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A cadenza left to the soloist’s invention.
Printed at a fermata, usually on a cadential six-four chord in a concerto, where the soloist improvises or chooses a cadenza; the orchestra waits and re-enters after the soloist’s closing trill or cadence. Ad libitum can also mean the cadenza may be left out.
Leaving the cadenza to the soloist was Classical practice; from Beethoven on, composers increasingly wrote their own. If you leave it open, end the preceding passage on a clear harmonic launching point and make the orchestra’s re-entry unmistakable. If you supply a cadenza but allow others, write yours out and mark it ad libitum.
Cadenza ad libitum 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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