I'm learning about transposing instruments, and now I'm looking at Dvorak's 9th symphony. In the second movement (Largo) I don't understand the key signature of the clarinet in A.
The first movement is written in E minor (1#) and the clarinet in A has two flats in its key signature (G minor). I know why this is the case: the clarinet in A transposes a minor third down (a written C sounds like an A). The key will thus shift three steps to the left in the circle of fifths.
But now the second movement. It's written in D flat major (5b) and the clarinet in A has three flats in its key signature (E flat major). Following the same logic as in the first movement, the clarinet in A should be written in E major (4#). Why is this not the case? Or am I doing something wrong?
I hope someone can help me out, thanks in advance!