289edo: Difference between revisions
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The '''289 equal temperament''' (289EDO) divides the octave into 289 equal parts of 4.15225 [[cent]]s each. It is the [[optimal patent val]] for [[13-limit]] [[Werckismic temperaments #History|history temperament]], which tempers out 364/363, 441/440 and 1001/1000, and provides a good tuning for the 11-limit version also, and is also the optimal patent val for [[Schismatic_family|sextilififths]] in both the 11- and 13-limit. It is uniquely consistent in the 9-odd-limit, and tempers out the schisma, 32805/32768 in the 5-limit; 4375/4374 and 65625/65536 in the 7-limit; 441/440 and 4000/3993 in the 11-limit; and 364/363, 676/675, 1001/1000, 1575/1573 and 2080/2079 in the 13-limit. | The '''289 equal temperament''' (289EDO) divides the octave into 289 equal parts of 4.15225 [[cent]]s each. It is the [[optimal patent val]] for [[13-limit]] [[Werckismic temperaments #History|history temperament]], which tempers out 364/363, 441/440 and 1001/1000, and provides a good tuning for the 11-limit version also, and is also the optimal patent val for [[Schismatic_family|sextilififths]] in both the 11- and 13-limit. It is uniquely consistent in the 9-odd-limit, and tempers out the schisma, 32805/32768 in the 5-limit; 4375/4374 and 65625/65536 in the 7-limit; 441/440 and 4000/3993 in the 11-limit; and 364/363, 676/675, 1001/1000, 1575/1573 and 2080/2079 in the 13-limit. | ||
Since 289 is square of 17, 289 = 17 × 17, 289EDO | Since 289 is square of 17, 289 = 17 × 17, 289EDO [[support]]s the chlorine temperament, which tempers out the septendecima {{monzo|-52 -17 34}} and the ragisma 4375/4374. | ||
[[Category:Edo]] | [[Category:Edo]] | ||
[[Category:history]] | [[Category:history]] | ||
[[Category:sextilififths]] | [[Category:sextilififths]] | ||