Ploidacot/Beta-hexacot
| Pergen | [P8, ccP5/6] |
| Numeral form | 2-sheared 6-cot |
| Pure generator size | 516.99 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 16, 23, 30, 37 |
| Characteristic multival entry | 6 |
Beta-hexacot is a temperament archetype where the generator is an acute fourth of about 516–518¢, six of which make 6/1 (sixth harmonic, two octaves above a perfect fifth), and the period is a 2/1 octave. Beta-hexacot temperaments also include all dicot and omega-tricot intervals. Beta-hexacot temperaments typically generate the 7L 2s, 7L 9s, and 7L 16s MOS scales.
Intervals and notation
Due to dividing the sixth harmonic into so many steps, standard notation becomes almost useless for beta-hexacot. Regardless, notation has been provided for where beta-hexacot intervals align with standard dicot intervals (which use neutral chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −24 | 792.180 | Ab | minor sixth |
| −23 | 109.172 | ||
| −22 | 626.165 | ||
| −21 | 1143.157 | Cd | semidiminished octave |
| −20 | 460.150 | ||
| −19 | 977.142 | ||
| −18 | 294.135 | Eb | minor third |
| −17 | 811.127 | ||
| −16 | 128.120 | ||
| −15 | 645.112 | Gd | semidiminished fifth |
| −14 | 1162.105 | ||
| −13 | 479.097 | ||
| −12 | 996.090 | Bb | minor seventh |
| −11 | 313.082 | ||
| −10 | 830.075 | ||
| −9 | 147.067 | Dd | neutral second |
| −8 | 664.060 | ||
| −7 | 1181.052 | ||
| −6 | 498.045 | F | perfect fourth |
| −5 | 1015.037 | ||
| −4 | 332.030 | ||
| −3 | 849.022 | Ad | neutral sixth |
| −2 | 166.015 | ||
| −1 | 683.007 | ||
| 0 | 0.000 | C | perfect unison |
| 1 | 516.993 | ||
| 2 | 1033.985 | ||
| 3 | 350.978 | Ed | neutral third |
| 4 | 867.970 | ||
| 5 | 184.963 | ||
| 6 | 701.955 | G | perfect fifth |
| 7 | 18.948 | ||
| 8 | 535.940 | ||
| 9 | 1052.933 | Bd | neutral seventh |
| 10 | 369.925 | ||
| 11 | 886.918 | ||
| 12 | 203.910 | D | major second |
| 13 | 720.903 | ||
| 14 | 37.895 | ||
| 15 | 554.888 | Ft | semiaugmented fourth |
| 16 | 1071.880 | ||
| 17 | 388.873 | ||
| 18 | 905.865 | A | major sixth |
| 19 | 222.858 | ||
| 20 | 739.850 | ||
| 21 | 56.843 | Ct | semiaugmented unison |
| 22 | 573.835 | ||
| 23 | 1090.828 | ||
| 24 | 407.820 | E | major third |
Temperament interpretations
An obvious interpretation for beta-hexacot is gravity, where the generator is 27/20, three of them make 11/9 above an octave, and six of them make a perfect fifth above two octaves. There are some extensions for the full 11-limit: marvo (65d & 72), zarvo (65 & 72), and gravid (58 & 65).