Ploidacot/Diploid dicot

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Diploid dicot
Pergen [P8/2, P4/2]
Numeral form 2-ploid 2-cot
Pure generator size 249.02 ¢
Pure period size 600 ¢
Forms 6, 10, 14, 24
Characteristic multival entry 4

Diploid dicot is a temperament archetype where the generator is a neutral third, two of which stack to a 3/2 perfect fifth, and the period is half a 2/1 octave, or 600 ¢. In other words, this is the same as the hemipythagorean structure. The generator can also be characterized as an inframinor third or ultramajor second, two of which reach a perfect fourth. Diploid dicot temperaments usually generate the decatonic scale 4L 6s and the 14-note scale 10L 4s.

Intervals and notation

Diploid dicot 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 dicot intervals align with standard dicot intervals (which use neutral chain-of-fifths notation).

Diploid dicot intervals (assuming pure fifth and octave)
# Ploid 1 Ploid 2
Cents Notation Name Cents Notation Name
−7 543.157 1143.157 Cd semidiminished octave
−6 294.135 Eb minor third 894.135
−5 45.112 645.112 Gd semidiminished fifth
−4 396.090 996.090 Bb minor seventh
−3 147.067 Dd neutral second 747.067
−2 498.045 F perfect fourth 1098.045
−1 249.022 849.022 Ad neutral sixth
0 0 C perfect unison 600
1 350.978 Ed neutral third 950.978
2 101.955 701.955 G perfect fifth
3 452.933 1052.933 Bd neutral seventh
4 203.910 D major second 803.910
5 554.888 Ft semiaugmented fourth 1154.888
6 305.865 905.865 A major sixth
7 56.843 Ct semiaugmented unison 656.843

Temperament interpretations

A diploid dicot temperament must temper out at least two commas: one to equate a pair of intervals to the semioctave, and one to equate another pair of intervals to the hemififth. As a result, diploid dicot temperaments must have at least 4 primes.

There are few temperaments that follow specifically the diploid dicot archetype, and those that do are often the lucky intersection of a diploid and an (alpha-)dicot temperament; lucky, because it's possible that the intersection of such a pair of temperaments produces a new one that cannot be expressed through diploid dicot, or any kind of chain of fifths.

Sruti

The intersection of septimal diaschismic and namo, which equates all of 16/13, 27/22, 11/9 and 39/32 to the neutral third, 45/32 and 64/45 with the semioctave. It is not very good for a diaschismic extension.

Semihemi

The intersection of hemififths and kalismic and barbados, which maps 15/13 to the hemifourth, 49/40 to the hemififth, and 99/70 to the semioctave. It is quite accurate, and solid as a hemififths extension, where primes 5 and 7 are along the dicot chain, and primes 11 and 13 are along the diploid chain.