Auk: Difference between revisions
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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. | '''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)). | ||
(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 == | == Interval chain == | ||
{|class="wikitable" | {|class="wikitable" | ||
|- | |- | ||
!# | ! # | ||
!Cents | ! Cents | ||
!Approximate ratios | ! Approximate ratios | ||
|- | |- | ||
|0 | | 0 | ||
|0.00 | | 0.00 | ||
|[[1/1]] | | [[1/1]] | ||
|- | |- | ||
|1 | | 1 | ||
|546.95 | | 546.95 | ||
|112/81 | | 112/81 | ||
|- | |- | ||
|2 | | 2 | ||
|392.94 | | 392.94 | ||
|[[26/21]], 25088/19683 | | [[26/21]], 25088/19683 | ||
|- | |- | ||
|3 | | 3 | ||
|236.93 | | 236.93 | ||
|832/729 | | 832/729 | ||
|- | |- | ||
|4 | | 4 | ||
|81.92 | | 81.92 | ||
|1352/1323 | | 1352/1323 | ||
|- | |- | ||
|5 | | 5 | ||
|628.87 | | 628.87 | ||
| | | | ||
|- | |- | ||
|6 | | 6 | ||
|473.86 | | 473.86 | ||
| | | | ||
|} | |} | ||
[[Category: | [[Category:Auk| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | |||
[[Category:Non-octave temperaments]] | |||