Ploidacot/Gamma-hexacot
| Pergen | [P8, ccP4/6] |
| Numeral form | 3-sheared 6-cot |
| Pure generator size | 483.01 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 17, 22, 27, 32, 37 |
| Characteristic multival entry | 6 |
Gamma-hexacot is a temperament archetype where the generator is a grave fourth of about 482–484 ¢, six of which make 16/3 (perfect eighteenth, two octaves above a perfect fourth), and the period is a 2/1 octave. Gamma-hexacot temperaments also include all alpha-dicot and tricot intervals. Gamma-hexacot temperaments typically generate the 5L 7s, 5L 12s, and 5L 17s MOS scales.
Intervals and notation
While there is no agreed-upon notation system for gamma-hexacot, the following is based on interpreting the generator as a grave fourth, and allowing for an ^ or v to stand for 1/6 of a diatonic semitone, so ^^^C and vvvDb are enharmonic.
| # | Cents | Notation | Name |
|---|---|---|---|
| −24 | 407.820 | E | major third |
| −23 | 890.828 | vA | |
| −22 | 173.835 | vvD | |
| −21 | 656.843 | ^^^F#/vvvG | |
| −20 | 1139.850 | ^^B | |
| −19 | 422.858 | ^E | |
| −18 | 905.865 | A | major sixth |
| −17 | 188.873 | vD | |
| −16 | 671.880 | vvG | |
| −15 | 1154.888 | ^^^B/vvvC | |
| −14 | 437.895 | ^^E | |
| −13 | 920.903 | ^A | |
| −12 | 203.910 | D | major second |
| −11 | 686.918 | vG | |
| −10 | 1169.925 | vvC | |
| −9 | 452.933 | ^^^E/vvvF | |
| −8 | 935.940 | ^^A | |
| −7 | 218.948 | ^D | |
| −6 | 701.955 | G | perfect fifth |
| −5 | 1184.963 | vC | |
| −4 | 467.970 | vvF | |
| −3 | 950.978 | ^^^A/vvvBb | |
| −2 | 233.985 | ^^D | |
| −1 | 716.993 | ^G | |
| 0 | 0.000 | C | perfect unison |
| 1 | 483.007 | vF | |
| 2 | 966.015 | vvBb | |
| 3 | 249.022 | ^^^D/vvvEb | |
| 4 | 732.030 | ^^G | |
| 5 | 15.037 | ^C | |
| 6 | 498.045 | F | perfect fourth |
| 7 | 981.052 | vBb | |
| 8 | 264.060 | vvEb | |
| 9 | 747.067 | ^^^G/vvvAb | |
| 10 | 30.075 | ^^C | |
| 11 | 513.082 | ^F | |
| 12 | 996.090 | Bb | minor seventh |
| 13 | 279.097 | vEb | |
| 14 | 762.105 | vvAb | |
| 15 | 45.112 | ^^^C/vvvDb | |
| 16 | 528.120 | ^^F | |
| 17 | 1011.127 | ^Bb | |
| 18 | 294.135 | Eb | minor third |
| 19 | 777.142 | vAb | |
| 20 | 60.150 | vvDb | |
| 21 | 543.157 | ^^^F/vvvGb | |
| 22 | 1026.165 | ^^Bb | |
| 23 | 309.172 | ^Eb | |
| 24 | 792.180 | Ab | minor sixth |
Temperament interpretations
An obvious interpretation for gamma-hexacot is hemiseven, where the generator is 45/34, two of which make 7/4, three make 15/13 above an octave, four make 26/17~32/21 above an octave, six make 4/3 above two octaves, seven make 30/17 above two octaves, seventeen make 9/5 above six octaves, and nineteen make 11/7 above seven octaves.