Ploidacot/Diploid monocot

< Ploidacot

Diploid monocot

Pergen	[P8/2, P5]
Numeral form	2-ploid 1-cot
Pure generator size	101.96 ¢
Pure period size	600 ¢
Forms	10, 12, 22
Characteristic multival entry	2

Diploid monocot is a temperament archetype where the generator is a 3/2 perfect fifth and the period is half a 2/1 octave, or 600 ¢. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" [math]\displaystyle{ \frac{3}{2\sqrt{2}} }[/math]. Diploid monocot temperaments usually generate the 2L 8s MOS structure and either 2L 10s (and thus 12L 2s) or 10L 2s as children.

Intervals and notation

Diploid monocot notation is complicated as it conventionally requires either the introduction of new "hemipythagorean" 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 diploid monocot intervals align with standard monocot intervals.

Diploid monocot intervals (assuming pure fifth and octave)

#	Ploid 1			Ploid 2
	Cents	Notation	Name	Cents	Notation	Name
−6	588.27	Gb	diminished fifth	1188.27	—	—
−5	90.22	Db	minor second	690.22	—	—
−4	192.18	—	—	792.18	Ab	minor sixth
−3	294.13	Eb	minor third	894.13	—	—
−2	396.09	—	—	996.09	Bb	minor seventh
−1	498.04	F	perfect fourth	1098.04	—	—
0	0	C	unison	600	—	—
1	101.96	—	—	701.96	G	perfect fifth
2	203.91	D	major second	803.91	—	—
3	305.87	—	—	905.87	A	major sixth
4	407.82	E	major third	1007.82	—	—
5	509.78	—	—	1109.78	B	major seventh
6	11.73	—	—	611.73	F#	augmented fourth

Temperament interpretations

By definition, diploid monocot temperaments equate some interval to its octave complement.

Diaschismic

Diaschismic sets 3/2 equal to 16/15 plus a semioctave, setting the semioctave equal to 45/32~64/45, and mapping 5/4 to 2 generators down. Diaschismic naturally extends to prime 17 by setting the flat 16/15 generator also equal to 17/16. Diaschismic is tuned best with fifths slightly sharp of just.

To extend to the 7-limit, a simple mapping (pajara) sets 7/5 equal to the semioctave, meaning 7/4 is a semioctave above 5/4. This suggests tuning the generator to about 709 ¢ (or equivalently 109 ¢). With a slightly less sharp fifth, septimal diaschismic maps 7/4 to 8 generators down.

Injera

Injera extends meantone by setting 7/5 equal to 10/7, so that both 5/4 and 7/4 are found at 4 generators up, offset by a 600 ¢ tritone representing both 7/5 and 10/7.

Kalismic

Kalismic sets the semioctave to 99/70~140/99, so that 10/9 and 11/7 are a semioctave apart, as well as are 11/10 and 14/9. The tone is split into two 35/33 semitones, and the Pythagorean comma into two fwiwismas.