How do microtonal accidentals represent intervals smaller than a semitone?

In the context of musical notation, microtonal accidentals are used to represent intervals smaller than a standard semitone, which is the smallest interval in the conventional Western equal temperament system.12

To accommodate these smaller intervals, composers and theorists have adapted standard accidental signs—such as the sharp and flat—by modifying them to indicate specific microtonal divisions. For example, these modified symbols can signify intervals such as one-third sharp, two-thirds sharp, or other fractional divisions of a semitone.1

While standard accidentals raise or lower a note by a full semitone, these specialized notations allow for the precise representation of microtonal music, which may utilize intervals like quarter tones (50 cents), sixth tones, or even smaller divisions. This approach enables the notation of complex pitch structures that fall outside the traditional 12-tone chromatic scale.123