Polytonality is the act of using more than two keys (or tonalities) at the same time, in the same piece of music. Bitonality, though often considered to be a part of polytonality, is the act of using only two keys at the same time. Both of these techniques create tension and ambiguity. A fully harmonized polytonality will sometimes add a sense of discomfort (though it doesn't necessarily have to). In fact, a polytonal song often ends with the dominant key in order to keep the song from feeling restless or unresolved.
Polytonality rose to popularity in early 20th century classical music. Though it had been used before in pieces such as Beethoven's Eroica Symphony, it wasn't until the early 20th century that composers began to really explore its possibilities. In some ways, polytonality hit its stride with Arnold Schoenberg, even though he didn't directly experiment with the form. After years of composing and pushing tonality to its limits, he decided to abandon the concept altogether. This created a concept called atonality. At the same time, Igor Stravinsky (who was also frustrated with the constraints of tonality) began experimenting with polytonality as a way to break through the tonal walls. These two concepts, polytonality and atonality, eventually unofficially banded together to form a musical movement based on the era's increasing irritation with strict musical rules. This movement brought polytonality to the fore and led many musicians to experiment with the idea.
The most well-known examples of polytonality are found in Stravinsky's ballet Petroushka (which is actually bitonality) and his piece The Rite of Spring. And while Stravinsky eventually went on to experiment with serialism, many other 20th century composers took his cue and used polytonality in their pieces. Charles Ives, for example, was one of the first to use fully harmonized bitonality in classical music; Darius Milhaud also used it frequently. Other notable composers involved with polytonality include Gustav Mahler and Phillip Glass.
