Transposing instrument
A transposing instrument is any of those instruments whose score notation is written at a different pitch to the actual “sound” of the instrument. The various members of the clarinet flute saxophone, horn families, trumpets and cornets, kettledrums, and the double bass are all considered “transposing instruments”.
It is so to allow a performer to play any of a particular family of instruments in the correct pitch without having to mentally transpose the written notes as he plays. A concert flute and an alto flute, for example, which are of different pitches, can be played using exactly the same fingering. The player of the alto flute, which is pitched a fourth below the standard concert flute, can play his instrument using notation that is written a fourth above the actual pitch of his instrument. He can play either instrument to a written score without having to think about it. It is up to the composer to get it right.