Classical concerto, modern cadenza
Concerto cadenzas may be written or improvised. Today, the performer of a classical concerto often plays standard cadenzas, composed in the style or transcribed from earlier performances. As we are going to see today, there are also more adventurous approaches.
Karlheinz Stockhausen wrote cadenzas for Mozart's clarinet concerto & flute concerto No. 1, and for Haydn's trumpet concerto. The recording is available: Stockhausen conducts Haydn & Mozart (with his own cadenzas).
Beethoven improvises for Mozart...
(details at the Beethoven Gateway)
For Harvard professor Robert Levin, himself an amazing improviser, a cadenza to a classical concerto is a real one only when it is improvised. And he is a master at re-creating the magic of improvisation within a given style.
The new cadenza: modern, composed & improvised, with live electronics, too!
The approach pianist Seda Röder took for Beethoven's Emperor concerto inherits from both the composer's and the improviser's ways. She collaborated with composer Edgar Barroso on a live electronic music set-up. She was then able to improvise a cadenza with this augmented piano. Here is the video:
More details on Seda Röder's blog post "Beethoven Now".
Many artists have played modern cadenzas to classical concertos. Chick Corea's Mozart Sessions come to mind. You might have a favorite I am not aware of. Don't hesitate to share in a comment!