, and the [[vishnuzma]] (a.k.a. semisuper comma), {{monzo| 23 6 -14 }}.