Ploidacot/Alpha-tetracot
| Pergen | [P8, P12/4] |
| Numeral form | 1-sheared 4-cot |
| Pure generator size | 475.49 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 13, 18, 23, 28, 33 |
| Characteristic multival entry | 4 |
Alpha-tetracot is a temperament archetype where the generator is a sub-fourth, four of which make a perfect twelfth of 3/1, and the period is a 2/1 octave. Alpha-tetracot temperaments typically generate the 5L 3s, 5L 8s, 5L 13s, and 5L 18s MOS scales, and they split the diatonic semitone into four equal parts, creating "supermajor", "interseptal", and "subminor" intervals and containing all alpha-dicot intervals.
Alpha-tetracot temperaments often generate 5L 23s and 5L 28s as chromatic scales, and for particularly sharp tunings 23L 5s or 28L 5s.
Intervals and notation
While there is no agreed-upon notation system for alpha-tetracot, the notation provided here is based on interpreting the generator as a sub-fourth, and allowing for an ^ or v to stand for a quarter of a diatonic semitone, so ^^C and vvDb are enharmonic.
| # | Cents | Notation | Name |
|---|---|---|---|
| −12 | 294.13 | Eb | minor third |
| −11 | 769.62 | vAb | |
| −10 | 45.11 | ^^C/vvDb | |
| −9 | 520.60 | ^F | |
| −8 | 996.09 | Bb | minor seventh |
| −7 | 271.58 | vEb | |
| −6 | 747.07 | ^^G/vvAb | |
| −5 | 22.56 | ^C | |
| −4 | 498.04 | F | perfect fourth |
| −3 | 973.53 | vBb | |
| −2 | 249.02 | ^^D/vvEb | |
| −1 | 724.51 | ^G | |
| 0 | 0.00 | C | perfect unison |
| 1 | 475.49 | vF | |
| 2 | 950.98 | ^^A/vvBb | |
| 3 | 226.47 | ^D | |
| 4 | 701.96 | G | perfect fifth |
| 5 | 1177.44 | vC | |
| 6 | 452.93 | ^^E/vvF | |
| 7 | 928.42 | ^A | |
| 8 | 203.91 | D | major second |
| 9 | 679.40 | vG | |
| 10 | 1154.89 | ^^B/vvC | |
| 11 | 430.38 | ^E | |
| 12 | 905.87 | A | major sixth |
Temperament interpretations
An obvious interpretation for alpha-tetracot is buzzardsmic, a 2.3.7 subgroup temperament, where the generator is 21/16 and four of them make a perfect twelfth. There are some extensions for full 7-limit: buzzard (53 & 58), subfourth (58 & 63), and lemongrass (63 & 68).