Ploidacot/Pentaploid monocot

< Ploidacot

Pentaploid monocot

Pergen	[P8/5, P5]
Numeral form	5-ploid 1-cot
Pure generator size	18.04 ¢
Pure period size	240 ¢
Forms	20, 25, 30, 35
Characteristic multival entry	5

Pentaploid monocot is a temperament archetype where the generator is a 3/2 perfect fifth and the period is 1/5 of a 2/1 octave, or 240 ¢. The generator can also be characterized as a perfect fourth 4/3, or as a small comma of [math]\displaystyle{ \frac{2\sqrt[5]{8}}{3} }[/math]. Pentaploid monocot temperaments usually generate the 5L 10s, 5L 15s, and 5L 20s MOS scales.

Intervals and notation

While there is no agreed-upon notation system for pentaploid monocot, the following is based on interpreting the generator as a fifth, allowing for an ^ or v to stand for 1/5 of a diatonic semitone, so ^^^C and vvDb are enharmonic.

Pentaploid monocot intervals (assuming pure fifth and octave)

#	Ploid 1			Ploid 2			Ploid 3			Ploid 4			Ploid 5
	Cents	Notation	Name	Cents	Notation	Name	Cents	Notation	Name	Cents	Notation	Name	Cents	Notation	Name
−6	108.27	^Db	—	348.27	vvFb	—	588.27	Gb	diminished fifth	828.27	^^Ab	—	1068.27	vCb	—
−5	90.22	Db	minor second	330.22	^^Eb	—	570.22	vGb	—	810.22	^Ab	—	1050.22	vvCb	—
−4	72.18	vDb	—	312.18	^Eb	—	552.18	vvGb	—	792.18	Ab	minor sixth	1032.18	^^Bb	—
−3	54.13	vvDb	—	294.13	Eb	minor third	534.13	^^F	—	774.13	vAb	—	1014.13	^Bb	—
−2	36.09	^^C	—	276.09	vEb	—	516.09	^F	—	756.09	vvAb	—	996.09	Bb	minor seventh
−1	18.04	^C	—	258.04	vvEb	—	498.04	F	perfect fourth	738.04	^^G	—	978.04	vBb	—
0	0	C	unison	240	^^D	—	480	vF	—	720	^G	—	960	vvBb	—
1	221.96	^D	—	461.96	vvF	—	701.96	G	perfect fifth	941.96	^^A	—	1181.96	vC	—
2	203.91	D	major second	443.91	^^E	—	683.91	vG	—	923.91	^A	—	1163.91	vvC	—
3	185.87	vD	—	425.87	^E	—	665.87	vvG	—	905.87	A	major sixth	1145.87	^^B	—
4	167.82	vvD	—	407.82	E	major third	647.82	^^F#	—	887.82	vA	—	1127.82	^B	—
5	149.78	^^C#	—	389.78	vE	—	629.78	^F#	—	869.78	vvA	—	1109.78	B	major seventh
6	131.73	^C#	—	371.73	vvE	—	611.73	F#	augmented fourth	851.73	^^G#	—	1091.73	vB	—

Temperament interpretations

By definition, pentaploid monocot temperaments split the octave in five.

Quintile

Main article: Quintile family

Quintile temperament sets ~59049/51200 as a period, and uses a fifth as a generator.