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 log<sub>2</sub>3 past [[15601edo|15601]], before [[79335edo|79335]], and has a fifth which is about 0.00000039 cents compressed. 31867edo is consistent through the [[21-odd-limit|21-odd limit]], tempering out |305 -106 -59> and |-122 285 -142> in the 5-limit; |-7 30 -9 -7>, |51 -13 -1 -10>, and |-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.

The '''31867 edo''' divides the octave into 31867 equal parts of 0.03765651 cents each. 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 cents compressed. 31867edo is consistent through the [[21-odd-limit|21-odd limit]], tempering out |305 -106 -59> and |-122 285 -142> in the 5-limit; |-7 30 -9 -7>, |51 -13 -1 -10>, and |-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.

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

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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 log<sub>2</sub>3 past [[15601edo\|15601]], before [[79335edo\|79335]], and has a fifth which is about 0.00000039 cents compressed. 31867edo is consistent through the [[21-odd-limit\|21-odd limit]], tempering out \|305 -106 -59> and \|-122 285 -142> in the 5-limit; \|-7 30 -9 -7>, \|51 -13 -1 -10>, and \|-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.		The '''31867 edo''' divides the octave into 31867 equal parts of 0.03765651 cents each. 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 cents compressed. 31867edo is consistent through the [[21-odd-limit\|21-odd limit]], tempering out \|305 -106 -59> and \|-122 285 -142> in the 5-limit; \|-7 30 -9 -7>, \|51 -13 -1 -10>, and \|-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.

	[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->		[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->