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]], with another such convergent not occurring until [[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 member of the log23 convergent series with a 3-2 [[Telicity #k-Strong Telicity|telicity k-strength]] greater ~~that~~ 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]].

=== Prime harmonics ===

[[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]], with another such convergent not occurring until [[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 member of the log<sub>2</sub>3 convergent series with a 3-2 [[Telicity #k-Strong Telicity|telicity k-strength]] greater that 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]].
+=== Prime harmonics ===
 {{Harmonics in equal|190537|columns=12}}
-[[Category:Equal divisions of the octave|######]] <!-- 6-digit number -->
+[[Category:3-limit record edos|######]] <!-- 6-digit number -->