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For technical data, see [[No-twos subgroup temperaments #Deneb]].
For technical data, see [[No-twos subgroup temperaments #Deneb]].
== Extensions ==
=== Add 13 ===
There are several possible extensions to 3.5.11.13 and higher no-2s no-7s limits, but it's mainly weak extensions. The only practical [[strong extension]] of Deneb to 3.5.11.13, b28 & b39, maps [[13/9]] to +13 generators up. This only really works for generators sharp of 5\28edt. 3.5.11 Deneb can suffice using the diatonic-like 11-note MOS {{mos scalesig|6L 5s<3/1>|link=1}}, but this extension requires at least the 17-note MOS {{mos scalesig|11L 6s<3/1>|link=1}} to properly use the ratios of 13.
[[Fomalhaut]] is a [[weak extension]] of Deneb to higher limits that splits the interval of [[11/3]] in three. Fomalhaut was considered in the no-2s no-7s 23-limit (3.5.11.13.17.19.23) from the start. It is considerably more complex than Deneb, and requires at least an 18-note MOS to properly use (technically, all prime harmonics 3-23 are accessible in the 13-note MOS, but the 13-note MOS is very [[hard]], and said prime harmonics are in different directions).
Another possible extension of Deneb to 3.5.11.13 is [[No-twos subgroup temperaments#Threneb|Threneb]], which temper out the threedie, [[2197/2187]]. This splits the tritave into 3 [[13/9]]s, and 13/9 becomes the new period while the generator remains the same. The EDT join of this extension is b39&b45 (only EDTs that are a multiple of 3 are supported). Unfortunately, the smaller MOS scales generated by this are once again very [[hard]].
Also, the 3.5.7.11 temperament [[Mintra]], although it's mainly known as a strong extension of [[Mintaka]], is additionally a weak extension of Deneb and a weak extension of [[BPS]], combining all three temperaments into an efficient no-2s 11-limit temperament. The way it is a weak extension of Deneb is that [[27/11]] (the tritave-complement of 11/9) is split into two [[11/7]]s. Mintra can then be further extended to 3.5.7.11.13.
=== Add 8 ===
5 generators stacked actually is a very good approximation of [[8/3]], so if you're okay with introducing limited factors of 2, Deneb can be easily extended to the 3.8.5.11 subgroup (or using the technically "canonical" ordering, 8.3.5.11, but using [[8/1]] as an equivalence would be rather impractical). This extension tempers out [[121/120]] and [[2200/2187]] and is related to the octave-repeating [[amity]]/[[hitchcock]] temperament. Interestingly, in the 3.8.5.11 extension, ~[[8/1]] = ~[[55/27]]<sup>2</sup> * ~[[64/33]], with ~55/27 being the aforementioned sharp quasi-octave, and ~64/33 being the undecimal infraoctave. Furthermore, ~55/27 and ~64/33 share the same scale degree in Deneb[11].


== Interval chain ==
== Interval chain ==
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<nowiki>*</nowiki> In 3.5.11-subgroup [[CWE tuning]]
<nowiki>*</nowiki> In 3.5.11-subgroup [[CWE tuning]]
== 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 similar to softer diatonic scales because both approximate [[7edo]]/[[11edt]].


== Chords and harmony ==
== Chords and harmony ==
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Due to the presence of a quasi-octave and quasi-fifth, there are Mavila-esque neutral triads splitting the quasi-fifth in half (1-[[11/9]]-[[81/55]]). Technically, Deneb makes 1-[[11/9]]-[[81/55]] an [[essentially tempered dyadic chord]].
Due to the presence of a quasi-octave and quasi-fifth, there are Mavila-esque neutral triads splitting the quasi-fifth in half (1-[[11/9]]-[[81/55]]). Technically, Deneb makes 1-[[11/9]]-[[81/55]] an [[essentially tempered dyadic chord]].
== 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 similar to softer diatonic scales because both approximate [[7edo]]/[[11edt]].
== Extensions ==
=== Add 13 ===
There are several possible extensions to 3.5.11.13 and higher no-2s no-7s limits, but it's mainly weak extensions. The only practical [[strong extension]] of Deneb to 3.5.11.13, b28 & b39, maps [[13/9]] to +13 generators up. This only really works for generators sharp of 5\28edt. 3.5.11 Deneb can suffice using the diatonic-like 11-note MOS {{mos scalesig|6L 5s<3/1>|link=1}}, but this extension requires at least the 17-note MOS {{mos scalesig|11L 6s<3/1>|link=1}} to properly use the ratios of 13.
[[Fomalhaut]] is a [[weak extension]] of Deneb to higher limits that splits the interval of [[11/3]] in three. Fomalhaut was considered in the no-2s no-7s 23-limit (3.5.11.13.17.19.23) from the start. It is considerably more complex than Deneb, and requires at least an 18-note MOS to properly use (technically, all prime harmonics 3-23 are accessible in the 13-note MOS, but the 13-note MOS is very [[hard]], and said prime harmonics are in different directions).
Another possible extension of Deneb to 3.5.11.13 is [[No-twos subgroup temperaments#Threneb|Threneb]], which temper out the threedie, [[2197/2187]]. This splits the tritave into 3 [[13/9]]s, and 13/9 becomes the new period while the generator remains the same. The EDT join of this extension is b39&b45 (only EDTs that are a multiple of 3 are supported). Unfortunately, the smaller MOS scales generated by this are once again very [[hard]].
Also, the 3.5.7.11 temperament [[Mintra]], although it's mainly known as a strong extension of [[Mintaka]], is additionally a weak extension of Deneb and a weak extension of [[BPS]], combining all three temperaments into an efficient no-2s 11-limit temperament. The way it is a weak extension of Deneb is that [[27/11]] (the tritave-complement of 11/9) is split into two [[11/7]]s. Mintra can then be further extended to 3.5.7.11.13.
=== Add 8 ===
5 generators stacked actually is a very good approximation of [[8/3]], so if you're okay with introducing limited factors of 2, Deneb can be easily extended to the 3.8.5.11 subgroup (or using the technically "canonical" ordering, 8.3.5.11, but using [[8/1]] as an equivalence would be rather impractical). This extension tempers out [[121/120]] and [[2200/2187]] and is related to the octave-repeating [[amity]]/[[hitchcock]] temperament. Interestingly, in the 3.5.8.11 extension, ~[[8/1]] = ~[[55/27]]<sup>2</sup> * ~[[64/33]], with ~55/27 being the aforementioned sharp quasi-octave, and ~64/33 being the undecimal infraoctave. Furthermore, ~55/27 and ~64/33 share the same scale degree in Deneb[11].


== Tunings ==
== Tunings ==
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| 340.649
| 340.649
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| 340.811
| [[Delta-rational]] [[9:11:15]] tuning
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