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Re: GG: Beethoven's the Second Concerto

somebody asked what the musical definition of a cadenza is --

The word "cadenza" must be related to the word "cadence."  In tonal music,
the most basic cadence is from the chord based on the fifth note of the
scale (the dominant) to the chord based on the first note of the scale (the
tonic).  In a classical period concerto, near the end of a movement the
orchestra comes to a skidding halt on the fifth degree of the scale, usually
on a chord with notes a sixth and a fourth above the root note.

If we're in C major, it's

G in the bass, C and E above it.

After the soloists blabbers on for a few minutes, the cadenza always ends
with a trill over a chord composed of the same fifth degree in the bass, but
instead of a sixth and a fourth above it, the fifth and the third, so:

G in the bass, B and D above it.  This is your basic dominant chord.

This chord, with the soloist's magnificent trill over it, resolves in turn
to the home chord (the tonic), signalling closure.  The movement's "all over
but the shouting"... 

The entire cadenza, to theorists anyway, is just an elaborated cadence, an
extension of the idea that the 6-4 is resolving down to the 5-3.

To most listeners, though, the cadenza is a lot more than this -- it can be
the most entrancing part of the entire movement ... there is a certain drama
in the fact that the orchestra is silent, and the solo instrumentalist,
alone, can create an atmosphere that's very focused and intense.

The music of a cadenza is usually something like a rhapsodic,
improvisational development section based on the different themes and motifs
you heard earlier in the movement.  So it can, in a way, sum up the musical
ideas of the body of the movement.

I'm pretty sure cadenzas were originally improvised, and they frequently are
a moment of virtuosity for the soloist.  Some cadenzas go through an
incredible number of keys before settling down on that familiar trill over
the dominant chord.  At any event, after the trill is resolved to the tonic,
you still get 20 measures or so of straightforward music -- this is
psychologically necessary to balance the destabilizing meanderings of the
soloist's cadenza.

As a pianist, I've performed Mozart concertos with improvising cadenzas on
the spot, although I noticed it seemed to make conductors nervous.

Sometimes composers broke the formula of how the ending of the cadenza
worked.  What Beethoven does with the ending of the cadenza and the
concluding section of the first movement of the third concerto (in C minor)
is really magical.