A quark is a proposed term for an interval that is 1/3 the size of a diatonic semitone. As a result it can also be called a sixth-tone (although it may not be 1/6 the size of the tempered whole tone). Since the width of a diatonic semitone is variable and depends on the tuning, a quark can take a range of different values. The term is derived from subatomic physics, where there are three quarks in a baryon.
One could argue that these tunings are much less overtly xenharmonic than those based on quarter-tones or third-tones. In 36edo, for example, all intervals are either equivalent to a 12edo interval, or are 33.3 cents higher or lower. As such, all "new" intervals are variations on familiar ones ("red notes" and "blue notes"), rather than representing entirely new categories; this is quite a different situation from what occurs in 24edo. 41edo is similar to 36edo in this respect and may be notated similarly, although it does contain neutral intervals.
Furthermore, the quark is usually small enough that it is typically perceived as a consonance (i. e., an "out-of-tune" but pleasant-sounding unison) rather than a dissonance. 31edo may be considered a transitional case in that its diesis may or may not be perceived this way depending on timbre.
Of course, the main drawback to using quark-based scales as opposed to simpler ones, is that the step size is smaller and there are more pitches.