Ploidacot/Triploid alpha-dicot

From Xenharmonic Wiki
Jump to navigation Jump to search
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.