Deneb

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Add infobox. Rewrite, polish interval table. Add tunings section.

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⟩.

This temperament was first discovered and named by CompactStar in 2023 after the star Deneb, following a series of non-octave temperaments that are named after stars.

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

Interval chain

In the following table, prime harmonics and subharmonics are labeled in bold.

# Cents* Approximate ratios
0 0.000 1/1
1 340.052 11/9
2 680.104 81/55, 121/81
3 1020.156 9/5
4 1360.208 11/5
5 1700.260 121/45
6 138.357 27/25
7 478.409 33/25
8 818.461 121/75
9 1158.513 243/125
10 1498.565 297/125
# Cents* Approximate ratios
0 0.000 1/1
-1 1561.903 27/11
-2 1221.851 55/27, 243/121
-3 881.799 5/3
-4 541.747 15/11
-5 201.695 135/121
-6 1763.598 25/9
-7 1423.546 25/11
-8 1083.494 225/121
-9 743.442 125/81
-10 403.390 125/99

* In 3.5.11-subgroup CWE tuning