Deneb

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 scales 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.

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

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

Comma list: 6655/6561

Gencom: [3/1 11/9; 6655/6561]

Mapping: [⟨1 2 2], ⟨0 -3 1]]

POTE tuning: ~11/9 = 340.242

EDTs: 28, 11, 17, 6, 39, 5, 67, 45, 50, 16, 23, 73, 61, 62