Deneb: Difference between revisions
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'''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 scale]]s 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]]. | '''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 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}}. Good tunings for this temperament are [[11edt]], [[17edt]], [[28edt]], [[39edt]], and [[45edt]]. | ||
== Interval chain (POTE tuning) == | == Interval chain (POTE tuning) == | ||
{|class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
!Generators up | ! Generators up | ||
!Cents | ! Cents | ||
!Generators down | ! Generators down | ||
!Cents | ! Cents | ||
|- | |- | ||
|0 | | 0 | ||
|0.00 | | 0.00 | ||
|0 | | 0 | ||
|0.00 | | 0.00 | ||
|- | |- | ||
|1 | | 1 | ||
|340.24 | | 340.24 | ||
|1 | | 1 | ||
|1561.72 | | 1561.72 | ||
|- | |- | ||
|2 | | 2 | ||
|680.48 | | 680.48 | ||
|2 | | 2 | ||
|1221.48 | | 1221.48 | ||
|- | |- | ||
|3 | | 3 | ||
|1020.72 | | 1020.72 | ||
|3 | | 3 | ||
|881.24 | | 881.24 | ||
|- | |- | ||
|4 | | 4 | ||
|1360.96 | | 1360.96 | ||
|4 | | 4 | ||
|541.00 | | 541.00 | ||
|- | |- | ||
|5 | | 5 | ||
|1701.20 | | 1701.20 | ||
|5 | | 5 | ||
|200.76 | | 200.76 | ||
|- | |- | ||
|6 | | 6 | ||
|139.48 | | 139.48 | ||
|6 | | 6 | ||
|1762.48 | | 1762.48 | ||
|- | |- | ||
|7 | | 7 | ||
|479.72 | | 479.72 | ||
|7 | | 7 | ||
|1422.24 | | 1422.24 | ||
|- | |- | ||
|8 | | 8 | ||
|819.96 | | 819.96 | ||
|8 | | 8 | ||
|1082.00 | | 1082.00 | ||
|- | |- | ||
|9 | | 9 | ||
|1160.20 | | 1160.20 | ||
|9 | | 9 | ||
|741.76 | | 741.76 | ||
|} | |} | ||
== Harmony == | == 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. | 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 == | == Temperament data == | ||
[[ | For formal temperament data, see [[No-twos subgroup temperaments#Deneb]]. | ||
[[ | [[Category:Deneb| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | |||
[[Category:Non-octave temperaments]] | |||
Latest revision as of 04:28, 23 March 2026
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
For formal temperament data, see No-twos subgroup temperaments#Deneb.