289edo: Difference between revisions

Line 1:

The '''289 equal temperament''' divides the octave into 289 equal parts of 4.~~152 cents~~ each. It is the [[~~Optimal_patent_val|~~optimal patent val]] for [[~~13-limit|~~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-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 supports the chlorine temperament, which tempers out the septendecima {{monzo|-52 -17 34}} and the ragisma 4375/4374.

[[Category:Edo]]

[[Category:history]]

[[Category:~~sextilifths~~]]

[[Category:sextilififths]]

@@ Line 1: / Line 1: @@
-The '''289 equal temperament''' divides the octave into 289 equal parts of 4.152 cents each. It is the [[Optimal_patent_val|optimal patent val]] for [[13-limit|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-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 supports the chlorine temperament, which tempers out the septendecima {{monzo|-52 -17 34}} and the ragisma 4375/4374.
+[[Category:Edo]]
 [[Category:history]]
-[[Category:sextilifths]]
+[[Category:sextilififths]]