Nota: I could write here about the circle of fifths and practical methods to transpose from any tonality to any other, but I think it’s beside the scope here. So the following concerns only playing a score written for instruments in C with an instrument in Bb. It’s complicated enough as it is.
Your clarinet being in Bb just means that, when you play what you (the clarinetist) call a C, a Bb (absolute, on the piano if you will) is heard. Your clarinet sounds two semitones lower than it is written.
Thus, if you want to play a piano C, you have to play a clarinet D,; if you want to play a piano E, you have to play a clarinet F#. The clef has nothing to do with it. If you want to play a part written for instrument in C, you have to read it as if the music were written two semitones above.
Now, in practice, that’s not how you should proceed, because your brain can’t keep up with adding two semitones to each note while reading the music at the same time.
But the “good” news is: you can read the piece as if the piece were written in another clef. If your piece is written with a treble clef, read it as if it were written in an third-line C clef1. If it is written with a bass clef, read it as if it were written with a second-line C clef1.2
But now, you still have an issue with alterations. Because there’s only one semitone between B (resp. E) and C (resp. F), if you want to play an piano B (resp. E), you’ve got to play a clarinet C# (resp. F#). Similarly, piano Bb means you play clarinet C natural, etc.
In your piece, each B is flat “by default” because of the key signature. But you read the piano Bb as clarinet C flat, so you have to mentally remove the (clarinet) Cb from the signature. Similarly, each E is natural by default, thus you have to play a clarinet F# each time. You need to mentally add a (clarinet) F# to your signature. The piece is in D minor which is (clarinet) E minor.
The only things remaining are accidentals. By applying the “two semitones higher”, you can deduce a simple rule: before (clarinet) C and F, accidentals are read as if one alteration higher. Flats become naturals, naturals become sharps, sharps become double sharps.
- Well, you might want to pay some attention to the octave.
- If you don’t know your C clefs (I know I don’t), well, just read it slowly until either you can or you remember the piece well enough that it is no longer a problem. In the long run, learning your clef is probably a good idea.