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 {{nowrap|1L 4s{{angbr|3/1}}|5L 1s{{angbr|3/1}}|6L 5s{{angbr|3/1}}|and 11L 6s{{angbr|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) ==  
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For formal temperament data, see [[No-twos subgroup temperaments#Deneb]].
For formal temperament data, see [[No-twos subgroup temperaments#Deneb]].


[[Category:Temperaments]]
[[Category:Deneb| ]] <!-- main article -->
[[Category:Nonoctave]]
[[Category:Rank-2 temperaments]]
[[Category:Rank 2]]
[[Category:Non-octave temperaments]]
[[Category:Tritave-equivalent 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.