| The terminology I am using, Derived from Leonard Ratner at Stanford University, speaks
of the key modulated to from the exposition of the sonata-allegro as the
"second key area" usually V in the major key and III in the minor key.
Usually it is marked by a new subject, remember that the sonata-allegro form arises out
of the use of contrasts to signal these phases in the form, But the first major variant
on the form, not historically, but the easiest to understand, is that the second key is
prepared with the transition and yet there is no contesting theme.
The most famous example of this I know is the first movement of Mozart's Haffner
Symphony # 35 in D K 385. Mozart must have been so taken with the expository theme and
its possibilities to generate transitional and closing material that he decided not to
compose a second theme for the A-Major second key area. I think that there are other
examples of this in Haydn in String Quartets and Symphony. I will cite these as I come
across them.
Sonata Form: Added Coda Subject
Another easy to understand variant is the addition of a new theme in the coda of the
movement after the recapitulation and rhyme of the second key. The most famous example
I know is the finale of Beethoven's Fifth Symphony in C-Minor Op 67. There is another
example in the Last Movement of Mozart's D-Minor Piano Concerto # 20 K 466, but be
careful, that may be a composite Sonata-Rondo form, more on that later.
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