The second movement (Andante con moto) of Beethoven's Fifth Symphony begins serenely in A-flat major; then, almost without warning, it switches to a triumphant theme in C major. The modulation is swiftly and effortlessly done. So, how is it done? I've been studying the relevant part of the score to fathom out the trick. This is the passage:
(By the way, the horns and trumpets are in C; the clarinets are B-flat.) There appears to be two intermediate chords involved: A diminished seventh, followed by A-flat dominant seventh. So the harmonic progression appears to be:
A♭ – Adim7 – A♭7 – C
My question is: How is this progression represented in Roman-numeral notation?