Quark

A quark is an interval that is one-third the size of a possibly tempered Pythagorean diatonic semitone (256/243). 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 the diatonic semitone is variable and depends on the tuning, a quark can take a range of different values. The term "quark" is derived from subatomic physics, where there are three quarks in a baryon.

Equal temperaments with quark-sized steps include 26edo, 31edo, 36edo (the "standard" quark or sixth-tone), 41edo, and 46edo, though this list is far from exhaustive. Most commonly, quarks are encountered in the slendric temperament, as supported by the aforementioned EDOs, where three 8/7 intervals stack to 3/2, and after five 8/7s is reached the octave short this residual interval known as the quark, here representing 49/48~64/63 tempered together; two quarks then represent 28/27.

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, most of the "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. Conversely, some types of quark could legitimately be considered quarter-tones in their own right, for example, in 26edo, where the quark is literally one quarter of the whole tone.

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.