Ploidacot/Gamma-pentacot
Gamma-pentacot is a temperament archetype where the generator is a subneutral third, five of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Gamma-pentacot temperaments typically generate the 4L 3s, 7L 4s, and 7L 11s MOS scales, and they split the chromatic semitone into five equal parts, creating "supraminor", "subneutral", "supraneutral", and "submajor" intervals.
| Pergen | [P8, P11/5] |
| Numeral form | 3-sheared 5-cot |
| Pure generator size | 339.61 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 7, 11, 18, 25, 32 |
| Characteristic multival entry | 5 |
Gamma-pentacot temperaments often generate 7L 18s, 7L 25s, 7L 32s, and 7L 39s as chromatic scales, and for particularly flat tunings 18L 7s, 25L 7s, 32L 7s, or 39L 7s.
Intervals and notation
While there is no agreed-upon notation system for gamma-pentacot, the notation provided here is based on interpreting the generator as a subneutral third, and allowing for an ^ or v to stand for 1/5 of a chromatic semitone, so ^^^C and vvC# are enharmonic.
| # | Cents | Notation | Name |
|---|---|---|---|
| −30 | 611.730 | F# | augmented fourth |
| −29 | 951.339 | ^^A | sub-semiaugmented sixth |
| −28 | 90.948 | vC# | subaugmented unison |
| −27 | 430.557 | ^E | supermajor third |
| −26 | 770.166 | vvG# | supra-semiaugmented fifth |
| −25 | 1109.775 | B | major seventh |
| −24 | 249.384 | ^^D | sub-semiaugmented second |
| −23 | 588.993 | vF# | subaugmented fourth |
| −22 | 928.602 | ^A | supermajor sixth |
| −21 | 68.211 | vvC# | supra-semiaugmented unison |
| −20 | 407.820 | E | major third |
| −19 | 747.429 | ^^G | sub-semiaugmented fifth |
| −18 | 1087.038 | vB | submajor seventh |
| −17 | 226.647 | ^D | supermajor second |
| −16 | 566.256 | vvF# | supra-semiaugmented fourth |
| −15 | 905.865 | A | major sixth |
| −14 | 45.474 | ^^C | sub-semiaugmented unison |
| −13 | 385.083 | vE | submajor third |
| −12 | 724.692 | ^G | super-fifth |
| −11 | 1064.301 | vvB | supraneutral seventh |
| −10 | 203.910 | D | major second |
| −9 | 543.519 | ^^F | sub-semiaugmented fourth |
| −8 | 883.128 | vA | submajor sixth |
| −7 | 22.737 | ^C | super-unison |
| −6 | 362.346 | vvE | supraneutral third |
| −5 | 701.955 | G | perfect fifth |
| −4 | 1041.564 | ^^Bb | subneutral seventh |
| −3 | 181.173 | vD | submajor second |
| −2 | 520.782 | ^F | super-fourth |
| −1 | 860.391 | vvA | supraneutral sixth |
| 0 | 0.000 | C | perfect unison |
| 1 | 339.609 | ^^Eb | subneutral third |
| 2 | 679.218 | vG | sub-fifth |
| 3 | 1018.827 | ^Bb | supraminor seventh |
| 4 | 158.436 | vvD | supraneutral second |
| 5 | 498.045 | F | perfect fourth |
| 6 | 837.654 | ^^Ab | subneutral sixth |
| 7 | 1177.263 | vC | sub-octave |
| 8 | 316.872 | ^Eb | supraminor third |
| 9 | 656.481 | vvG | supra-semidiminished fifth |
| 10 | 996.090 | Bb | minor seventh |
| 11 | 135.699 | ^^Db | subneutral second |
| 12 | 475.308 | vF | sub-fourth |
| 13 | 814.917 | ^Ab | supraminor sixth |
| 14 | 1174.526 | vvC | supra-semidiminished octave |
| 15 | 294.135 | Eb | minor third |
| 16 | 633.744 | ^^Gb | sub-semidiminished fifth |
| 17 | 973.353 | vBb | subminor seventh |
| 18 | 112.962 | ^Db | supraminor second |
| 19 | 452.571 | vvF | supra-semidiminished fourth |
| 20 | 792.180 | Ab | minor sixth |
| 21 | 1131.789 | ^^Cb | sub-semidiminished octave |
| 22 | 271.398 | vEb | subminor third |
| 23 | 611.007 | ^Gb | supradiminished fifth |
| 24 | 950.616 | vvBb | supra-semidiminished seventh |
| 25 | 90.225 | Db | minor second |
| 26 | 429.834 | ^^Fb | sub-semidiminished fourth |
| 27 | 769.443 | vAb | subminor sixth |
| 28 | 1109.052 | ^Cb | supradiminished octave |
| 29 | 248.661 | vvEb | supra-semidiminished third |
| 30 | 588.270 | Gb | diminished fifth |
Temperament interpretations
An obvious interpretation for gamma-pentacot is amity, 5/4 is equated to 4 octaves minus 13 generators, and 7/4 is equated to 17 generators minus 4 octaves. Other interpretations include sixix, which interprets 6/5 as a generator.