Midtrinary: non-trinary identities that are not strictly atrinary/exotrinary; an umbrella term for midbinary, midtertiary genders, and other labels referencing gender trinary.
Examples: demitrinary (but not necessarily demiatrinary as the other part can be anontrinary)/viatrinary/ideotrinary, multigender experiences involving at least one trinary gender (multrinary/multitrinary), trinaryflux, etc.
This term was not defined yet, but used in an illustrative infographic from gender juxtaposition diagrams.
It should be noted that trinaries could depend on one’s cultural arities, as the tertiary trinary gender could be a culturally specific identity (“third gender”) or could just be neutral (neutrois/agender). Sometimes trinary/nontrinary doesn’t apply to the individual either, for example when one’s gender is from a quinary or senary system.
Atrinary, Aternary, or Atertiary (abbreviated AT) is an umbrella term referring to any genders that are completely unrelated to maleness, masculinity, femaleness, femininity, neutrois-ness, or neutrality, and is nowhere in between those things. While also not necessarily being genderless (although agender individuals may also identify as atrinary). An atrinary individual may feel a strong sense of gender, however that gender is completely unrelated from the gender trinary.
Midbinary, also known as endobinary, is a term for any non-binary gender or experience that references or is associated with one or both binary genders.
Anontrinary or Anonternary is a gender that isn’t trinary/ternary (man, woman, and neutrois), but even still, is outside of non-trinary/non-ternary.
Neutrois is a non-binary gender identity which is often associated with a “neutral” or “null” gender.