289edo: Difference between revisions

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| Consistency = 9

}}

~~The '''~~289 equal divisions of the octave''' ('''289edo'''), or the '''289(-tone) equal temperament''' ('''289tet''', '''289et''') when viewed from a [[regular temperament]] perspective, divides the octave into 289 equal parts of about 4.15 [[cent]]s each.

==Theory==

== Theory ==

289edo is the [[optimal patent val]] for [[13-limit]] [[History (temperament)|history]] temperament, which tempers out [[364/363]], [[441/440]] and [[676/675]], 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.

289 is 17 squared. In light of containing [[17edo]] as a subset, 289edo [[support]]s the [[chlorine]] temperament, which tempers out the [[septendecima]] {{monzo|-52 -17 34}} and the ragisma 4375/4374.

=== Prime harmonics ===

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 | Consistency = 9
 }}
-The '''289 equal divisions of the octave''' ('''289edo'''), or the '''289(-tone) equal temperament''' ('''289tet''', '''289et''') when viewed from a [[regular temperament]] perspective, divides the octave into 289 equal parts of about 4.15 [[cent]]s each.
+{{EDO intro|289}}
-==Theory==
+== Theory ==
 edo is the [[optimal patent val]] for [[13-limit]] [[History (temperament)|history]] temperament, which tempers out [[364/363]], [[441/440]] and [[676/675]], 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<!-- How specifically the square property of 289 ensures it supports chlorine? -->, 289 = 17 × 17, 289edo [[support]]s the [[chlorine]] temperament, which tempers out the [[septendecima]] {{monzo|-52 -17 34}} and the ragisma 4375/4374.
+is 17 squared. In light of containing [[17edo]] as a subset, 289edo [[support]]s the [[chlorine]] temperament, which tempers out the [[septendecima]] {{monzo|-52 -17 34}} and the ragisma 4375/4374.
 === Prime harmonics ===