Ploidacot/Triploid dicot
Triploid dicot is a temperament archetype with a 1/3-octave period, and a generator of a neutral third. In a pure tuning, the generator is exactly a half of 3/2. But the alternative generator, a quartertone, with size around 49¢ is rather easier to grasp.
| Pergen | [P8/3, P5/2] |
| Numeral form | 3-ploid 2-cot |
| Pure generator size | 49.02 ¢ |
| Pure period size | 400 ¢ |
| Forms | 18, 21, 24 |
| Characteristic multival entry | 6 |
Triploid dicot temperaments usually generate the 3L 12s, 3L 15s, and 3L 18s MOS structures.
Intervals and notation
While there is no agreed-upon notation system for triploid dicot, the following is based on interpreting the generator as a quartertone (1/6 of a minor third), allowing for an ^ or v to stand for 1/3 of an inversed diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the Pythagorean comma), along with neutral chain-of-fifths notation, so vvC# and ^Db are enharmonic.
| # | Ploid 1 | Ploid 2 | Ploid 3 | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Cents | Notation | Name | Cents | Notation | Name | Cents | Notation | Name | |
| −12 | 211.73 | ^D | — | 611.73 | F# | augmented fourth | 1011.73 | vA# | — |
| −11 | 260.75 | Dt | semiaugmented second | 660.75 | vFt# | — | 1060.75 | ^Bd | — |
| −10 | 309.78 | vD# | — | 709.78 | ^G | — | 1109.78 | B | major seventh |
| −9 | 358.80 | ^Ed | — | 758.80 | Gt | semiaugmented fifth | 1158.80 | vBt | — |
| −8 | 7.82 | ^C | — | 407.82 | E | major third | 807.82 | vG# | — |
| −7 | 56.84 | Ct | semiaugmented unison | 456.84 | vEt | — | 856.84 | ^Ad | — |
| −6 | 105.87 | vC# | — | 505.87 | ^F | — | 905.87 | A | major sixth |
| −5 | 154.89 | ^Dd | — | 554.89 | Ft | semiaugmented fourth | 954.89 | vAt | — |
| −4 | 203.91 | D | major second | 603.91 | vF# | — | 1003.91 | ^Bb | — |
| −3 | 252.93 | vDt | — | 652.93 | ^Gd | — | 1052.93 | Bd | neutral seventh |
| −2 | 301.96 | ^Eb | — | 701.96 | G | perfect fifth | 1101.96 | vB | — |
| −1 | 350.98 | Ed | neutral third | 750.98 | vGt | — | 1150.98 | ^Cd | — |
| 0 | 0 | C | unison | 400 | vE | — | 800 | ^Ab | — |
| 1 | 49.02 | vCt | — | 449.02 | ^Fd | — | 849.02 | Ad | neutral sixth |
| 2 | 98.04 | ^Db | — | 498.04 | F | perfect fourth | 898.04 | vA | — |
| 3 | 147.07 | Dd | neutral second | 547.07 | vFt | — | 947.07 | ^Bdb | — |
| 4 | 196.09 | vD | — | 596.09 | ^Gb | — | 996.09 | Bb | minor seventh |
| 5 | 245.11 | ^Edb | — | 645.11 | Gd | semidiminished fifth | 1045.11 | vBd | — |
| 6 | 294.13 | Eb | minor third | 694.13 | vG | — | 1094.13 | ^Cb | — |
| 7 | 343.16 | vEd | — | 743.16 | ^Adb | — | 1143.16 | Cd | semidiminished octave |
| 8 | 392.18 | ^Fb | — | 792.18 | Ab | minor sixth | 1192.18 | vC | — |
| 9 | 41.20 | ^Ddb | — | 441.20 | Fd | semidiminished fourth | 841.20 | vAd | — |
| 10 | 90.22 | Db | minor second | 490.22 | vF | — | 890.22 | ^Bbb | — |
| 11 | 139.25 | vDd | — | 539.25 | ^Gdb | — | 939.25 | Bdb | semidiminished seventh |
| 12 | 188.27 | ^Ebb | — | 588.27 | Gb | diminished fifth | 988.27 | vBb | — |
Temperament interpretations
An obvious interpretation for triploid dicot is hemiaug, a weak extension of augmented. The period is 5/4~14/11 and the generator is 36/35~40/39~45/44, so that 3/2 is two periods down two generators, 7/4 at one octave down five generators, 11/8 at two periods down five generators, and 13/8 at two periods up one generator.