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 divisions of the octave''' ('''289edo''') divides the octave into 289 equal parts of 4.15225 [[cent]]s each. 289edo is the [[optimal patent val]] for [[13-limit]] [[History (temperament)|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 [[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~~ [[support]]s the chlorine temperament, which tempers out the septendecima {{monzo|-52 -17 34}} and the ragisma 4375/4374.

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~~]]

=== Prime harmonics ===

[[Category:~~history~~]]

[[Category:~~sextilififths~~]]

[[Category:Equal divisions of the octave]]

[[Category:History (temperament)]]

[[Category:Sextilififths]]

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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 divisions of the octave''' ('''289edo''') divides the octave into 289 equal parts of 4.15225 [[cent]]s each. 289edo is the [[optimal patent val]] for [[13-limit]] [[History (temperament)|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 [[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 [[support]]s the chlorine temperament, which tempers out the septendecima {{monzo|-52 -17 34}} and the ragisma 4375/4374.
+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]]
+=== Prime harmonics ===
-[[Category:history]]
+{{Harmonics in equal|289}}
-[[Category:sextilififths]]
+[[Category:Equal divisions of the octave]]
+[[Category:History (temperament)]]
+[[Category:Sextilififths]]