289edo: Difference between revisions

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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.

{{Infobox ET

| Prime factorization = 17<sup>2</sup>

| Step size = 4.15225¢

| Fifth = 169\289 (701.73¢)

| Semitones = 27:22 (112.11¢ : 91.35¢)

| 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.

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.

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-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.
+{{Infobox ET
+| Prime factorization = 17<sup>2</sup>
+| Step size = 4.15225¢
+| Fifth = 169\289 (701.73¢)
+| Semitones = 27:22 (112.11¢ : 91.35¢)
+| 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 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.