Auk
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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> ("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 |