270edo: Difference between revisions

Line 2:

== Theory ==

270edo is an extremely strong [[13-limit]] system, distinct and [[consistent]] through the [[15-odd-limit]] with all intervals in the 15-odd-limit being ~~more in-tune~~ than ~~out-of-tune with 270edo~~ with only the exception of [[15/13]] which barely misses (and which can be interpreted as the result of tempering [[676/675]]). This results in it being a record edo for [[Pepper ambiguity]] in the 11-, 13- and 15-odd-limits. 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]].

270edo is an extremely strong [[13-limit]] system, distinct and [[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 (and which can be interpreted as the result of tempering [[676/675]]). This results in it being a record edo for [[Pepper ambiguity]] in the 11-, 13- and 15-odd-limits. 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]].

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

@@ Line 2: / Line 2: @@
 == Theory ==
-edo is an extremely strong [[13-limit]] system, distinct and [[consistent]] through the [[15-odd-limit]] with all intervals in the 15-odd-limit being more in-tune than out-of-tune with 270edo with only the exception of [[15/13]] which barely misses (and which can be interpreted as the result of tempering [[676/675]]). This results in it being a record edo for [[Pepper ambiguity]] in the 11-, 13- and 15-odd-limits. 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]].
+edo is an extremely strong [[13-limit]] system, distinct and [[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 (and which can be interpreted as the result of tempering [[676/675]]). This results in it being a record edo for [[Pepper ambiguity]] in the 11-, 13- and 15-odd-limits. 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]].
 In the [[5-limit]] it tempers out the ennealimma, {{monzo| 1 -27 18 }}, the [[vulture comma]], {{monzo| 24 -21 4 }}, and the [[Vishnuzmic family|vishnuzma]] or semisuper comma, {{monzo| 23 6 -14 }}.