Ploidacot/Alpha-hexacot
Alpha-hexacot is a temperament archetype where the generator is a minor third of about 316–318¢, six of which make a perfect twelfth of 3/1, and the period is a 2/1 octave. Alpha-hexacot temperaments also include all alpha-dicot and alpha-tricot intervals. Alpha-hexacot temperaments typically generate the 4L 7s and 4L 11s MOS scales.
Intervals and notation
Due to dividing the twelfth into so many steps, standard notation becomes almost useless for alpha-hexacot. Regardless, notation has been provided for where alpha-hexacot intervals align with standard monocot intervals (which use chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −24 | 792.180 | Ab | minor sixth |
| −23 | 1109.172 | ||
| −22 | 226.165 | ||
| −21 | 543.157 | ||
| −20 | 860.150 | ||
| −19 | 1177.142 | ||
| −18 | 294.135 | Eb | minor third |
| −17 | 611.127 | ||
| −16 | 928.120 | ||
| −15 | 45.112 | ||
| −14 | 362.105 | ||
| −13 | 679.097 | ||
| −12 | 996.090 | Bb | minor seventh |
| −11 | 113.082 | ||
| −10 | 430.075 | ||
| −9 | 747.067 | ||
| −8 | 1064.060 | ||
| −7 | 181.052 | ||
| −6 | 498.045 | F | perfect fourth |
| −5 | 815.037 | ||
| −4 | 1132.030 | ||
| −3 | 249.022 | ||
| −2 | 566.015 | ||
| −1 | 883.007 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 316.993 | ||
| 2 | 633.985 | ||
| 3 | 950.978 | ||
| 4 | 67.970 | ||
| 5 | 384.963 | ||
| 6 | 701.955 | G | perfect fifth |
| 7 | 1018.948 | ||
| 8 | 135.940 | ||
| 9 | 452.933 | ||
| 10 | 769.925 | ||
| 11 | 1086.918 | ||
| 12 | 203.910 | D | major second |
| 13 | 520.903 | ||
| 14 | 837.895 | ||
| 15 | 1154.888 | ||
| 16 | 271.880 | ||
| 17 | 588.873 | ||
| 18 | 905.865 | A | major sixth |
| 19 | 22.858 | ||
| 20 | 339.850 | ||
| 21 | 656.843 | ||
| 22 | 973.835 | ||
| 23 | 90.828 | ||
| 24 | 407.820 | E | major third |
Temperament interpretations
An obvious interpretation for alpha-hexacot is kleismic, where the generator is 6/5, three of which make 26/15~45/26, four make 25/24~26/25~27/26 above an octave, five make 5/4 above an octave, and six make a perfect twelfth. There are some extensions for full 13-limit: the most accurate mapping of 7 and 11 gives catakleismic (19 & 53).