Ploidacot/Hexacot
Hexacot is a temperament archetype where the generator is a semitone of about 116–118¢, six of which make a perfect fifth of 3/2, and the period is a 2/1 octave. Hexacot temperaments also include all dicot and tricot intervals, as the dicot generator is split further into three, or the tricot generator is split further into two. Hexacot temperaments typically generate the 1L 9s and 10L 1s MOS scales.
Intervals and notation
Due to dividing the fifth into so many steps, standard notation becomes almost useless for hexacot. Regardless, notation has been provided for where hexacot intervals align with standard dicot intervals (which use neutral chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −24 | 792.180 | Ab | minor sixth |
| −23 | 909.172 | ||
| −22 | 1026.165 | ||
| −21 | 1143.157 | Cd | semidiminished octave |
| −20 | 60.150 | ||
| −19 | 177.142 | ||
| −18 | 294.135 | Eb | minor third |
| −17 | 411.127 | ||
| −16 | 528.120 | ||
| −15 | 645.112 | Gd | semidiminished fifth |
| −14 | 762.105 | ||
| −13 | 879.097 | ||
| −12 | 996.090 | Bb | minor seventh |
| −11 | 1113.082 | ||
| −10 | 30.075 | ||
| −9 | 147.067 | Dd | neutral second |
| −8 | 264.060 | ||
| −7 | 381.052 | ||
| −6 | 498.045 | F | perfect fourth |
| −5 | 615.037 | ||
| −4 | 732.030 | ||
| −3 | 849.022 | Ad | neutral sixth |
| −2 | 966.015 | ||
| −1 | 1083.007 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 116.993 | ||
| 2 | 233.985 | ||
| 3 | 350.978 | Ed | neutral third |
| 4 | 467.970 | ||
| 5 | 584.963 | ||
| 6 | 701.955 | G | perfect fifth |
| 7 | 818.948 | ||
| 8 | 935.940 | ||
| 9 | 1052.933 | Bd | neutral seventh |
| 10 | 1169.925 | ||
| 11 | 86.918 | ||
| 12 | 203.910 | D | major second |
| 13 | 320.903 | ||
| 14 | 437.895 | ||
| 15 | 554.888 | Ft | semiaugmented fourth |
| 16 | 671.880 | ||
| 17 | 788.873 | ||
| 18 | 905.865 | A | major sixth |
| 19 | 1022.858 | ||
| 20 | 1139.850 | ||
| 21 | 56.843 | Ct | semiaugmented unison |
| 22 | 173.835 | ||
| 23 | 290.828 | ||
| 24 | 407.820 | E | major third |
A notable feature of hexacot is the small diesis, known as the quark, encountered after 10 steps, which represents one-third of a diatonic semitone. This makes hexacot scales cluster around 10edo.
Temperament interpretations
An obvious interpretation for hexacot is miracle, where the generator is 16/15~15/14, three of them make 11/9, and six of them make a perfect fifth. See miracle extensions for extensions.