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I am looking for the noun that is the thing that is either major or minor in respect to a chord such as a triad. I suppose it could also be an adjective. It would be 'x' in the following question: "What is the x of the GAB triad?".
EDIT: I meant to use a proper example triad such as 'GBD'... see comment below. I'm happy I made the mistake as I learned from that comment's explanation of what a GAB chord would be. :-)
The term you are looking for is "Quality": The quality of a chord (triad) refers to whether it is major, minor, diminished, augmented, etc. I believe it can also be extended to 7th chords.
In your specific example "GAB" is neither major nor minor. It might be considered a major-add-9 chord since there is a major third G-B and often the fifth is omitted in a chord, so it could be called a major chord, (though it still depends on the musical context).
Minor/major is used referring to intervals, scales and chords. Intervals can be big (major) or small (minor) in regards of their nr. of semitones.
The chord quality or chord type of major/minor is characterized by the gender.
German theorists use the term Tongeschlecht = tone gender: major/minor = dur/moll = male/female (-> dur = hard, moll = soft!)
Edit:
The question asks for a generic term that includes the qualities major and minor of a chord.
After rethinking my answer I have to say:
Meanwhile I’m also convinced that this dichotomy is characterizing the key and tonality of a piece or a melody and is not referred to single chords.
