In the Pitch category one will observe tuning systems/esthetics/composers where I find that microtonality is used mainly to create certain scales or other pitch structures. Timbre is of less importance.

The quality of a sound governed by the rate of vibrations producing it; the degree of highness or lowness of a tone.

Pitch, Oxford dictionary

Since the pitch is determined mostly by frequency, it is usually identified with it. The pitch depends also, in a lower degree, on the sound level and on the physiology of the auditory system.

The particular quality of a sound (e.g. an individual musical note) that fixes its position in the scale. Certain sounds used in music that occupy no particular scale position, such as those produced by cymbals or the side drum, can be said to be of indefinite pitch. Pitch is determined by what the ear judges to be the most fundamental wave-frequency of the sound (even when, as for example with difference tones, this is an aural illusion, not actually present in the physical sound wave). Experimental studies, in which listeners have been tested for their perception and memory of pitch differences among sounds with wave-frequencies known to the experimenter, have shown that marked differences of timbre, loudness and musical context affect pitch, albeit in relatively small degree. But long-term memory, called Periodicals, , enables some people to identify the pitch of sounds quite apart from their contextual relation to other sounds. Such aspects of pitch are discussed in (…)

Pitch, Grove