Ploidacot/Triploid monocot
| Pergen | [P8/3, P5] |
| Numeral form | 3-ploid 1-cot |
| Pure generator size | 98.04 ¢ |
| Pure period size | 400 ¢ |
| Forms | 9, 12, 15 |
| Characteristic multival entry | 3 |
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 as children.
Notation
Triploid monocot notation is complicated as it conventionally requires either the introduction of new "1/3-pythagorean" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where triploid monocot intervals align with standard monocot intervals.
| # | Ploid 1 | Ploid 2 | Ploid 3 | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Cents | Name | Notation | Cents | Name | Notation | Cents | Name | Notation | |
| −5 | 90.22 | minor second | Db | 490.22 | — | — | 890.22 | — | — |
| −4 | 392.18 | — | — | 792.18 | minor sixth | Ab | 1192.18 | — | — |
| −3 | 294.13 | minor third | Eb | 694.13 | — | — | 1094.13 | — | — |
| −2 | 196.09 | — | — | 596.09 | — | — | 996.09 | minor seventh | Bb |
| −1 | 98.04 | — | — | 498.04 | perfect fourth | F | 898.04 | — | — |
| 0 | 0 | unison | C | 400 | — | — | 800 | — | — |
| 1 | 301.96 | — | — | 701.96 | perfect fifth | G | 1101.96 | — | — |
| 2 | 203.91 | major second | D | 603.91 | — | — | 1003.91 | — | — |
| 3 | 105.87 | — | — | 505.87 | — | — | 905.87 | major sixth | A |
| 4 | 7.82 | — | — | 407.82 | major third | E | 807.82 | — | — |
| 5 | 309.78 | — | — | 709.78 | — | — | 1109.78 | major seventh | B |
Temperament interpretations
By definition, triploid monocot temperaments equate some interval to its octave complement.
Augmented
Augmented sets 5/4 as a period, and uses a fifth as a free generator. There are some extensions for 7-limit or higher prime limits: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9).