This character is a Other Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it is written from left to right. When changing direction it is not mirrored. The word that U+1D196 forms with similar adjacent characters prevents a line break inside it.
The Wikipedia has the following information about this codepoint:
The trill (or shake, as it was known from the 16th until the early 20th century) is a musical ornament consisting of a rapid alternation between two adjacent notes, usually a semitone or tone apart, which can be identified with the context of the trill (compare mordent and tremolo). It is sometimes referred to by the German Triller, the Italian trillo, the French trille or the Spanish trino. A cadential trill is a trill associated with each cadence. A groppo or gruppo is a specific type of cadential trill which alternates with the auxiliary note directly above it and ends with a musical turn as additional ornamentation.
A trill provides rhythmic interest, melodic interest, andβthrough dissonanceβharmonic interest. Sometimes it is expected that the trill will end with a turn (by sounding the note below rather than the note above the principal note, immediately before the last sounding of the principal note), or some other variation. Such variations are often marked with a few appoggiaturas following the note bearing the trill indication.