Ploidacot/Triploid alpha-dicot

< Ploidacot

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.