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{{Breadcrumb}} | {{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 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 | |||
! Name | |||
|- | |- | ||
| | | −10 | ||
| | | 90.22 | ||
| | | Db | ||
| | | minor second | ||
|- | |- | ||
| | | −9 | ||
| | | 441.20 | ||
| | | Fd | ||
| | | semidiminished fourth | ||
|- | |- | ||
| | | −8 | ||
| | | 792.18 | ||
| | | Ab | ||
| | | minor sixth | ||
|- | |- | ||
| | | −7 | ||
| | | 1143.16 | ||
| | | Cd | ||
| | | semidiminished octave | ||
|- | |- | ||
| | | −6 | ||
| | | 294.13 | ||
| | | Eb | ||
| | | minor third | ||
|- | |- | ||
| | | −5 | ||
| | | 645.11 | ||
| | | Gd | ||
| | | semidiminished fifth | ||
|- | |- | ||
| | | −4 | ||
| | | 996.09 | ||
| | | Bb | ||
| | | minor seventh | ||
|- | |- | ||
| | | −3 | ||
| | | 147.07 | ||
| | | Dd | ||
| | | neutral second | ||
|- | |- | ||
| | | −2 | ||
| | | 498.04 | ||
| | | F | ||
| | | perfect fourth | ||
|- | |- | ||
| | | −1 | ||
| | | 849.02 | ||
| | | Ad | ||
| | | neutral sixth | ||
|- | |- | ||
| | | 0 | ||
| | | 0 | ||
| | | C | ||
| | | perfect unison | ||
|- | |- | ||
| | | 1 | ||
| | | 350.98 | ||
| | | Ed | ||
| | | neutral third | ||
|- | |- | ||
| | | 2 | ||
| | | 701.96 | ||
| | | G | ||
| | | perfect fifth | ||
|- | |- | ||
| | | 3 | ||
| | | 1052.93 | ||
| | | Bd | ||
| | | neutral seventh | ||
|- | |- | ||
| | | 4 | ||
| | | 203.91 | ||
| | | D | ||
| | | major second | ||
|- | |- | ||
| | | 5 | ||
| | | 554.89 | ||
| | | Ft | ||
| | | semiaugmented fourth | ||
|- | |- | ||
| | | 6 | ||
| | | 905.87 | ||
| | | A | ||
| | | major sixth | ||
|- | |- | ||
| | | 7 | ||
| | | 56.84 | ||
| | | Ct | ||
| | | semiaugmented unison | ||
|- | |- | ||
| | | 8 | ||
| | | 407.82 | ||
| | | E | ||
| | | major third | ||
|- | |- | ||
|10 | | 9 | ||
| | | 758.80 | ||
|B | | Gt | ||
|major seventh | | semiaugmented fifth | ||
|- | |||
| 10 | |||
| 1109.78 | |||
| B | |||
| 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 | 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. | [[Neutral (temperament)|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 | 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 ( | 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. | ||
[[Category:Ploidacots|Dicot]] | |||