Interpolate is a formal word used to talk about interjecting or inserting something, especially words or a musical element. A critic might interpolate a comment into a conversation, or an artist may interpolate a melody or lyric from one song into another. In mathematical contexts, the word can also mean “to estimate values of data or a function between two known values,” or “to make insertions (as of estimated values).”
// She interpolated a highly critical comment into the discussion, which had been mostly positive to that point.
“But his reputation rested equally on his abilities as a composer and arranger for large ensembles, interpolating bebop's ... rhythms and extended improvisations into lush tapestries.” — Giovanni Russonello, The New York Times, 26 Jan. 2020
When Henry Cockeram put interpolate in his 1623 The English Dictionary; or, An Interpreter of Hard English Words he defined it in a way we no longer use: “to polish.” Cockeram’s definition ties the word very closely to its Latin root, polire, “to polish,” but the English word has a more direct source in Latin interpolare, meaning “to refurbish or alter,” or “to alter or corrupt something by inserting new or foreign matter.” This latter meaning persists in our English word today, though modern use of interpolate usually simply suggests the insertion of something into an existing text, work, etc., as in “she interpolated her own commentary into the report.” Musical elements can be interpolated too, as when an artist inserts a melody, lyric, etc., from one song into another without directly sampling. For example, the Beatles interpolated part of their early hit “She Loves You” into the closing moments of their later hit “All You Need Is Love.” In mathematical contexts, to interpolate is to estimate the values of data or a function between two known values.
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