In music and musical composition, especially 20th century and later, interpolation is an abrupt change of elements, with (almost immediate) continuation of the first idea. Pieces which are cited as featuring interpolation, among other techniques, are Music for Brass Quintet by Gunther Schuller and Threnody: To the Victims of Hiroshima by Krzysztof Penderecki, both (1960–61).
This device is commonly used to extend what would normally be a regular phrase into an irregular and extended phrase.
Such expansion by interpolation is achieved by the addition of extra music in the middle of a phrase (commonly through the use of sequence). A clear example exists in the second movement of Mozart's Piano Sonata No. 10, K.330.
Formerly, in the sung portions of the Mass, such as the introit or kyrie, it was permissible, especially during the medieval period, to amplify a liturgical formula by interpolating a farse (from Medieval Latin farsa, forcemeat),[clarification needed] also called trope. This might consist of an explanatory phrase or verse, usually in the form of an addition or paraphrase, often in the vulgar language.
In the classical suite, consisting strictly of the allemande, courante, saraband and gigue, composers often interpolated a gavotte, bourrée, minuet, musette or passepied
Interpolation has been used by one artist to refer to the addition of new material in a performance or recording of a previously existing piece of music.
In rap music, interpolation refers to using a melody – or portions of a melody (often with modified lyrics) – from a previously recorded song, but re-recording the melody instead of sampling it.