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Created page with "'''Dicot''' is a temperament archetype where the generator is a 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..."
 
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'''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.
{{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 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).


== 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
| 1143.16
|Cd
| Cd
|semidiminished octave
| semidiminished octave
|-
|-
| -6
| −6
|294.14
| 294.13
|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
| 498.04
|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
|-
|-
|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
| 1052.93
|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
| 1109.78
|B
| B
|major seventh
| major seventh
|}
|}


== 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 ====
The temperament named "[[dicot]]" is an exotemperament that 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, as the one before it would be the extreme temperament that "equates" 9/8 and 4/3.
 
=== Medium accuracy ===
 
==== Neutral ====
[[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.


=== Dicot ===
==== Mohajira ====
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).
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.


=== Neutral ===
==== Hemififths ====
[[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.
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.


=== Mohajira ===
=== High accuracy ===
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.


=== Hemififths ===
==== Newt ====
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.
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 hemififths, 13/8 at 40.5 fifths, 19/16 at -23.5 fifths.
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