Auk: Difference between revisions
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'''Auk''' is a nonoctave temperament in the 3/2.7.13 subgroup | '''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]] | |||
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 |