Ploidacot/Alpha-dicot: Difference between revisions

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-{{Breadcrumb}}
+{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=1|Cots=2|Pergen=[P8, P4/2]|Forms=5, 9, 14|Title=Alpha-dicot; omega-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]], so '''omega-dicot''' means the same thing and is unused.
-'''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 ==
-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]]).
+{| class="wikitable"
-<!-- This is the dicot table, not the alpha-dicot one - TODO {| class="wikitable"
+|+Alpha-dicot intervals (assuming pure octave and fifth)
-|+Dicot intervals (assuming pure fifth and octave)
 !#
 !Cents
 !Notation
 !Name
-|-
-| -10
-|90.22
-|Db
-|minor second
 |-
 | -9
-|441.20
+|1041.20
-|Fd
+|
-|semidiminished fourth
+|
 |-
 | -8
@@ Line 31: / Line 23: @@
 |-
 | -7
-|1,143.16
+|543.16
-|Cd
+|
-|semidiminished octave
+|
 |-
 | -6
@@ Line 41: / Line 33: @@
 |-
 | -5
-|645.11
+|45.11
-|Gd
+|
-|semidiminished fifth
+|
 |-
 | -4
@@ Line 51: / Line 43: @@
 |-
 | -3
-|147.07
+|747.07
-|Dd
+|
-|neutral second
+|
 |-
 | -2
@@ Line 61: / Line 53: @@
 |-
 | -1
-|849.02
+|249.02
-|Ad
+|
-|neutral sixth
+|
 |-
 |0
 |0
 |C
-|perfect unison/perfect octave
+|perfect unison
 |-
 |1
-|350.98
+|950.98
-|Ed
+|
-|neutral third
+|
 |-
 |2
@@ Line 81: / Line 73: @@
 |-
 |3
-|1,052.93
+|452.93
-|Bd
+|
-|neutral seventh
+|
 |-
 |4
@@ Line 91: / Line 83: @@
 |-
 |5
-|554.89
+|1154.89
-|Ft
+|
-|semiaugmented fourth
+|
 |-
 |6
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 |-
 |7
-|56.84
+|656.84
-|Ct
+|
-|semiaugmented unison
+|
 |-
 |8
@@ Line 111: / Line 103: @@
 |-
 |9
-|758.80
+|158.8
-|Gt
+|
-|semiaugmented fifth
+|
-|-
-|10
-|1,109.78
-|B
-|major seventh
 |}
--->
 == Temperament interpretations ==
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 === 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 best 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]].
 === 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]].
 === 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 [[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.
+{{Todo| unify precision }}