Western music has a fixed pitch system referred to as concert pitch, which includes twelve pitches, over several octaves. By playing every note of an 88-key piano, you are in fact only playing twelve different pitches but in different octaves.
Sounds differ in pitch because of the vibration frequency given off, and this frequency is often governed by how thick or thin the material being played is. A thick guitar string, for example, gives off a lower frequency than a thin string, and therefore a lower sound is heard. The common note from which other notes are taken is the A above middle C, which has a frequency of 440 hertz. The A an octave below has a frequency of 220 hertz.
Using this as a benchmark, all other pitches give off a specific vibration frequency, which in turn can be programmed into a chromatic tuner. Therefore, the tuner is calibrated to recognize the exact frequency of all the pitches of Western music and will show what note is being played on the instrument and whether the instrument is giving off precisely the same frequency intended for the desired note.
Through this method of vibration frequency recognition, a chromatic tuner allows any tuned instrument to tune exactly to a predetermined system. This is so exact that, if used properly, two instruments can use different chromatic tuners and still play perfectly in tune together.