190537edo: Difference between revisions

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{{ED intro}} It is the denominator of the next convergent for log23 past [[111202edo|111202]], with another such convergent not occurring until [[10590737edo|10590737]].

~~The '''~~190537edo~~''' divides~~ the ~~octave into 190537 equal parts of 0~~.~~0063 cents each~~. It is the ~~denominator~~ of the ~~next convergent for~~ log23 ~~past~~ [[~~111202edo~~|~~111202~~]], ~~before~~ [[~~10590737edo|10590737~~]].

190537edo has a [[consistency]] limit of 11, which is rather impressive for a convergent. However, it is strongest in the 2.3.7.17.23 subgroup. Notably, it is the first member of the log23 convergent series with a 3-2 [[Telicity #k-Strong Telicity|telicity ''k''-strength]] greater than 1 since [[665edo]] and it even surpasses 665edo in telicity ''k''-strength. However, the downside is that the step size is many times smaller than the [[JND]]. The 3-limit comma this edo tempers out has been named the [[Archangelic comma]].

== Theory ==

~~190537edo has a consistency limit of 11, which is rather impressive for a convergent. However, it's strongest~~ in ~~the 2.3.7.17.23 subgroup. Notably, it's the first EDO with a 3-2 [[telicity]] k-strength greater that 1 since [[665edo]] and it even surpasses 665edo in telicity k-strength.~~

=== Prime harmonics ===

~~{{Harmonics in equal|190537}}~~

=== Supersets ===

* [[571611edo]] (3×)

* [[762148edo]] (4×)

* [[1714833edo]] (9×)

* [[1905370edo]] (10×)

* [[2667518edo]] (14×)

* [[4191814edo]] (22×)

[[Category:~~Equal divisions of the octave~~|#####]]

[[Category:3-limit record edos|######]]

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 {{Infobox ET}}
+{{ED intro}} It is the denominator of the next convergent for log<sub>2</sub>3 past [[111202edo|111202]], with another such convergent not occurring until [[10590737edo|10590737]].
-The '''190537edo''' divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log<sub>2</sub>3 past [[111202edo|111202]], before [[10590737edo|10590737]].
+edo has a [[consistency]] limit of 11, which is rather impressive for a convergent. However, it is strongest in the 2.3.7.17.23 subgroup. Notably, it is the first member of the log<sub>2</sub>3 convergent series with a 3-2 [[Telicity #k-Strong Telicity|telicity ''k''-strength]] greater than 1 since [[665edo]] and it even surpasses 665edo in telicity ''k''-strength. However, the downside is that the step size is many times smaller than the [[JND]]. The 3-limit comma this edo tempers out has been named the [[Archangelic comma]].
 == Theory ==
-edo has a consistency limit of 11, which is rather impressive for a convergent.  However, it's strongest in the 2.3.7.17.23 subgroup.  Notably, it's the first EDO with a 3-2 [[telicity]] k-strength greater that 1 since [[665edo]] and it even surpasses 665edo in telicity k-strength.
+=== Prime harmonics ===
+{{Harmonics in equal|190537|columns=12}}
-{{Harmonics in equal|190537}}
+=== Supersets ===
+* [[571611edo]] (3×)
+* [[762148edo]] (4×)
+* [[1714833edo]] (9×)
+* [[1905370edo]] (10×)
+* [[2667518edo]] (14×)
+* [[4191814edo]] (22×)
-[[Category:Equal divisions of the octave|#####]] <!-- 6-digit number -->
+[[Category:3-limit record edos|######]] <!-- 6-digit number -->