View source for Auk

'''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)).

For more technical data, see [[Subgroup temperaments #Auk]].

== Interval chain ==
{|class="wikitable"
|-
! #
! Cents
! Approximate ratios
|-
| 0
| 0.00
| [[1/1]]
|-
| 1
| 546.95
| 112/81
|-
| 2
| 392.94
| [[26/21]], 25088/19683
|-
| 3
| 236.93
| 832/729
|-
| 4
| 81.92
| 1352/1323
|-
| 5
| 628.87
| 
|-
| 6
| 473.86
| 
|}

[[Category:Auk| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Non-octave temperaments]]