Some actually are written in concert pitch. A trombone, for example,is a Bb instrument but music for it is written in C, bass clef.

It normally has to do with the harmonic series of the instrument.

A great advantage to having transposing instruments can be easily shown with the saxophone family. A note is (almost always) fingered the same way on each type of sax. If it were otherwise, I would have to learn different fingerings for the alto versus the tenor sax. This would be a nightmare when switching off.

There's much more to it, of course, but that's a very brief overview.

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