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{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=0|Cots=2|Pergen=[P8, P5/2]|Forms=7, 10, 17|Title=Dicot|Wedgie=2}}
{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=0|Cots=2|Pergen=[P8, P5/2]|Forms=7, 10, 17|Title=Dicot|Wedgie=2}}


'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.
'''Dicot''' is a temperament archetype where the generator is a [[Neutral third (interval region)|neutral third]], two of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Dicot temperaments usually generate the [[7L 3s]] MOS structure, fittingly named "dicoid", and one of its children [[10L 7s]] or [[7L 10s]]. Dicot temperaments involve "neutral" intervals - right in the middle of typical diatonic intervals. More precisely, they are ''interchromatic'', as the neutrals are found between [[Apotome|apotomes]] (chromatic semitones).
 
Its name is the genesis of [[ploidacot]], as it comes from the exotemperament [[dicot]].


== Intervals and notation ==
== Intervals and notation ==
Dicot temperaments can be notated using [[Neutral chain-of-fifths notation|neutral chain-of-fifths notation.]]
Dicot temperaments can be notated using [[Neutral chain-of-fifths notation|neutral chain-of-fifths notation]].


{| class="wikitable"
{| class="wikitable"
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|-
|-
| −7
| −7
| 1,143.16
| 1143.16
| Cd
| Cd
| semidiminished octave
| semidiminished octave
|-
|-
| −6
| −6
| 294.14
| 294.13
| Eb
| Eb
| minor third
| minor third
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|-
|-
| −2
| −2
| 498.05
| 498.04
| F
| F
| perfect fourth
| perfect fourth
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| 0
| 0
| C
| C
| perfect unison/perfect octave
| perfect unison
|-
|-
| 1
| 1
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|-
|-
| 3
| 3
| 1,052.93
| 1052.93
| Bd
| Bd
| neutral seventh
| neutral seventh
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|-
|-
| 10
| 10
| 1,109.78
| 1109.78
| B
| B
| major seventh
| major seventh
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== Temperament interpretations ==
== Temperament interpretations ==
By definition, dicot temperaments equate some interval to its fifth complement.
By definition, dicot temperaments map a pair of intervals to the neutral third, equating them.
 
=== Low accuracy ===
 
==== Dicot temperament ====
Dicot equates 5/4 with 6/5, as well as 5/3 with 8/5 with It is well tuned either way with a sharpened generator of around 360{{c}} (optimizing for the tuning of 5/4) or a flattened generator of around 340{{c}} (optimizing for the tuning of 5/3). Despite its noticeable innacuracy, it is the first "usable" dicot temperament.
 
=== Medium accuracy ===


=== Dicot ===
==== Neutral ====
The temperament named "[[dicot]]" is an exotemperament, equating the neutral third to 5/4. This means that 6/5 is the same interval, and the neutral sixth represents both 5/3 and 8/5. It is best tuned with either a sharpened generator of around 360{{c}} (optimizing for the tuning of 5/4) or a flattened generator of around 340{{c}} (optimizing for the tuning of 5/3).
[[Neutral (temperament)|Neutral]] (AKA the 2.3.11 restriction of [[rastmic]]) is the temperament equating [[11/9]] with [[27/22]]. This maps 11/9 to the neutral third and [[11/8]] to the semiaugmented fourth. [[Namo]] extends neutral so that [[16/13]] is mapped at the same neutral third. Namo is often used as an 11- and 13-limit extension of other temperaments.


=== Neutral ===
==== Mohajira ====
[[Neutral]] is the temperament equating [[11/9]] with [[27/22]]. This makes 11/9 the neutral third and [[11/8]] the semiaugmented fourth. [[Namo]] extends neutral so that [[16/13]] is found at the same neutral third. Namo is often used as an 11- and 13-limit extension of other temperaments.
When neutral is combined with [[meantone]] (which maps the major third to [[5/4]]), the result is [[mohajira]], which tunes the generator of ~11/9 to about 348{{c}} and extends to the full 11-limit by setting 7/4 equal to the semidiminished seventh.


=== Mohajira ===
==== Hemififths ====
When neutral is combined with [[meantone]] (which sets the major third equal to [[5/4]]), the result is [[mohajira]], which tunes the generator of ~11/9 to about 348{{c}} and extends to the full 11-limit by setting 7/4 equal to the semidiminished seventh.
As its name implies, [[hemififths]] has hemififths as generators, equating [[49/40]] with [[60/49]]. 7/4 maps to a semiaugmented sixth, and consequently 5/4 maps to a sesqui-augmented (one-and-a-half augmented) second.


=== Hemififths ===
=== High accuracy ===
Fittingly to its name, [[hemififths]] divides the fifth evenly into two {{nowrap|[[49/40]]~[[60/49]]<nowiki/>s}}. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (one-and-a-half augmented) second.


{{Todo| unify precision }}
==== Newt ====
Much like hemififths, [[newt]] equates 49/40 with 60/49, but primes are found much deeper in the dicot chain, albeit its accuracy is astounding – solidifying it as a [[microtemperament]]. It maps, with incredible exactitude: 7/4 to a subminor seventh (doubly diminished octave), 11/8 to a hyperfourth (3x-augmented second), 5/4 at -28.5 fifths, 13/8 at 40.5 fifths, 19/16 at -23.5 fifths.
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