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


'''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 tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.


== 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"
|+Dicot intervals (assuming pure fifth and octave)
|+ style="font-size: 105%;" | Dicot intervals (assuming pure fifth and octave)
!#
|-
!Cents
! #
!Notation
! Cents
!Name
! Notation
! Name
|-
|-
| -10
| −10
|90.22
| 90.22
|Db
| Db
|minor second
| minor second
|-
|-
| -9
| −9
|441.20
| 441.20
|Fd
| Fd
|semidiminished fourth
| semidiminished fourth
|-
|-
| -8
| −8
|792.18
| 792.18
|Ab
| Ab
|minor sixth
| minor sixth
|-
|-
| -7
| −7
|1,143.16
| 1,143.16
|Cd
| Cd
|semidiminished octave
| semidiminished octave
|-
|-
| -6
| −6
|294.14
| 294.14
|Eb
| Eb
|minor third
| minor third
|-
|-
| -5
| −5
|645.11
| 645.11
|Gd
| Gd
|semidiminished fifth
| semidiminished fifth
|-
|-
| -4
| −4
|996.09
| 996.09
|Bb
| Bb
|minor seventh
| minor seventh
|-
|-
| -3
| −3
|147.07
| 147.07
|Dd
| Dd
|neutral second
| neutral second
|-
|-
| -2
| −2
|498.05
| 498.05
|F
| F
|perfect fourth
| perfect fourth
|-
|-
| -1
| −1
|849.02
| 849.02
|Ad
| Ad
|neutral sixth
| neutral sixth
|-
|-
|0
| 0
|0
| 0
|C
| C
|perfect unison/perfect octave
| perfect unison/perfect octave
|-
|-
|1
| 1
|350.98
| 350.98
|Ed
| Ed
|neutral third
| neutral third
|-
|-
|2
| 2
|701.96
| 701.96
|G
| G
|perfect fifth
| perfect fifth
|-
|-
|3
| 3
|1,052.93
| 1,052.93
|Bd
| Bd
|neutral seventh
| neutral seventh
|-
|-
|4
| 4
|203.91
| 203.91
|D
| D
|major second
| major second
|-
|-
|5
| 5
|554.89
| 554.89
|Ft
| Ft
|semiaugmented fourth
| semiaugmented fourth
|-
|-
|6
| 6
|905.87
| 905.87
|A
| A
|major sixth
| major sixth
|-
|-
|7
| 7
|56.84
| 56.84
|Ct
| Ct
|semiaugmented unison
| semiaugmented unison
|-
|-
|8
| 8
|407.82
| 407.82
|E
| E
|major third
| major third
|-
|-
|9
| 9
|758.80
| 758.80
|Gt
| Gt
|semiaugmented fifth
| semiaugmented fifth
|-
|-
|10
| 10
|1,109.78
| 1,109.78
|B
| B
|major seventh
| major seventh
|}
|}


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=== Dicot ===
=== Dicot ===
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 cents (optimizing for the tuning of 5/4) or a flattened generator of around 340 cents (optimizing for the tuning of 5/3).
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 ===
=== Neutral ===
[[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.
[[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.


=== Mohajira ===
=== Mohajira ===
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 cents and extends to the full 11-limit by setting 7/4 equal to the semidiminished seventh.
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.


=== Hemififths ===
=== Hemififths ===
Fittingly to its name, [[hemififths]] divides the fifth evenly into two [[49/40]]~[[60/49]]<nowiki/>s. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (1.5x augmented) second.
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 }}
{{Todo| unify precision }}
Retrieved from "https://en.xen.wiki/w/Ploidacot/Dicot"