Deneb: Difference between revisions

Latest revision as of 05:21, 4 October 2026

Todo: rewrite, polish interval chain table

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 scales of the families 1L 4s⟨3/1⟩, 5L 1s⟨3/1⟩, 6L 5s⟨3/1⟩, and 11L 6s⟨3/1⟩.

Etymology

It was first discovered by 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)

Generators up	Cents	Generators down	Cents
0	0.00	0	0.00
1	340.24	1	1561.72
2	680.48	2	1221.48
3	1020.72	3	881.24
4	1360.96	4	541.00
5	1701.20	5	200.76
6	139.48	6	1762.48
7	479.72	7	1422.24
8	819.96	8	1082.00
9	1160.20	9	741.76

Temperament data

For formal temperament data, see No-twos subgroup temperaments#Deneb.

@@ Line 1: / Line 1: @@
-'''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}}
-WIP
+'''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}}.
-== 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 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.
+== 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"
+|-
+! Generators up
+! Cents
+! Generators down
+! Cents
+|-
+| 0
+| 0.00
+| 0
+| 0.00
+|-
+| 1
+| 340.24
+| 1
+| 1561.72
+|-
+| 2
+| 680.48
+| 2
+| 1221.48
+|-
+| 3
+| 1020.72
+| 3
+| 881.24
+|-
+| 4
+| 1360.96
+| 4
+| 541.00
+|-
+| 5
+| 1701.20
+| 5
+| 200.76
+|-
+| 6
+| 139.48
+| 6
+| 1762.48
+|-
+| 7
+| 479.72
+| 7
+| 1422.24
+|-
+| 8
+| 819.96
+| 8
+| 1082.00
+|-
+| 9
+| 1160.20
+| 9
+| 741.76
+|}
+== Temperament data ==
+For formal temperament data, see [[No-twos subgroup temperaments#Deneb]].
+[[Category:Deneb| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Non-octave temperaments]]