Ploidacot/Beta-tetracot: Difference between revisions
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{{Infobox ploidacot|Ploids=1|Shears=2|Cots=4|Pergen=[P8, P11/4]|Forms=11, 14, 17, 31|Title=Beta-tetracot|Wedgie=4}} | {{Infobox ploidacot|Ploids=1|Shears=2|Cots=4|Pergen=[P8, P11/4]|Forms=11, 14, 17, 31|Title=Beta-tetracot|Wedgie=4}} | ||
'''Beta-tetracot''' is a temperament archetype where the generator is a | '''Beta-tetracot''' is a temperament archetype where the generator is a supermajor third of about 424–426{{c}}, four of which make a perfect eleventh of [[8/3]], and the period is a [[2/1]] octave. Beta-tetracot temperaments typically generate the [[3L 5s]], [[3L 8s]], and [[3L 11s]] MOS scales, and containing all [[Ploidacot/Dicot|dicot]] intervals. | ||
Beta-tetracot temperaments often generate [[3L 14s]] or [[14L 3s]] as children, and for particularly sharp tunings [[11L 3s]]. | Beta-tetracot temperaments often generate [[3L 14s]] or [[14L 3s]] as children, and for particularly sharp tunings [[11L 3s]]. | ||
== Intervals and notation == | == Intervals and notation == | ||
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== Temperament interpretations == | == Temperament interpretations == | ||
An obvious interpretation for beta-tetracot is [[Squares|skwares]], where the generator is [[9/7]]~[[14/11]] and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c). | An obvious interpretation for beta-tetracot is [[Squares|skwares]], where the generator is {{nowrap|[[9/7]]~[[14/11]]}} and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares ({{nowrap|14c & 17c}}) and [[Smate family|smate]] ({{nowrap|14 & 17c}}). | ||
[[Category:Ploidacots]] | [[Category:Ploidacots|Beta-tetracot]] | ||
Latest revision as of 02:25, 29 January 2026
| Pergen | [P8, P11/4] |
| Numeral form | 2-sheared 4-cot |
| Pure generator size | 424.51 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 11, 14, 17, 31 |
| Characteristic multival entry | 4 |
Beta-tetracot is a temperament archetype where the generator is a supermajor third of about 424–426 ¢, four of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Beta-tetracot temperaments typically generate the 3L 5s, 3L 8s, and 3L 11s MOS scales, and containing all dicot intervals.
Beta-tetracot temperaments often generate 3L 14s or 14L 3s as children, and for particularly sharp tunings 11L 3s.
Intervals and notation
There is no agreed-upon notation for beta-tetracot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the double-diminished third (the difference between two diatonic semitones and one chromatic semitone). Note and interval names are provided where beta-tetracot intervals align with standard dicot intervals (which use neutral chain-of-fifths notation).
| # | Cents | Notation | Name |
|---|---|---|---|
| −12 | 905.87 | A | major sixth |
| −11 | 130.38 | ||
| −10 | 554.89 | Ft | semiaugmented fourth |
| −9 | 979.40 | ||
| −8 | 203.91 | D | major second |
| −7 | 628.42 | ||
| −6 | 1052.93 | Bd | neutral seventh |
| −5 | 277.44 | ||
| −4 | 701.96 | G | perfect fifth |
| −3 | 1126.47 | ||
| −2 | 350.98 | Ed | neutral third |
| −1 | 775.49 | ||
| 0 | 0.00 | C | perfect unison |
| 1 | 424.51 | ||
| 2 | 849.02 | Ad | neutral sixth |
| 3 | 73.53 | ||
| 4 | 498.04 | F | perfect fourth |
| 5 | 922.56 | ||
| 6 | 147.07 | Dd | neutral second |
| 7 | 571.58 | ||
| 8 | 996.09 | Bb | minor seventh |
| 9 | 220.60 | ||
| 10 | 645.11 | Gd | semidiminished fifth |
| 11 | 1069.62 | ||
| 12 | 294.13 | Eb | minor third |
Temperament interpretations
An obvious interpretation for beta-tetracot is skwares, where the generator is 9/7~14/11 and four of them make a perfect eleventh. Immediately it extends to full 11-limit squares (14c & 17c) and smate (14 & 17c).