Commonly used scales such as the major and minor heptatonic scales contain only two different intervals between their neighbouring notes: the major second (whole tone) and the minor second (semitone). The common major scale has the semitones between its 3rd and 4th step, and 7th and 8th step, whereas the minor between 2nd and 3rd and 5th and 6th.
To create a trichord we take any note from the scale as a base note and and 2nd next and 4th next notes starting from the base one. The intervals between the base and 2nd and 2nd and 4th are always major or minor thirds (if we're using the scales mentioned above). These four combinations of major and minor thirds are all possible tertian trichords and their naming is well documented (e.g. C, Cm, Caug, Cdim).
Now, if we instead take a scale that contains different intervals between its neighbouring notes (semitones, whole tones, a whole tone plus a semitone), we can end up with different intervals between a base note and its 2nd next and between the 2nd next and 4th next: we could have a chord made out of a major second and major third.
In other words, the three notes have 2 and 4 semitones between the chord's notes.
How do we name such non-tertial chords? Are there rules for naming secundal-tertian or other hybrid (tertian-quartal?) chords?