Deneb: Difference between revisions
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{{Todo|inline=1|complete page|comment=Add infobox. Rewrite, polish interval table. Add tunings section. }} | {{Todo|inline=1|complete page|comment=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 is one of the simplest temperaments in the 3.5.11 subgroup with decent accuracy | '''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 is one of the simplest temperaments in the 3.5.11 subgroup with decent accuracy. | ||
This temperament was first discovered and named by {{u|CompactStar}} in 2023 after the star {{w|Deneb}}, following a series of non-octave temperaments that are named after stars. | This temperament was first discovered and named by {{u|CompactStar}} in 2023 after the star {{w|Deneb}}, following a series of non-octave temperaments that are named after stars. | ||
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== Scales == | == Scales == | ||
Reasonable tunings of Deneb possess [[MOS scale]]s of the families {{mos scalesig|1L 4s<3/1>|link=1}}, {{mos scalesig|5L 1s<3/1>|link=1}}, {{mos scalesig|6L 5s<3/1>|link=1}}, and {{mos scalesig|11L 6s<3/1>|link=1}}. Interestingly, the {{mos scalesig|6L 5s<3/1>}} Deneb[11] scale is melodically | Reasonable tunings of Deneb possess [[MOS scale]]s of the families {{mos scalesig|1L 4s<3/1>|link=1}}, {{mos scalesig|5L 1s<3/1>|link=1}}, {{mos scalesig|6L 5s<3/1>|link=1}}, and {{mos scalesig|11L 6s<3/1>|link=1}}. Interestingly, the {{mos scalesig|6L 5s<3/1>}} Deneb[11] scale is melodically similar to the diatonic scale, probably since both approximate [[7edo]]/[[11edt]]. | ||
== Interval chain == | == Interval chain == | ||
Revision as of 04:50, 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 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.
Scales
Reasonable tunings of Deneb possess MOS scales of the families 1L 4s⟨3/1⟩, 5L 1s⟨3/1⟩, 6L 5s⟨3/1⟩, and 11L 6s⟨3/1⟩. Interestingly, the 6L 5s⟨3/1⟩ Deneb[11] scale is melodically similar to the diatonic scale, probably since both approximate 7edo/11edt.
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