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
Due to dividing the eighteenth into so many steps, standard notation becomes almost useless for gamma-hexacot. Regardless, notation has been provided for where gamma-hexacot intervals align with standard monocot intervals (which use chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −24 | 407.820 | E | major third |
| −23 | 890.828 | ||
| −22 | 173.835 | ||
| −21 | 656.843 | ||
| −20 | 1139.850 | ||
| −19 | 422.858 | ||
| −18 | 905.865 | A | major sixth |
| −17 | 188.873 | ||
| −16 | 671.880 | ||
| −15 | 1154.888 | ||
| −14 | 437.895 | ||
| −13 | 920.903 | ||
| −12 | 203.910 | D | major second |
| −11 | 686.918 | ||
| −10 | 1169.925 | ||
| −9 | 452.933 | ||
| −8 | 935.940 | ||
| −7 | 218.948 | ||
| −6 | 701.955 | G | perfect fifth |
| −5 | 1184.963 | ||
| −4 | 467.970 | ||
| −3 | 950.978 | ||
| −2 | 233.985 | ||
| −1 | 716.993 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 483.007 | ||
| 2 | 966.015 | ||
| 3 | 249.022 | ||
| 4 | 732.030 | ||
| 5 | 15.037 | ||
| 6 | 498.045 | F | perfect fourth |
| 7 | 981.052 | ||
| 8 | 264.060 | ||
| 9 | 747.067 | ||
| 10 | 30.075 | ||
| 11 | 513.082 | ||
| 12 | 996.090 | Bb | minor seventh |
| 13 | 279.097 | ||
| 14 | 762.105 | ||
| 15 | 45.112 | ||
| 16 | 528.120 | ||
| 17 | 1011.127 | ||
| 18 | 294.135 | Eb | minor third |
| 19 | 777.142 | ||
| 20 | 60.150 | ||
| 21 | 543.157 | ||
| 22 | 1026.165 | ||
| 23 | 309.172 | ||
| 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.