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| {{Infobox ET}} | | {{Infobox ET}} |
| '''114edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 114 parts, each of 10.52632 [[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, 176/175 and [[Quartisma|117440512/117406179]], 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.
| | {{ED intro}} |
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| == Prime harmonics == | | == 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. |
| | |
| | === Odd harmonics === |
| {{Harmonics in equal|114}} | | {{Harmonics in equal|114}} |
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| == Period of 19-limit Shrutar == | | === Subsets and supersets === |
| | Since 114 factors into {{factorization|114}}, 114 edo has subset edos {{EDOs| 2, 3, 6, 19, 38, and 57 }}. |
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| {| class="wikitable"
| | == Intervals == |
| |-
| | {{Interval table}} |
| ! |Degree
| |
| ! |Cents
| |
| !Difference from 68edo
| |
| |-
| |
| | |2
| |
| | |21.05263
| |
| |3.40557¢
| |
| |-
| |
| | |3
| |
| | |31.57895
| |
| | -3.71517¢
| |
| |-
| |
| | | 5
| |
| | | 52.63158
| |
| | -0.3096¢
| |
| |-
| |
| | |7
| |
| | |73.68421
| |
| |3.096¢
| |
| |-
| |
| | |8
| |
| | |84.21053
| |
| | -4.02477¢
| |
| |-
| |
| | |10
| |
| | |105.26316
| |
| | -0.619195¢
| |
| |-
| |
| | |12
| |
| | | 126.31579
| |
| |2.78638¢
| |
| |-
| |
| | |13
| |
| | |136.842105
| |
| | -4.334365¢
| |
| |-
| |
| | |15
| |
| | |157.89474
| |
| | -0.9288¢
| |
| |-
| |
| | | 17
| |
| | |178.94737
| |
| |2.47678¢
| |
| |-
| |
| | |18
| |
| | | 189.47369
| |
| | -4.644¢
| |
| |-
| |
| | |20
| |
| | |210.52632
| |
| | -1.23839¢
| |
| |-
| |
| | |22
| |
| | |231.57895
| |
| |2.16718¢
| |
| |-
| |
| | |23
| |
| | |242.10526
| |
| | -4.953560372
| |
| |-
| |
| | |25
| |
| | |263.157895
| |
| | -1.548¢
| |
| |-
| |
| | |27
| |
| | |284.21053
| |
| |1.857585¢
| |
| |-
| |
| | |29
| |
| | |305.26316
| |
| |5.26316¢
| |
| |-
| |
| | |30
| |
| | |315.78947
| |
| | -1.857585¢
| |
| |-
| |
| | |32
| |
| | |336.842105
| |
| |1.548¢
| |
| |-
| |
| | |34
| |
| | |357.89474
| |
| |4.95356¢
| |
| |-
| |
| | |35
| |
| | | 368.42105
| |
| | -2.16718¢
| |
| |-
| |
| | |37
| |
| | |389.47368
| |
| |1.23839¢
| |
| |-
| |
| | |39
| |
| | |410.52632
| |
| |4.64396¢
| |
| |-
| |
| | |40
| |
| | |421.05263
| |
| | -2.47678¢
| |
| |-
| |
| | |42
| |
| | |442.10526
| |
| |0.92879¢
| |
| |-
| |
| | |44
| |
| | |463.157895
| |
| |4.334365¢
| |
| |-
| |
| | |45
| |
| | |473.68421
| |
| | -2.78638¢
| |
| |-
| |
| | |47
| |
| | |494.73684
| |
| |0.619195¢
| |
| |-
| |
| | |49
| |
| | |515.78947
| |
| |4.02477¢
| |
| |-
| |
| | |50
| |
| | |526.31579
| |
| | -3.095975¢
| |
| |-
| |
| | |52
| |
| | |547.36842
| |
| |0.3096¢
| |
| |-
| |
| | |54
| |
| | |568.42105
| |
| |3.71517¢
| |
| |-
| |
| | |55
| |
| | |578.94737
| |
| | -3.40557¢
| |
| |}
| |
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| [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
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| [[Category:Shrutar]] | | [[Category:Shrutar]] |
| | [[Category:Bisector]] |