Deneb
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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⟩.
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