Firstly, I'll apologise in advance - I'm a self-taught rock 'musician' and I have virtually no knowledge of music theory (didn't stop me playing hundreds of gigs though!).
I have a four-string bass in standard tuning (EADG), and my girlfriend has a flugelhorn. I was trying to learn a piece of piano music on my bass, struggling to read sheet music. It's rather hard to play both the bass and the treble parts on a bass, so I asked my girlfriend to play the high part.
Playing the music as written, she appeared to be consistently a semitone lower. Perplexed, we tried getting her to play notes into a guitar tuner app on my phone, which suggested she was slightly sharper than a semitone lower than the note she thought she was playing.
I've read that the flugelhorn's fundamental pitch is B♭. Does this mean that what's written as a C in sheet music written for a flugelhorn is actually a B (ie a semitone lower than a C) for everyone else? Hence any music would need to be transposed a tone to be readable to her whilst in tune with everyone else? Is her flugelhorn just out of tune? Are all brass instruments built this way, or can you get flugelhorns/trumpets that are built with a fundamental pitch of C?