Ploidacot/Alpha-pentacot
Alpha-pentacot is a temperament archetype where the generator is a submajor third of about 379–381¢, five of which make a perfect twelfth of 3/1 (third harmonic, also known as "tritave"), and the period is a 2/1 octave. Alpha-pentacot temperaments typically generate the 3L 4s, 3L 7s, 3L 10s, and 3L 13s MOS scales, and either 3L 16s (and thus 19L 3s) or 16L 3s as children.
Intervals and notation
There is no agreed-upon notation for alpha-pentacot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the minor third. Note and interval names are provided where alpha-pentacot intervals align with standard monocot intervals (which use chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −20 | 792.180 | Ab | minor sixth |
| −19 | 1172.571 | ||
| −18 | 352.962 | ||
| −17 | 733.353 | ||
| −16 | 1113.744 | ||
| −15 | 294.135 | Eb | minor third |
| −14 | 674.526 | ||
| −13 | 1054.917 | ||
| −12 | 235.308 | ||
| −11 | 615.699 | ||
| −10 | 996.090 | Bb | minor seventh |
| −9 | 176.481 | ||
| −8 | 556.872 | ||
| −7 | 937.263 | ||
| −6 | 117.654 | ||
| −5 | 498.045 | F | perfect fourth |
| −4 | 878.436 | ||
| −3 | 58.827 | ||
| −2 | 439.218 | ||
| −1 | 819.609 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 380.391 | ||
| 2 | 760.782 | ||
| 3 | 1141.173 | ||
| 4 | 321.564 | ||
| 5 | 701.955 | G | perfect fifth |
| 6 | 1082.346 | ||
| 7 | 262.737 | ||
| 8 | 643.128 | ||
| 9 | 1023.519 | ||
| 10 | 203.910 | D | major second |
| 11 | 584.301 | ||
| 12 | 964.692 | ||
| 13 | 145.083 | ||
| 14 | 525.474 | ||
| 15 | 905.865 | A | major sixth |
| 16 | 86.256 | ||
| 17 | 466.647 | ||
| 18 | 847.038 | ||
| 19 | 27.429 | ||
| 20 | 407.820 | E | major third |
Temperament interpretations
An obvious interpretation for alpha-pentacot is magic, where the generator is 5/4 and five of them stack to make 3/1. There are many extensions for 7-limit: septimal magic (19 & 22), muggles (16 & 19), brightstone (22 & 25), and darkstone (3d & 16).
Music
- Magical life (2023) by Xenllium – in 19-tone alpha-pentacot with pure fifths (also known as pure-fifth magic scale)