Tempo rubato
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Tempo rubato (Italian stolen time) is a musical term for slightly speeding up or slowing down the tempo of a piece at the discretion of the soloist or the conductor. It was used frequently in music of the Romantic Period, and is especially common in piano music. It also requires the use of altering the relationships among the written note values and the played ones.
Rubato, even when not notated, is often used liberally by many singers for added musical effect by singing at a slightly different tempo than that of the accompaniment. Frédéric Chopin used a strict form of rubato in some of his pieces: the left hand was to be played at the exact tempo of the piece, while the right hand was to be played freely, with rubato. However it is more usual in modern performances for the accompaniment and melody to speed up and slow down at the same rate.
Franz Schubert and Alexander Scriabin also used rubato to bring emotion to their pieces.
For instance, if a piece of music had a quarter note followed by an eighth note, and the tempo was slowed down so the quarter note was as a sixteenth note tied to a quarter note, the eighth note would have to be sped up to a sixteenth note so as to make up for the lost time.
One perfect example of a piece including tempo rubato is Chopin's Heroic Polonaise.