Why are Bb and Eb instruments written in C?

The notation used for Bb and Eb instruments isn't C. It's simply using the standard musical notation with the appropriate key signature indicating the transposing difference. For instance, a Bb clarinet is written in the key of C, but with a key signature of two flats (Bb and Eb), which visually reflects the pitch adjustments needed. This convention allows musicians to read the same sheet music regardless of their instrument's transposition, and it's been established for centuries to facilitate ensemble playing. Transposition simplifies the music notation and ensures uniformity in a multi-instrument setting.