257edo: Difference between revisions

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'''257edo''' is the [[EDO|equal division of the octave]] into 257 parts of 4.66926 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <257 407 597 721| (optimal patent val), <257 408 597 722| (257bd), <257 407 596 721| (257c), and <257 407 597 722| (257d). Using the ~~optimal~~ patent val, it tempers out [[Würschmidt comma]], 393216/390625 and |-36, 33, -7> in the 5-limit; 1029/1024, 177147/175000, and 393216/390625 in the 7-limit. Using the 257bd val, it tempers out the kleisma, 15625/15552 and |69, -42, -1> in the 5-limit; 4000/3969, 6144/6125, and 40353607/39858075 in the 7-limit. Using the 257c val, it tempers out the ampersand comma, 34171875/33554432 and the [[Maja family|maja comma]], 762939453125/753145430616 in the 5-limit; 225/224, 1029/1024, and 854492187500/847288609443 in the 7-limit; 243/242, 385/384, 441/440, and 152587890625/148550704533 in the 11-limit, providing for the 11-limit [[Gamelismic clan|miracle temperament]]. Using the 257d val, it tempers out 1728/1715, 413343/409600, and 703125/702464 in the 7-limit.

'''257edo''' is the [[EDO|equal division of the octave]] into 257 parts of 4.66926 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <257 407 597 721| (optimal patent val), <257 408 597 722| (257bd), <257 407 596 721| (257c), and <257 407 597 722| (257d). Using the patent val, it tempers out [[Würschmidt comma]], 393216/390625 and |-36 33 -7> in the 5-limit; 1029/1024, 177147/175000, and 393216/390625 in the 7-limit. Using the 257bd val, it tempers out the kleisma, 15625/15552 and |69 -42 -1> in the 5-limit; 4000/3969, 6144/6125, and 40353607/39858075 in the 7-limit. Using the 257c val, it tempers out the ampersand comma, 34171875/33554432 and the [[Maja family|maja comma]], 762939453125/753145430616 in the 5-limit; 225/224, 1029/1024, and 854492187500/847288609443 in the 7-limit; 243/242, 385/384, 441/440, and 152587890625/148550704533 in the 11-limit, providing for the 11-limit [[Gamelismic clan|miracle temperament]]. Using the 257d val, it tempers out 1728/1715, 413343/409600, and 703125/702464 in the 7-limit.

257edo is the 55th [[prime EDO]].

Revision as of 11:27, 5 December 2018 view source Xenllium (talk \| contribs) autopatrolled, emailconfirmed 5,012 edits Created page with "'''257edo''' is the equal division of the octave into 257 parts of 4.66926 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possi..." Tags: Mobile edit Mobile web edit		Revision as of 06:48, 14 December 2018 view source Xenllium (talk \| contribs) autopatrolled, emailconfirmed 5,012 edits No edit summary Tags: Mobile edit Mobile web edit Newer edit →
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	'''257edo''' is the [[EDO\|equal division of the octave]] into 257 parts of 4.66926 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <257 407 597 721\| (optimal patent val), <257 408 597 722\| (257bd), <257 407 596 721\| (257c), and <257 407 597 722\| (257d). Using the ~~optimal~~ patent val, it tempers out [[Würschmidt comma]], 393216/390625 and \|-36, 33, -7> in the 5-limit; 1029/1024, 177147/175000, and 393216/390625 in the 7-limit. Using the 257bd val, it tempers out the kleisma, 15625/15552 and \|69, -42, -1> in the 5-limit; 4000/3969, 6144/6125, and 40353607/39858075 in the 7-limit. Using the 257c val, it tempers out the ampersand comma, 34171875/33554432 and the [[Maja family\|maja comma]], 762939453125/753145430616 in the 5-limit; 225/224, 1029/1024, and 854492187500/847288609443 in the 7-limit; 243/242, 385/384, 441/440, and 152587890625/148550704533 in the 11-limit, providing for the 11-limit [[Gamelismic clan\|miracle temperament]]. Using the 257d val, it tempers out 1728/1715, 413343/409600, and 703125/702464 in the 7-limit.		'''257edo''' is the [[EDO\|equal division of the octave]] into 257 parts of 4.66926 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <257 407 597 721\| (optimal patent val), <257 408 597 722\| (257bd), <257 407 596 721\| (257c), and <257 407 597 722\| (257d). Using the patent val, it tempers out [[Würschmidt comma]], 393216/390625 and \|-36 33 -7> in the 5-limit; 1029/1024, 177147/175000, and 393216/390625 in the 7-limit. Using the 257bd val, it tempers out the kleisma, 15625/15552 and \|69 -42 -1> in the 5-limit; 4000/3969, 6144/6125, and 40353607/39858075 in the 7-limit. Using the 257c val, it tempers out the ampersand comma, 34171875/33554432 and the [[Maja family\|maja comma]], 762939453125/753145430616 in the 5-limit; 225/224, 1029/1024, and 854492187500/847288609443 in the 7-limit; 243/242, 385/384, 441/440, and 152587890625/148550704533 in the 11-limit, providing for the 11-limit [[Gamelismic clan\|miracle temperament]]. Using the 257d val, it tempers out 1728/1715, 413343/409600, and 703125/702464 in the 7-limit.

	257edo is the 55th [[prime EDO]].		257edo is the 55th [[prime EDO]].