Why are some instruments, like the saxophone or trumpet, tuned differently from the piano or guitar?

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I play the alto saxophone and can never play the same music as the keyboard player or even the trumpet player in our band? When the keyboard plays in C I have to play in A. Why is that?

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I’ve seen the answer to this question right here: http://thebandleague.com/blog/?p=492
Basically it is because some instruments – mostly horns –  have a different “natural root” because of the length of the instrument (like a clarinet), or the length of the tubing (eg., trumpet). When you blow into them without pressing any keys or valves they make a sound having a pitch determined by this length. This is often called the “natural root” note of the instrument. This varies from instrument to instrument because they are different sizes (have longer or shorter tubes). So the sound waves come out at different frequencies.
It is much easier for the player of the instrument to make this root note the point of reference the major scales are built around. So, for example, the root note of the Alto Sax is Eb, but the player thinks of that as a C. When the sax man plays a “C”, it is the same note as an “A” on the piano. It is actually 9 semi-tones lower than the keyboard note.
To get them “playing on the same page”, so to speak, the music for the sax has to be written in the key of A. And what is a “C” on the keyboard is played as an “A” on the sax, 9 semi-tones higher.
Yes, this is confusing.

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