More nerdifying

So, okay, you have an electronic tuner in front of you and are trying to get your saxophone to play to the standardized A=440 Hz.  You play a stable note, like middle G (three fingers of left hand down, no octave key) and the tuner reads sharp.  You know this because the tuner's needle (whether a real needle or an LCD version of a needle) leans to the right from the center.  Your saxophone is sharp. 

To make the horn play in tune, you pull out the mouthpiece a bit.  This works because you have effectively lengthened the tube, and long tubes, generally speaking, play lower pitches.  (Think long Alp horns, or trombones.)  If your saxophone (or flute or clarinet or whatever) plays flat (below pitch, the needle reads to the left of center on the face of the tuner) you need to shorten the tube: push in the mouthpiece, headjoint (though flutes have a special head cork that can also be adjusted if it is severely out of tune), or barrel (clarinets).  Same process and concept behind brass instruments, but for trumpets and trombones and horns, the player pulls out or pushes in "tuning slides" that are located around the body of the instrument.

Now go play in tune.