Ploidacot/Tetracot
Tetracot is a temperament archetype where the generator is a submajor second, four of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Tetracot temperaments typically generate the 1L 5s and 6L 1s MOS scales, and they split the chromatic semitone into four equal parts, creating "supraminor", "neutral", and "submajor" intervals.
Intervals and notation
While there is no agreed-upon notation system for tetracot, the notation provided here is based on interpreting the generator as a submajor second, and produced by extending dicot notation, allowing for an ^ or v to stand for a quarter of a chromatic semitone. Eb^^ = Evv = Ed.
| # | Cents | Notation | Name |
|---|---|---|---|
| -9 | 820.60 | ^Ab | supraminor sixth |
| -8 | 996.09 | Bb | minor seventh |
| -7 | 1,171.58 | vC | suboctave |
| -6 | 147.07 | Dd | neutral second |
| -5 | 322.56 | ^Eb | supraminor third |
| -4 | 498.05 | F | perfect fourth |
| -3 | 673.53 | vG | subfifth |
| -2 | 849.02 | Ad | neutral sixth |
| -1 | 1,024.51 | ^Bb | supraminor seventh |
| 0 | 0.00 | C | perfect unison / perfect octave |
| 1 | 175.49 | vD | submajor second |
| 2 | 350.98 | Ed | neutral third |
| 3 | 526.47 | ^F | superfourth |
| 4 | 701.96 | G | perfect fifth |
| 5 | 877.44 | vA | submajor sixth |
| 6 | 1,052.93 | Bd | neutral seventh |
| 7 | 28.42 | ^C | superunison |
| 8 | 203.91 | D | major second |
| 9 | 379.40 | vE | submajor third |
A notable feature of tetracot is the small diesis encountered after 7 steps. This makes tetracot scales cluster around 7edo.
Temperament interpretations
Tetracot
The temperament named "tetracot" is one of the simplest 5-limit interpretations. The step is interpreted as 10/9, meaning the submajor third is interpreted as 5/4. It is best tuned with a sharpened generator of around 176 cents.
Monkey
Usually framed as an extension of tetracot due to the availability of tetracot's 5-limit mapping, monkey maps 7/4 to 15 steps down, the subminor seventh.