Ploidacot/Beta-hexacot: Difference between revisions
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{{Infobox ploidacot|Ploids=1|Shears=2|Cots=6|Pergen=[P8, ccP5/6]|Forms=16, 23, 30, 37|Title=Beta-hexacot|Wedgie=6}} | {{Infobox ploidacot|Ploids=1|Shears=2|Cots=6|Pergen=[P8, ccP5/6]|Forms=16, 23, 30, 37|Title=Beta-hexacot|Wedgie=6}} | ||
'''Beta-hexacot''' is a temperament archetype where the generator is an acute fourth of about | '''Beta-hexacot''' is a temperament archetype where the generator is an acute fourth of about 516–518{{c}}, 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 [[Ploidacot/Dicot|dicot]] and [[Ploidacot/Omega-tricot|omega-tricot]] intervals. Beta-hexacot temperaments typically generate the [[7L 2s]], [[7L 9s]], and [[7L 16s]] MOS scales. | ||
== Intervals and notation == | == Intervals and notation == | ||
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== Temperament interpretations == | == Temperament interpretations == | ||
An obvious interpretation for beta-hexacot is [[gravity]], where the generator is [[27/20]], two of which make [[20/11]], three make [[11/9]]~[[27/22]] above an octave, and six 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). | An obvious interpretation for beta-hexacot is [[gravity]], where the generator is [[27/20]], two of which make [[20/11]], three make {{nowrap|[[11/9]]~[[27/22]]}} above an octave, and six make a perfect fifth above two octaves. There are some extensions for the full 11-limit: marvo ({{nowrap|65d & 72}}), zarvo ({{nowrap|65 & 72}}), and gravid ({{nowrap|58 & 65}}). | ||
[[Category:Ploidacots|Beta-hexacot]] | [[Category:Ploidacots|Beta-hexacot]] | ||
Latest revision as of 12:29, 26 January 2026
| 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
While there is no agreed-upon notation system for beta-hexacot, the following is based on interpreting the generator as an acute fourth, and allowing for an ^ or v to stand for 1/6 of a chromatic semitone, so ^^^Eb = vvvE = Ed.
| # | Cents | Notation | Name |
|---|---|---|---|
| −24 | 792.180 | Ab | minor sixth |
| −23 | 109.172 | ^Db | |
| −22 | 626.165 | ^^Gb | |
| −21 | 1143.157 | Cd | semidiminished octave |
| −20 | 460.150 | vvF | |
| −19 | 977.142 | vBb | |
| −18 | 294.135 | Eb | minor third |
| −17 | 811.127 | ^Ab | |
| −16 | 128.120 | ^^Db | |
| −15 | 645.112 | Gd | semidiminished fifth |
| −14 | 1162.105 | vvC | |
| −13 | 479.097 | vF | |
| −12 | 996.090 | Bb | minor seventh |
| −11 | 313.082 | ^Eb | |
| −10 | 830.075 | ^^Ab | |
| −9 | 147.067 | Dd | neutral second |
| −8 | 664.060 | vvG | |
| −7 | 1181.052 | vC | |
| −6 | 498.045 | F | perfect fourth |
| −5 | 1015.037 | ^Bb | |
| −4 | 332.030 | ^^Eb | |
| −3 | 849.022 | Ad | neutral sixth |
| −2 | 166.015 | vvD | |
| −1 | 683.007 | vG | |
| 0 | 0.000 | C | perfect unison |
| 1 | 516.993 | ^F | |
| 2 | 1033.985 | ^^Bb | |
| 3 | 350.978 | Ed | neutral third |
| 4 | 867.970 | vvA | |
| 5 | 184.963 | vD | |
| 6 | 701.955 | G | perfect fifth |
| 7 | 18.948 | ^C | |
| 8 | 535.940 | ^^F | |
| 9 | 1052.933 | Bd | neutral seventh |
| 10 | 369.925 | vvE | |
| 11 | 886.918 | vA | |
| 12 | 203.910 | D | major second |
| 13 | 720.903 | ^G | |
| 14 | 37.895 | ^^C | |
| 15 | 554.888 | Ft | semiaugmented fourth |
| 16 | 1071.880 | vvB | |
| 17 | 388.873 | vE | |
| 18 | 905.865 | A | major sixth |
| 19 | 222.858 | ^D | |
| 20 | 739.850 | ^^G | |
| 21 | 56.843 | Ct | semiaugmented unison |
| 22 | 573.835 | vvF# | |
| 23 | 1090.828 | vB | |
| 24 | 407.820 | E | major third |
Temperament interpretations
An obvious interpretation for beta-hexacot is gravity, where the generator is 27/20, two of which make 20/11, three make 11/9~27/22 above an octave, and six 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).