Ploidacot/Omega-tricot
Omega-tricot is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of 4/3, and the period is a 2/1 octave. Omega-tricot temperaments usually generate the 1L 6s and 7L 1s MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.
Notation
While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second. ^^C and vC# are enharmonic.
| # | Cents | Notation | Name |
|---|---|---|---|
| -9 | 905.865 | A | major sixth |
| -8 | 1071.88 | vB | submajor seventh |
| -7 | 37.895 | ^C | superunison |
| -6 | 203.91 | D | major second |
| -5 | 369.925 | vE | submajor third |
| -4 | 535.94 | ^F | superfourth |
| -3 | 701.955 | G | perfect fifth |
| -2 | 867.97 | vA | submajor sixth |
| -1 | 1033.985 | ^Bb | supraminor seventh |
| 0 | 0 | C | perfect unison / perfect octave |
| 1 | 166.015 | vD | submajor second |
| 2 | 332.03 | ^Eb | supraminor third |
| 3 | 498.045 | F | perfect fourth |
| 4 | 664.06 | vG | subfifth |
| 5 | 830.075 | ^Ab | supraminor sixth |
| 6 | 996.09 | Bb | minor seventh |
| 7 | 1162.105 | vC | suboctave |
| 8 | 128.12 | ^Db | supraminor second |
| 9 | 294.135 | Eb | minor third |
Temperament interpretations
Porcupine
In porcupine, the generator is 11/10, two generators make 6/5, and three make 4/3. This is tuned best with a considerably flat generator of about 162 cents or so, and naturally extends to the full 11-limit as in superpyth, so the minor seventh is 7/4.
Superpine
In superpine, the subminor seventh (C-vBb, 13 generators up) is mapped to 7/4, and the mappings for 3 and 5 are as in meantone, so -3 generators is 3/2 and -12 generators is 5/4. It is best tuned with a slightly sharp generator of about 168 cents.