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