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 {{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~~]].

'''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 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}}.

== Etymology ==

It was seemingly first discovered by [[User:CompactStar|CompactStar]] in 2023. The name is most likely just because of the existing theme of several tritave-equivalent temperaments being named after stars.

== Interval chain (POTE tuning) ==

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~~== 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 ==

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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 {{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]].
+{{todo|rewrite, polish interval chain table|inline=1}}
+'''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 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}}.
+== Etymology ==
+It was seemingly first discovered by [[User:CompactStar|CompactStar]] in 2023. The name is most likely just because of the existing theme of several tritave-equivalent temperaments being named after stars.
 == Interval chain (POTE tuning) ==
@@ Line 59: / Line 63: @@
 | 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 ==