Ploidacot/Triploid monocot

Triploid monocot
Pergen	[P8/3, P5]
Numeral form	3-ploid 1-cot
Pure generator size	98.04 ¢
Pure period size	400 ¢
Forms	9, 12, 15
Characteristic multival entry	3

Triploid monocot is a temperament archetype where the generator is a 3/2 perfect fifth and the period is 1/3 of a 2/1 octave, or 400 ¢. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" [math]\displaystyle{ \frac{2\sqrt[3]{4}}{3} }[/math]. Triploid monocot temperaments usually generate the 3L 6s MOS structure and either 3L 9s (and thus 12L 3s) or 9L 3s as children.

Notation

Triploid monocot 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 monocot intervals align with standard monocot intervals.

While there is no agreed-upon notation system for triploid monocot, the following is based on interpreting the generator as a semitone (1/3 of a minor third), allowing for an ^ or v to stand for a 1/3 of of an inversed diminished second (equivalent to the Pythagorean comma), so vvC# and ^Db are enharmonic.

Triploid monocot intervals (assuming pure fifth and octave)
#	Ploid 1			Ploid 2			Ploid 3
#	Cents	Name	Notation	Cents	Name	Notation	Cents	Name	Notation
−6	188.27	—	^Ebb	588.27	diminished fifth	Gb	988.27	—	vBb
−5	90.22	minor second	Db	490.22	—	vF	890.22	—	^Bbb
−4	392.18	—	^Fb	792.18	minor sixth	Ab	1192.18	—	vC
−3	294.13	minor third	Eb	694.13	—	vG	1094.13	—	^Cb
−2	196.09	—	vD	596.09	—	^Gb	996.09	minor seventh	Bb
−1	98.04	—	^Db	498.04	perfect fourth	F	898.04	—	vA
0	0	unison	C	400	—	vE	800	—	^Ab
1	301.96	—	^Eb	701.96	perfect fifth	G	1101.96	—	vB
2	203.91	major second	D	603.91	—	vF#	1003.91	—	^Bb
3	105.87	—	vC#	505.87	—	^F	905.87	major sixth	A
4	7.82	—	^C	407.82	major third	E	807.82	—	vG#
5	309.78	—	vD#	709.78	—	^G	1109.78	major seventh	B
6	211.73	—	^D	611.73	augmented fourth	F#	1011.73	—	vA#

A notable feature of triploid monocot is the small comma, encountered after 4 steps, which represents 1/3 of a Pythagorean comma (or its equivalence, inversed diminished second). This makes triploid monocot scales cluster around 12edo.

Temperament interpretations

By definition, triploid monocot temperaments split the octave in three.

Augmented

Augmented sets 5/4 as a period, and uses a fifth as a free generator. There are some extensions for 7-limit or higher prime limits: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9).