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Twice as fast.
Printed above the staff at the point where the doubled tempo begins, often straight after a slow introduction; it lasts until the next tempo word. The relation is to the beat just before it, so the reader must know which note value carries the beat.
A precise proportional instruction: the new beat moves twice as fast as the old, so a slow introduction turns into its fast main section with a built-in tempo relation. It is clearest when the notation keeps the same beat unit; if you change metre at the same moment, a note-value equation is safer. To halve the speed instead, use doppio valore or an equation.
Chopin, Piano Sonata No. 2 in B-flat minor, Op. 35, first movement, m. 5: “Doppio movimento”, ending the four-bar Grave introduction at sfp; editions differ over whether the exposition repeat returns here or to the Grave.
Doppio movimento is one of 1755 terms in the Gradus musical dictionary: the words, abbreviations and instrument names that appear in printed scores, plus the vocabulary composers use to talk about them.
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