289edo: Difference between revisions

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== Theory ==

289edo is a strong 5-limit system with decent 11- and 13-limit interpretations despite in[[consistency]] in the [[13-odd-limit]]. It [[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.

289edo is a strong 5-limit system with decent [[11-limit|11-]] and [[13-limit]] interpretations despite in[[consistency]] in the [[13-odd-limit]]. As an equal temperament, it [[tempering out|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.

It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[~~History~~ (temperament)|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.

It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[history (temperament)|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.

=== Prime harmonics ===

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 == Theory ==
-edo is a strong 5-limit system with decent 11- and 13-limit interpretations despite in[[consistency]] in the [[13-odd-limit]]. It [[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.
+edo is a strong 5-limit system with decent [[11-limit|11-]] and [[13-limit]] interpretations despite in[[consistency]] in the [[13-odd-limit]]. As an equal temperament, it [[tempering out|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.
-It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[History (temperament)|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.
+It is the [[optimal patent val]] for the [[13-limit]] rank-5 temperament tempering out 364/363, and the 13-limit [[history (temperament)|history]] temperament, which tempers out 364/363, 441/440 and 676/675. It provides a good tuning for the 11-limit version also. It is also the optimal patent val for [[sextilififths]], [[quintaschis]], and [[quincy]] in both the 11- and 13-limit.
 === Prime harmonics ===