The trill (or shake, as it was known from the 16th until the 19th 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. 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 a cadence.
In the baroque period, a number of signs indicating specific patterns with which a trill should be begun or ended were used. In the Klavierbüchlein für Wilhelm Friedemann Bach, Johann Sebastian Bach lists a number of these signs together with the correct way to interpret them. Unless one of these specific signs is indicated, the details of how to play the trill are up to the performer. In general, however, trills in this period are executed beginning on the auxiliary note, before the written note, often producing the effect of a harmonic suspension which resolves to the principal note. But, if the note preceding the ornamented note is itself one scale degree above the principal note, then the dissonant note has already been stated, and the trill typically starts on the principal note.
Several trill symbols and techniques common in the Baroque and early Classical period have fallen entirely out of use, including for instance the brief Pralltriller, represented by a very brief wavy line, referred to by Carl Philipp Emanuel Bach in his Essay on the True Art of Playing Keyboard Instruments (Versuch) (1753–1762).
Beyond the baroque period, specific signs for ornamentation are very rare. Continuing through the time of Mozart, the default expectations for the interpretation of trills continued to be similar to those of the baroque. In music after the time of Mozart, the trill usually begins on the principal note.
All of these are only rules of thumb, and, together with the overall rate of the trill and whether that rate is constant or variable, can only be determined by considering the context in which the trill appears, and is usually to a large degree a matter of opinion with no single "right" way of executing the ornament.