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 tend to involve "neutral" intervals, which are in-between conventional diatonic intervals.
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 | 1,143.16 | Cd | semidiminished octave |
| -6 | 294.14 | Eb | minor third |
| -5 | 645.11 | Gd | semidiminished fifth |
| -4 | 996.09 | Bb | minor seventh |
| -3 | 147.07 | Dd | neutral second |
| -2 | 498.05 | F | perfect fourth |
| -1 | 849.02 | Ad | neutral sixth |
| 0 | 0 | C | perfect unison/perfect octave |
| 1 | 350.98 | Ed | neutral third |
| 2 | 701.96 | G | perfect fifth |
| 3 | 1,052.93 | 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 | 1,109.78 | B | major seventh |
Temperament interpretations
By definition, dicot temperaments equate some interval to its fifth complement.
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).
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.
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.
Hemififths
Fittingly to its name, hemififths divides the fifth evenly into two 49/40~60/49s. 7/4 is the semiaugmented sixth, and consequently 5/4 is the sesqui-augmented (1.5x augmented) second.