31867edo: Difference between revisions

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~~The '''31867 edo''' divides the octave into 31867 equal parts of 0.03765651 cents each.~~ It is the denominator of the next convergent for ~~log2(~~3) past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is 0.00000039 ~~cents flat. 31867edo is consistent through the [[21-odd-limit|21-odd limit]]~~.

{{ED intro}} It is the denominator of the next convergent for log<sub>2</sub>3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039{{c}} compressed.

[[Category:~~Edo~~]]

31867edo inherits its mapping for the prime [[11/1|11]] from [[2897edo]], which is the only mapping shared between the two edo systems – unfortunately, this means that the prime 11 is not good for stacking in this system. However, despite this, 31867edo is [[consistent]] through the [[21-odd-limit]].

As an equal temperament, 31867et [[tempering out|tempers out]] {{monzo| 305 -106 -59 }} and {{monzo| -122 285 -142 }} in the 5-limit; {{monzo| -7 30 -9 -7 }}, {{monzo| 51 -13 -1 -10 }}, and {{monzo| -8 2 -62 53 }} in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.

=== Prime harmonics ===

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

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-The '''31867 edo''' divides the octave into 31867 equal parts of 0.03765651 cents each. It is the denominator of the next convergent for log2(3) past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is 0.00000039 cents flat. 31867edo is consistent through the [[21-odd-limit|21-odd limit]].
+{{Infobox ET}}
+{{ED intro}} It is the denominator of the next convergent for log<sub>2</sub>3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039{{c}} compressed.
-[[Category:Edo]]
+edo inherits its mapping for the prime [[11/1|11]] from [[2897edo]], which is the only mapping shared between the two edo systems – unfortunately, this means that the prime 11 is not good for stacking in this system. However, despite this, 31867edo is [[consistent]] through the [[21-odd-limit]].
+As an equal temperament, 31867et [[tempering out|tempers out]] {{monzo| 305 -106 -59 }} and {{monzo| -122 285 -142 }} in the 5-limit; {{monzo| -7 30 -9 -7 }}, {{monzo| 51 -13 -1 -10 }}, and {{monzo| -8 2 -62 53 }} in the 7-limit; 6576668672/6576582375, 13841287201/13841203200, 11816941917501/11816406250000, and 28247524900000/28245855390489 in the 11-limit; [[123201/123200]], 1990656/1990625, 72773428/72772425, 1977326743/1977300000, and 6866455078125/6866343676192 in the 13-limit; 194481/194480, 336141/336140, 2000033/2000000, 9765888/9765625, 58464700/58461513, and 114244000/114243723 in the 17-limit; 89376/89375, 104976/104975, 165376/165375, 633556/633555, 709632/709631, and 742586/742577 in the 19-limit.
+=== Prime harmonics ===
+{{Harmonics in equal|31867}}
+[[Category:3-limit record edos|#####]] <!-- 5-digit number -->