Ploidacot/Tetraploid monocot
Tetraploid monocot is a temperament archetype where the generator is a 3/2 perfect fifth and the period is a quarter of a 2/1 octave, or 300 ¢. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" [math]\displaystyle{ \frac{3}{2\sqrt{2}} }[/math]. Tetraploid monocot temperaments usually generate the 4L 4s MOS structure and either 4L 8s (and thus 12L 4s) or 8L 4s as children.
Intervals and notation
While there is no agreed-upon notation system for tetraploid monocot, the following is based on interpreting the generator as a semitone (half a whole tone), allowing for an ^ or v to stand for a quarter 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 | Ploid 4 | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cents | Notation | Name | Cents | Notation | Name | Cents | Notation | Name | Cents | Notation | Name | |
| −6 | 288.27 | vEb | — | 588.27 | Gb | diminished fifth | 888.27 | ^Bbb | — | 1188.27 | vvC/^^Dbb | — |
| −5 | 90.22 | Db | minor second | 390.22 | ^Fb | — | 690.22 | vvG/^^Abb | — | 990.22 | vBb | — |
| −4 | 192.18 | vvD/^^Ebb | — | 492.18 | vF | — | 792.18 | Ab | minor sixth | 1092.18 | ^Cb | — |
| −3 | 294.13 | Eb | minor third | 594.13 | ^Gb | — | 894.13 | vvA/^^Bbb | — | 1194.13 | vC | — |
| −2 | 96.09 | ^Db | — | 396.09 | vvE/^^Fb | — | 696.09 | vG | — | 996.09 | Bb | minor seventh |
| −1 | 198.04 | vD | — | 498.04 | F | perfect fourth | 798.04 | ^Ab | — | 1098.04 | vvB/^^Cb | — |
| 0 | 0 | C | unison | 300 | ^Eb | — | 600 | vvF#/^^Gb | — | 900 | vA | — |
| 1 | 101.96 | vvC#/^^Db | — | 401.96 | vE | — | 701.96 | G | perfect fifth | 1001.96 | ^Bb | — |
| 2 | 203.91 | D | major second | 503.91 | ^F | — | 803.91 | vvG#/^^Ab | — | 1103.91 | vB | — |
| 3 | 5.87 | ^C | — | 305.87 | vvD#/^^Eb | — | 605.87 | vF# | — | 905.87 | A | major sixth |
| 4 | 107.82 | vC# | — | 407.82 | E | major third | 707.82 | ^G | — | 1007.82 | vvA#/^^Bb | — |
| 5 | 209.78 | ^D | — | 509.78 | vvE#/^^F | — | 809.78 | vG# | — | 1109.78 | B | major seventh |
| 6 | 11.73 | vvB#/^^C | — | 311.73 | vD# | — | 611.73 | F# | augmented fourth | 911.73 | ^A | — |
A notable feature of tetraploid monocot is the small comma, encountered after 3 steps, which represents a quarter of a Pythagorean comma (or its equivalence, inversed diminished second). This makes tetraploid monocot scales cluster around 12edo.
Temperament interpretations
By definition, tetraploid monocot temperaments split the octave in four.
Diminished
Diminished temperament sets 6/5~7/6 as a period, and uses a fifth as a free generator.
Bidia
Bidia is a weak extension for diaschismic temperament and splits the period again into 1/4 octave. It has very clear extensions through 23-limit. It behaves very well by tempering two 17/12s or four 19/16s into one octave in the 17- and 19-limit. It sets ~25/21 also ~19/16 as a period.
See Diaschismic family #Bidia for details.
Undim
Undim was named for it is some sort of opposite to diminished, and sets ~1215/1024 as a period.
See Undim family #Undim for details.