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Recitative
A short piece in a style of singing that replicates speech (reciting), with rhythms dictated by the natural flow and stresses of speech (rather than dictated by meter or beat) and sparse accompaniment (so the singer has freedom to mimic speaking). Usually used to advance the plot and as introductions to arias.
Aria
The main pieces in operas and oratorios. During the Baroque period, a common format for an aria was ABA.
Choruses
Group songs in operas and oratorios. In any form, for any reason. (And in operas, sometimes for no reason!) They can be chorales or fugues or anything.