First off, let me say that I'm new to playing music and any sort of music theory. I'm learning to play the B flat clarinet. I know that other instruments, such as the violin or flute, are in the key of C.
If I understand correctly, this means that when I play a C, it is actually a full step (C -> B -> Bb) off of the C from a violin. So why call it a C on the clarinet? Why not call it whatever it would be in the key of C, and call it a C instrument? What is the benefit of having it on a different key? Because then all C keyed music must be transposed (is that the right word?) to fit the clarinet.
I know that clarinet is not the only instrument that does this. I had always been under the impression that the note C was a sound at a specific frequency, and that all C's are at this same frequency, or a mathematically equivalent shift in the octave scale. This does not appear to be the case.
Furthermore, this means if I have a tuner that is in the key of C, that it won't actually show as C when I play C on my clarinet...
So, why have instruments in different "keys"? What is the benefit? And is it correct to say that a note of C does not actually imply a certain frequency of sound?