Auk: Difference between revisions

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

Latest revision as of 09:19, 29 April 2025

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> ("neptunian"), 4L 1s<3/2>, 5L 4s<3/2>, and 9L 5s<3/2>. 9edf is a particularly good equal temperament that supports 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

# 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