Ploidacot/Triploid alpha-dicot

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Triploid alpha-dicot
Pergen [P8/3, P4/2]
Numeral form 3-ploid 1-sheared 2-cot
Pure generator size 150.98 ¢
Pure period size 400 ¢
Forms 6, 9, 15, 24
Characteristic multival entry 6

Triploid alpha-dicot is a temperament archetype with a 1/3-octave period, and a generator of a hemifourth. In a pure tuning, the generator is exactly a half of 4/3. But the alternative generator with size around 151¢ is rather easier to grasp.

Triploid alpha-dicot temperaments usually generate the 6L 3s and 9L 6s MOS structures.

Intervals and notation

Triploid alpha-dicot notation is complicated as it conventionally requires either the introduction of new "1/3-pythagorean" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where triploid alpha-dicot intervals align with standard monocot intervals (which use chain-of-fifths notation).

Triploid alpha-dicot intervals (assuming pure fifth and octave)
# Ploid 1 Ploid 2 Ploid 3
Cents Notation Name Cents Notation Name Cents Notation Name
−5 45.11 — — 445.11 — — 845.11 — —
−4 196.09 — — 596.09 — — 996.09 Bb minor seventh
−3 347.07 — — 747.07 — — 1147.07 — —
−2 98.04 — — 498.04 F perfect fourth 898.04 — —
−1 249.02 — — 649.02 — — 1049.02 — —
0 0 C unison 400 — — 800 — —
1 150.98 — — 550.98 — — 950.98 — —
2 301.96 — — 701.96 G perfect fifth 1101.96 — —
3 52.93 — — 452.93 — — 852.93 — —
4 203.91 D major second 603.91 — — 1003.91 — —
5 354.89 — — 754.89 — — 1154.89 — —

Temperament interpretations

Perhaps the most typical interpretation of this ploidacot is triforce. The period is 5/4~14/11 and the generator is 11/10~12/11~35/32, so that 3/2 is a period up two generators, 7/4 at two periods up one generator, and 11/8 at a period up one generator.