Deneb

Todo: complete page 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⟩. It is one of the simplest temperaments in the 3.5.11 subgroup with decent accuracy.

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

One important feature of subgroups involving 3 and 11 is the quasi-octave at the interval designated 243/121; in this temperament, it is equated to 55/27 and placed 2 generators down. Unless you are using an unusually sharp generator, this quasi-octave will be very smeary, being almost 22 cents sharp in the CWE tuning, but it is probably still meriting of special treatment in terms of consonance and dissonance. (Incidentally, extending Deneb to actually equate the quasi-octave to 2/1 would result in the 2.3.5.11 version of dicot)

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