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| '''114edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 114 parts, each of 10.52632 [[cent|cent]]s. In the [[5-limit|5-limit]] it [[tempering_out|tempers out]] 2048/2025, in the [[7-limit|7-limit]] 245/243, in the [[11-limit|11-limit]] 121/120 and 176/175, in the [[13-limit|13-limit]] 196/195 and 325/324, in the [[17-limit|17-limit]] 136/135 and 154/153, in the [[19-limit|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family|shrutar temperament]]; it is in fact the [[Optimal_patent_val|optimal patent val]] for [[Shrutar|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.
| | {{Infobox ET}} |
| | {{ED intro}} |
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| ===Period of 19-limit Shrutar=== | | == Theory == |
| | In the [[5-limit]] the equal temperament [[tempering out|tempers out]] 2048/2025 ([[diaschisma]]), in the [[7-limit]] [[245/243]], in the [[11-limit]] [[121/120]], [[176/175]] and notably the [[quartisma]], in the [[13-limit]] [[196/195]] and [[325/324]], in the [[17-limit]] [[136/135]] and [[154/153]], in the [[19-limit]] [[286/285]] and [[343/342]]. These commas make for 114edo being an excellent tuning for the [[shrutar]] temperament; it is in fact the [[optimal patent val]] for shrutar in the 11-, 13-, 17-, and 19-limit, as well as the rank-3 [[bisector]] temperament. |
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| {| class="wikitable"
| | === Odd harmonics === |
| |- | | {{Harmonics in equal|114}} |
| ! | Degree
| | |
| ! | Cents
| | === Subsets and supersets === |
| |-
| | Since 114 factors into {{factorization|114}}, 114 edo has subset edos {{EDOs| 2, 3, 6, 19, 38, and 57 }}. |
| | | 2 | | |
| | | 21.05263
| | == Intervals == |
| |-
| | {{Interval table}} |
| | | 3
| | |
| | | 31.57895
| | [[Category:Shrutar]] |
| |-
| | [[Category:Bisector]] |
| | | 5
| |
| | | 52.63158
| |
| |-
| |
| | | 7
| |
| | | 73.68421
| |
| |-
| |
| | | 8
| |
| | | 84.21053
| |
| |-
| |
| | | 10
| |
| | | 105.26316
| |
| |-
| |
| | | 12
| |
| | | 126.31579
| |
| |-
| |
| | | 13
| |
| | | 136.842105
| |
| |-
| |
| | | 15
| |
| | | 157.89474
| |
| |-
| |
| | | 17
| |
| | | 178.94737
| |
| |-
| |
| | | 18
| |
| | | 189.47369
| |
| |-
| |
| | | 20
| |
| | | 210.52632
| |
| |-
| |
| | | 22
| |
| | | 231.57895
| |
| |-
| |
| | | 23
| |
| | | 242.10526
| |
| |-
| |
| | | 25
| |
| | | 263.157895
| |
| |-
| |
| | | 27
| |
| | | 284.21053
| |
| |-
| |
| | | 29
| |
| | | 305.26316
| |
| |-
| |
| | | 30
| |
| | | 315.78947
| |
| |-
| |
| | | 32
| |
| | | 336.842105
| |
| |-
| |
| | | 34
| |
| | | 357.89474
| |
| |-
| |
| | | 35
| |
| | | 368.42105
| |
| |-
| |
| | | 37
| |
| | | 389.47368
| |
| |-
| |
| | | 39
| |
| | | 410.52632
| |
| |-
| |
| | | 40
| |
| | | 421.05263
| |
| |-
| |
| | | 42
| |
| | | 442.10526
| |
| |-
| |
| | | 44
| |
| | | 463.157895
| |
| |-
| |
| | | 45
| |
| | | 473.68421
| |
| |-
| |
| | | 47
| |
| | | 494.73684
| |
| |-
| |
| | | 49
| |
| | | 515.78947
| |
| |-
| |
| | | 50
| |
| | | 526.31579
| |
| |-
| |
| | | 52
| |
| | | 547.36842
| |
| |-
| |
| | | 54
| |
| | | 568.42105
| |
| |-
| |
| | | 55
| |
| | | 578.94737
| |
| |}
| |
| [[Category:edo]]
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| [[Category:shrutar]] | |
| [[Category:theory]] | |