Ploidacot/Triploid monocot
Triploid monocot is a temperament archetype where the generator is a 3/2 perfect fifth and the period is 1/3 of a 2/1 octave, or 400 ¢. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" [math]\displaystyle{ \frac{2\sqrt[3]{4}}{3} }[/math]. Triploid monocot temperaments usually generate the 3L 6s MOS structure and either 3L 9s (and thus 12L 3s) or 9L 3s (when the fifth is flatter than 7\12) as children.
Intervals and notation
While there is no agreed-upon notation system for triploid monocot, the following is based on interpreting the generator as a semitone (1/3 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), so vvC# and ^Db are enharmonic.
| # | Ploid 1 | Ploid 2 | Ploid 3 | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Cents | Notation | Name | Cents | Notation | Name | Cents | Notation | Name | |
| −6 | 188.27 | ^Ebb | — | 588.27 | Gb | diminished fifth | 988.27 | vBb | — |
| −5 | 90.22 | Db | minor second | 490.22 | vF | — | 890.22 | ^Bbb | — |
| −4 | 392.18 | ^Fb | — | 792.18 | Ab | minor sixth | 1192.18 | vC | — |
| −3 | 294.13 | Eb | minor third | 694.13 | vG | — | 1094.13 | ^Cb | — |
| −2 | 196.09 | vD | — | 596.09 | ^Gb | — | 996.09 | Bb | minor seventh |
| −1 | 98.04 | ^Db | — | 498.04 | F | perfect fourth | 898.04 | vA | — |
| 0 | 0.00 | C | unison | 400.00 | vE | — | 800.00 | ^Ab | — |
| 1 | 301.96 | ^Eb | — | 701.96 | G | perfect fifth | 1101.96 | vB | — |
| 2 | 203.91 | D | major second | 603.91 | vF# | — | 1003.91 | ^Bb | — |
| 3 | 105.87 | vC# | — | 505.87 | ^F | — | 905.87 | A | major sixth |
| 4 | 7.82 | ^C | — | 407.82 | E | major third | 807.82 | vG# | — |
| 5 | 309.78 | vD# | — | 709.78 | ^G | — | 1109.78 | B | major seventh |
| 6 | 211.73 | ^D | — | 611.73 | F# | augmented fourth | 1011.73 | vA# | — |
A notable feature of triploid monocot is the small comma, encountered after 4 steps, which represents 1/3 of a Pythagorean comma (or its equivalence, inversed diminished second). This makes triploid monocot scales cluster around 12edo.
Temperament interpretations
By definition, triploid monocot temperaments split the octave in three.
Augmented
Augmented sets 5/4 as a period, and uses a fifth as a free generator. There are some extensions for 7-limit: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9). In the 11-limit, these extensions equate 5/4 and 14/11 as a period.