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{{Breadcrumb}}
{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=1|Cots=2|Pergen=[P8, P4/2]|Forms=5, 9, 14, 19|Title=Alpha-dicot|Wedgie=2}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.


'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]].
Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.
 
Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, and the more accurate tunings generate [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.


== Intervals and notation ==
== Intervals and notation ==
Alpha-dicot temperaments can be notated using [[Hemipyth#Notation|hemipyth notation]] with the semiquartal nicknames.
Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).


<!-- This is the dicot table, not the alpha-dicot one - TODO {| class="wikitable"
{| class="wikitable"
|+Dicot intervals (assuming pure fifth and octave)
|+ style="font-size: 105%;" | Alpha-dicot intervals (assuming pure octave and fifth)
!#
!Cents
!Notation
!Name
|-
|-
| -10
! #
|90.22
! Cents
|Db
! Notation
|minor second
! Name
|-
|-
| -9
| −9
|441.20
| 1041.20
|Fd
|  
|semidiminished fourth
|  
|-
|-
| -8
| −8
|792.18
| 792.18
|Ab
| Ab
|minor sixth
| minor sixth
|-
|-
| -7
| −7
|1,143.16
| 543.16
|Cd
|  
|semidiminished octave
|  
|-
|-
| -6
| −6
|294.14
| 294.13
|Eb
| Eb
|minor third
| minor third
|-
|-
| -5
| −5
|645.11
| 45.11
|Gd
|  
|semidiminished fifth
|  
|-
|-
| -4
| −4
|996.09
| 996.09
|Bb
| Bb
|minor seventh
| minor seventh
|-
|-
| -3
| −3
|147.07
| 747.07
|Dd
|  
|neutral second
|  
|-
|-
| -2
| −2
|498.05
| 498.04
|F
| F
|perfect fourth
| perfect fourth
|-
|-
| -1
| −1
|849.02
| 249.02
|Ad
|  
|neutral sixth
|  
|-
|-
|0
| 0
|0
| 0
|C
| C
|perfect unison/perfect octave
| perfect unison
|-
|-
|1
| 1
|350.98
| 950.98
|Ed
|  
|neutral third
|  
|-
|-
|2
| 2
|701.96
| 701.96
|G
| G
|perfect fifth
| perfect fifth
|-
|-
|3
| 3
|1,052.93
| 452.93
|Bd
|  
|neutral seventh
|  
|-
|-
|4
| 4
|203.91
| 203.91
|D
| D
|major second
| major second
|-
|-
|5
| 5
|554.89
| 1154.89
|Ft
|  
|semiaugmented fourth
|  
|-
|-
|6
| 6
|905.87
| 905.87
|A
| A
|major sixth
| major sixth
|-
|-
|7
| 7
|56.84
| 656.84
|Ct
|  
|semiaugmented unison
|  
|-
|-
|8
| 8
|407.82
| 407.82
|E
| E
|major third
| major third
|-
|-
|9
| 9
|758.80
| 158.80
|Gt
|  
|semiaugmented fifth
|  
|-
|10
|1,109.78
|B
|major seventh
|}
|}
-->


== Temperament interpretations ==
== Temperament interpretations ==
Line 128: Line 116:


=== Bug ===
=== Bug ===
[[Bug]] is an exotemperament, equating the neutral semitwelfth to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the neutral semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the best 5-limit interpretation of this ploidacot.
[[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the simplest (arguably) reasonable 5-limit interpretation of this ploidacot.


The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]].
The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]].


=== Semaphore ===
=== Semaphore ===
Given that bug sets the neutral semifourth close to 7/6, what happens if it is set equal to 7/6 in the 2.3.7 subgroup? Then, it is equated to [[8/7]], and [[49/48]] is tempered out. The neutral semitwelfth is equated to [[12/7]] and [[7/4]]. This is still an inaccurate temperament, but is on the edge as to whether it counts as exo.
Given that bug sets the semifourth close to 7/6, what happens if it is set equal to 7/6 in the 2.3.7 subgroup? Then, it is equated to [[8/7]], and [[49/48]] is tempered out. The semitwelfth is equated to [[12/7]] and [[7/4]]. This is still an inaccurate temperament, but is on the edge as to whether it counts as exo.


The best tunings tend to be around 950{{c}} here, with a far more accurate twelfth. But, just like how bug's semifourth generator was close to 7/6, this is close to [[26/15]].
The best tunings tend to be around 950{{c}} here, with a far more accurate twelfth. But, just like how bug's semifourth generator was close to 7/6, this is close to [[26/15]].


=== Barbados ===
=== Barbados ===
Here, the generator actually is 26/15, equated with [[45/26]]. This is a rather accurate temperament, tempering out the small comma of [[676/675]], but it is defined in the awkward 2.3.13/5 subgroup. The neutral semifourth here is [[15/13]][[~]][[52/45]].
Here, the generator actually is 26/15, equated with [[45/26]]. This is an accurate temperament, tempering out the unnoticeable comma of [[676/675]], but it is defined in the awkward 2.3.13/5 subgroup. The semifourth here is {{nowrap|[[15/13]][[~]][[52/45]]}}.


As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.
As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.
[[Category:Ploidacots|Alpha-dicot]]
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