Ploidacot/Pentacot
| Pergen | [P8, P5/5] |
| Numeral form | 5-cot |
| Pure generator size | 140.39 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 8, 9, 17, 26 |
| Characteristic multival entry | 5 |
Pentacot is a temperament archetype where the generator is a subneutral second of about 139–141¢, five of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Pentacot temperaments typically generate the 8L 1s, 9L 8s, and 17L 9s MOS scales.
Notation
There is no agreed-upon notation for 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 double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where pentacot intervals align with standard monocot intervals (which use chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −20 | 792.180 | Ab | minor sixth |
| −19 | 932.571 | ||
| −18 | 1072.962 | ||
| −17 | 13.353 | ||
| −16 | 153.744 | ||
| −15 | 294.135 | Eb | minor third |
| −14 | 434.526 | ||
| −13 | 574.917 | ||
| −12 | 715.308 | ||
| −11 | 845.699 | ||
| −10 | 996.090 | Bb | minor seventh |
| −9 | 1136.481 | ||
| −8 | 76.872 | ||
| −7 | 217.263 | ||
| −6 | 357.654 | ||
| −5 | 498.045 | F | perfect fourth |
| −4 | 638.436 | ||
| −3 | 778.827 | ||
| −2 | 919.218 | ||
| −1 | 1059.609 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 140.391 | ||
| 2 | 280.782 | ||
| 3 | 421.173 | ||
| 4 | 561.564 | ||
| 5 | 701.955 | G | perfect fifth |
| 6 | 842.346 | ||
| 7 | 982.737 | ||
| 8 | 1123.128 | ||
| 9 | 63.519 | ||
| 10 | 203.910 | D | major second |
| 11 | 344.301 | ||
| 12 | 484.692 | ||
| 13 | 625.083 | ||
| 14 | 765.474 | ||
| 15 | 905.865 | A | major sixth |
| 16 | 1046.256 | ||
| 17 | 1186.647 | ||
| 18 | 127.038 | ||
| 19 | 267.429 | ||
| 20 | 407.820 | E | major third |
Temperament interpretations
An obvious interpretation for pentacot is glacier, a 2.3.13 subgroup temperament, where the generator is 13/12 and five of them make a perfect fifth. There are many extensions for full 13-limit: jerome (26 & 43), tsaharuk (77 & 94), and quanic (94 & 111).