Interpolation in music refers to an abrupt change in musical elements from the main theme, Interpolation (also known as Replayed).
In classical music 
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 vernacular.
In popular music 
In hip hop music 
- Wittlich, Gary E. (ed.) (1975). Aspects of Twentieth-century Music, p.48 n.12 and p.49. Englewood Cliffs, N.J.: Prentice-Hall. ISBN 0-13-049346-5.
- William E. Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven, p. 255. ISBN 0-19-514399-X.
- Farse: Definition with Farse Pictures and Photos. Lexicus - Word Definitions for Puzzlers and Word Lovers.
- Catholic Encyclopedia: Trope. New Advent.
- James Montgomery, with additional reporting by Jem Aswad and Steven Roberts. Oct 3 2007 4:18 PM EDT. "Wu-Tang Clan's 'First-Ever Cleared Beatles Sample' Claim Is Incorrect", MTV News.
- Is Hip Hop Dead?, Mickey Hess, p.90, Praeger Publishers, 2007. ISBN 0-275-99461-9.
- Eric Grandy. October 4 at 11:08 AM. Line Out: "The Week in Samples", The Stranger.
- WhoSampled - a user-generated database of interpolations and samples in all types of music.