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appears at the end of the development section as a transition to the recapitulation
The extended virtuosic section for a soloist in a concerto is called a cadenza.
look it up on google, improvisation like a Classical Concerto Cadenza
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cadenza
the cadenza in Beethoven's 3rd concerto in c minor was written out because he did not trust the piano soloists.
Almost never. The main exception is for a soloist during a cadenza in a concerto.
Tchaikovsky only wrote one violin concerto: Violin Concerto in D Major.
Barber Violin Concerto was created in 1988.
Adams Violin Concerto was created in 1995.
Brahms's violin concerto was written by Brahms. The clue is in its name: the 'Brahms' violin concerto.
The free solo passage without orchestral accompaniment in a concerto is called a cadenza.