Deneb: Difference between revisions
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== Interval chain == | == 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 usually sharp generator, this quasi-octave will be very smeary, being almost 22 cents sharp in optimal 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]]) | 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 usually sharp generator or compressing the tritave, this quasi-octave will be very smeary, being almost 22 cents sharp in optimal 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'''. | In the following table, prime harmonics and subharmonics are labeled in '''bold'''. | ||
Revision as of 00:27, 14 October 2026
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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
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 usually sharp generator or compressing the tritave, this quasi-octave will be very smeary, being almost 22 cents sharp in optimal 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