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The Alto Saxophone and Alto Sax Transposition
Suppose the composer wants the sound coming out of the alto saxophone to be in the key of C. The composer needs to notate the music nine semitones higher (an interval of a major sixth) on the page—in the key of A. The alto sax player sees an A on the page, fingers the horn to play A, and out comes the sound of the note C, nine semitones lower—as the composer intended.
So, written music for the alto sax must be transposed up by an interval of a major sixth (all notes!), in order to sound the way the composer intended.
This all seems pretty odd, but it makes a lot of sense for wind players who read music. They don’t have to cope with learning new fingerings for each instrument in a family. Instead, it’s up to the composer or orchestrator to ensure that the music is transposed on the page properly for the intended instrument and the intended sound.
Some instruments are “octave transposing” instruments. The guitar, for instance. Notated music for the guitar is written an octave higher than it sounds when you play the music. When you play the note Middle C from the page, you still hear the note C, but it’s the C an octave below Middle C.