| When your string vibrates, it doesn't just vibrate in one way, it also vibrates in halves, thirds quarters, fifths, all the way up the string. This is called the overtone series, and is fundamental to all vibrations. Practically, if you divide your strings into fractional parts, you can play harmonics in most of these places. When one note you play has an overtone that is also a part of the series in an open string, that sets up a sympathetic vibration in another string. This is similar to when a singer sings a tone that shatters a glass, sma e concept, only you are more productive doing this because it will make you play in tune. When those overtones line up, it makes the pitches sound in tune.
Further reading in Hindemith's book called the construction of music or something similar | 
