Deneb: Difference between revisions

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-'''Deneb''' is a [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma 6655/6561 in the 3.5.11 subgroup, the amount by which 4 [[11/9]]'s exceed [[11/5]]. Having a generator of ~[[11/9]], it possesses [[MOS scale]]s of the families 1L 4s<3/1>, 5L 1s<3/1>, 6L 5s<3/1>, and 11L 6s<3/1>. Good tunings for this temperament are [[11edt]], [[17edt]], [[28edt]], [[39edt]] and [[45edt]].
+{{todo|rewrite, polish interval chain table|inline=1}}
+'''Deneb''' is a [[nonoctave]], [[tritave]]-repeating [[rank-2 temperament]] that tempers out the comma [[6655/6561]] in the 3.5.11 subgroup. It  is generated by a neutral third that represents a flat [[11/9]], and three generators stacked represent [[9/5]] (and due to tritave-equivalence, -3 generators stacked represents [[5/3]]). It possesses [[MOS scale]]s of the families {{mos scalesig|1L 4s<3/1>|link=1}}, {{mos scalesig|5L 1s<3/1>|link=1}}, {{mos scalesig|6L 5s<3/1>|link=1}}, and {{mos scalesig|11L 6s<3/1>|link=1}}.
+== Etymology ==
+It was first discovered by [[User:CompactStar|CompactStar]] in 2023. The name is most likely just because of the existing theme of several tritave-equivalent temperaments being named after stars.
 == Interval chain (POTE tuning) ==
-{|class="wikitable"
+{| class="wikitable"
 |-
-!Generators up
+! Generators up
-!Cents
+! Cents
-!Generators down
+! Generators down
-!Cents
+! Cents
 |-
-|0
+| 0
-|0.00
+| 0.00
-|0
+| 0
-|0.00
+| 0.00
 |-
-|1
+| 1
-|340.24
+| 340.24
-|1
+| 1
-|1561.72
+| 1561.72
 |-
-|2
+| 2
-|680.48
+| 680.48
-|2
+| 2
-|1221.48
+| 1221.48
 |-
-|3
+| 3
-|1020.72
+| 1020.72
-|3
+| 3
-|881.24
+| 881.24
 |-
-|4
+| 4
-|1360.96
+| 1360.96
-|4
+| 4
-|541.00
+| 541.00
 |-
-|5
+| 5
-|1701.20
+| 1701.20
-|5
+| 5
-|200.76
+| 200.76
 |-
-|6
+| 6
-|139.48
+| 139.48
-|6
+| 6
-|1762.48
+| 1762.48
 |-
-|7
+| 7
-|479.72
+| 479.72
-|7
+| 7
-|1422.24
+| 1422.24
 |-
-|8
+| 8
-|819.96
+| 819.96
-|8
+| 8
-|1082.00
+| 1082.00
 |-
-|9
+| 9
-|1160.20
+| 1160.20
-|9
+| 9
-|741.76
+| 741.76
 |}
-== Harmony ==
-Deneb does not have sevens and as such the most simple approach to no-twos harmony (using the chord 3:5:7) does not work. Due to its approximation of 11/9 and 11/5, the otonal chord 5:9:11 and its utonal inversion 45:55:99 is well-represented. The utonal chord in particular sounds surprisingly consonant for a no-twos chord, while the otonal chord sounds more strained but still somewhat consonant.
 == Temperament data ==
-[[Subgroup]]: 3.5.11
+For formal temperament data, see [[No-twos subgroup temperaments#Deneb]].
-[[Comma list]]: 6655/6561
-[[Gencom]]: [3/1 11/9; 6655/6561]
-[[Mapping]]: [{{val|1 2 2}}, {{val|0 -3 1}}]
-[[POTE tuning]]: ~[[11/9]] = 340.242
-[[EDT]]s: 28, 11, 17, 6, 39, 5, 67, 45, 50, 16, 23, 73, 61, 62
-[[Category:Temperaments]]
+[[Category:Deneb| ]] <!-- main article -->
-[[Category:Nonoctave]]
 [[Category:Rank-2 temperaments]]
+[[Category:Non-octave temperaments]]