214edo: Difference between revisions

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214edo is the equal division of the octave into 214 parts of 5.6075 ~~cents~~ each. It is (uniquely) consistent through the [[9-odd-limit]] ~~and~~ tempers out the following commas ~~up to the 13-limit~~: |51 19 9~~> and |2 9 -7>~~ in the 5-limit; ~~|-9 8 -4 2>~~, ~~|0 3 4 -5>~~, ~~6144~~ / ~~6125~~ and |22 -1 -10 1> in the 7-limit; 1375 / 1372 in the 11-limit; 1188 / 1183, 351 / 350 and 847 / 845 in the 13-limit~~. The patent val for 214-EDO is <214 339 497 601|~~. It can be viewed as a 2.13/5 subgroup temperament, as its approximations for lower prime limits are very poor but~~. However,~~ this makes ~~214-EDO~~ an exceptionally xenharmonic tuning.

'''214edo''' is the equal division of the [[octave]] into 214 parts of 5.6075 [[cent]]s each. It is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val| 214 339 497 601 740 792 }}, which tempers out the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo| -51 19 9 }} (untriton comma) in the 5-limit; [[6144/6125]] (porwell), 16875/16807 (mirkwai), 321489/321400 (varunisma), and {{monzo| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]] and 1375/1372 in the 11-limit; 1188/1183, [[351/350]] and [[847/845]] in the 13-limit. It can be viewed as a 2.13/5 subgroup temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.

[[Category:Equal divisions of the octave]]

Revision as of 20:08, 29 August 2019 view source Mike Battaglia (talk \| contribs) autopatrolled, Bureaucrats, confirmaccount-notify, emailconfirmed, Interface administrators, Sysops 1,399 edits 214edo, not 213edo ← Older edit		Revision as of 13:59, 27 December 2021 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 24,061 edits Corrections, cleanup and +category Newer edit →
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	214edo is the equal division of the octave into 214 parts of 5.6075 ~~cents~~ each. It is (uniquely) consistent through the [[9-odd-limit]] ~~and~~ tempers out the following commas ~~up to the 13-limit~~: \|51 19 9~~> and \|2 9 -7>~~ in the 5-limit; ~~\|-9 8 -4 2>~~, ~~\|0 3 4 -5>~~, ~~6144~~ / ~~6125~~ and \|22 -1 -10 1> in the 7-limit; 1375 / 1372 in the 11-limit; 1188 / 1183, 351 / 350 and 847 / 845 in the 13-limit~~. The patent val for 214-EDO is <214 339 497 601\|~~. It can be viewed as a 2.13/5 subgroup temperament, as its approximations for lower prime limits are very poor but~~. However,~~ this makes ~~214-EDO~~ an exceptionally xenharmonic tuning.		'''214edo''' is the equal division of the [[octave]] into 214 parts of 5.6075 [[cent]]s each. It is (uniquely) consistent through the [[7-odd-limit]]. The patent val for 214edo is {{val\| 214 339 497 601 740 792 }}, which tempers out the following commas: 78732/78125 ([[sensipent comma]]) and {{monzo\| -51 19 9 }} (untriton comma) in the 5-limit; [[6144/6125]] (porwell), 16875/16807 (mirkwai), 321489/321400 (varunisma), and {{monzo\| 22 -1 -10 1 }} (quasiorwellisma) in the 7-limit; [[540/539]] and 1375/1372 in the 11-limit; 1188/1183, [[351/350]] and [[847/845]] in the 13-limit. It can be viewed as a 2.13/5 subgroup temperament, as its approximations for lower prime limits are very poor but this makes 214edo an exceptionally xenharmonic tuning.

			[[Category:Equal divisions of the octave]]