Ploidacot/Dicot
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 involve "neutral" intervals - right in the middle of typical diatonic intervals. More precisely, they are interchromatic, as the neutrals are found between apotomes (chromatic semitones).
| Pergen | [P8, P5/2] |
| Numeral form | 2-cot |
| Pure generator size | 350.98 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 7, 10, 17 |
| Characteristic multival entry | 2 |
Its name is the genesis of ploidacot, as it comes from the exotemperament dicot.
Intervals and notation
Dicot temperaments can be notated using neutral chain-of-fifths notation.
| # | 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 |
| 9 | 758.80 | Gt | semiaugmented fifth |
| 10 | 1109.78 | B | major seventh |
Temperament interpretations
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 ¢ (optimizing for the tuning of 5/4) or a flattened generator of around 340 ¢ (optimizing for the tuning of 5/3). Despite its noticeable innacuracy, it is the first "usable" dicot temperament.
Medium accuracy
Neutral
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.
Mohajira
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 ¢ and extends to the full 11-limit by setting 7/4 equal to the semidiminished seventh.
Hemififths
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.
High accuracy
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.