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| '''Auk''' is a [[nonoctave]] [[regular temperament]] in the 3/2.7.13 subgroup that tempers out the comma 87808/85293. It thus equates 3 [[7/1]] (fifth-reduced to 112/81) with [[13/1]] (fifth-reduced to 832/729). The generator when reduced is a superfourth in the neighborhood of 550 cents, representing 112/81. It possesses non-trivial MOS of the families [[1L 3s (3/2-equivalent)|1L 3s<3/2>]] ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. [[9edf]] is a particularly good equal temperament that [[support]]s it. It contains tempered versions of the chords 1-832/729-112/81 (fifth-reduction of 1:7:13) and 1-[[63/52]]-112/81 (fifth-reduction of 1/(13:17:1)).
| | #redirect [[Subgroup temperaments #Auk]] |
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| For more technical data, see [[Subgroup temperaments #Auk]].
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| == Interval chain ==
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| {|class="wikitable"
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| |-
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| ! #
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| ! Cents
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| ! Approximate ratios
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| |-
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| | 0
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| | 0.00
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| | [[1/1]]
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| |-
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| | 1
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| | 546.95
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| | 112/81
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| |-
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| | 2
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| | 392.94
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| | [[26/21]], 25088/19683
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| |-
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| | 3
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| | 236.93
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| | 832/729
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| |-
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| | 4
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| | 81.92
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| | 1352/1323
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| |-
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| | 5
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| | 628.87
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| |-
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| | 6
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| | 473.86
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| |}
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| [[Category:Auk| ]] <!-- main article -->
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| [[Category:Rank-2 temperaments]] | | [[Category:Rank-2 temperaments]] |
| [[Category:Non-octave temperaments]] | | [[Category:Non-octave temperaments]] |