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| (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 393216/390625 ([[Würschmidt comma]]) 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 15625/15552 (kleisma) 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 34171875/33554432 (ampersand comma) and 762939453125/753145430616 ([[Maja family|maja comma]]) 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.

==Theory==

257edo is good at 2.11.13.37.41.53.59.67 subgroup.

It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <257 407 597 721| (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 393216/390625 ([[Würschmidt comma]]) 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 15625/15552 (kleisma) 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 34171875/33554432 (ampersand comma) and 762939453125/753145430616 ([[Maja family|maja comma]]) 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]].

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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: &lt;257 407 597 721| (patent val), &lt;257 408 597 722| (257bd), &lt;257 407 596 721| (257c), and &lt;257 407 597 722| (257d). Using the patent val, it tempers out 393216/390625 ([[Würschmidt comma]]) and |-36 33 -7&gt; in the 5-limit; 1029/1024, 177147/175000, and 393216/390625 in the 7-limit. Using the 257bd val, it tempers out 15625/15552 (kleisma) and |69 -42 -1&gt; in the 5-limit; 4000/3969, 6144/6125, and 40353607/39858075 in the 7-limit. Using the 257c val, it tempers out 34171875/33554432 (ampersand comma) and 762939453125/753145430616 ([[Maja family|maja comma]]) 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.
+{{EDO intro|257}}
+==Theory==
+{{harmonics in equal|257}}
+edo is good at 2.11.13.37.41.53.59.67 subgroup.
+It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: &lt;257 407 597 721| (patent val), &lt;257 408 597 722| (257bd), &lt;257 407 596 721| (257c), and &lt;257 407 597 722| (257d). Using the patent val, it tempers out 393216/390625 ([[Würschmidt comma]]) and |-36 33 -7&gt; in the 5-limit; 1029/1024, 177147/175000, and 393216/390625 in the 7-limit. Using the 257bd val, it tempers out 15625/15552 (kleisma) and |69 -42 -1&gt; in the 5-limit; 4000/3969, 6144/6125, and 40353607/39858075 in the 7-limit. Using the 257c val, it tempers out 34171875/33554432 (ampersand comma) and 762939453125/753145430616 ([[Maja family|maja comma]]) 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.
 edo is the 55th [[prime EDO]].