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Most music we commonly hear consists not of just one melody, but rather several pitches typically occurring simultaneously. The term interval can describe not only the distance between any two pitches but also the resulting impression of consonance or dissonance. Since its development in Europe nearly a thousand years ago, the careful combination of melodies to control the sequence of consonance and dissonance has become known as harmony.
More complex combinations of more than two pitches can also be classified. One of the most important, called a triad, consists of three simultaneous pitches that form particular consonances with each other. Since at least the 16th century, most European harmony is based on triads, the ways in which the triads are related to the tonality, and the particular successions of triads, known as chord progressions or harmonic progressions.
Of course most music would not use exclusively consonances any more than a playwright would create a play with no conflict. Most harmonic progressions include dissonances which subsequently resolve to consonances. In the style of European Romanticism in music, especially towards the end of the 1800s, composers increasingly extended these dissonances to express intensity of emotions. Sometimes they would create dissonances with notes outside of the mode. As shown in the section on mode, such pitches are called chromatic and chromaticism describes music that makes great use of them. Chromatic harmony is often more dissonant and, when taken to extremes, this style is sometimes called Expressionism.
Of course, not all harmony has to be based on triads. Some composers in the twentieth century used dissonant harmony in an atonal context. Other composers used harmonies based on different intervals than those used in triads. Sometimes it makes more sense to discuss the harmonies of minimalist composers as "pitch sets" which may change very little over time.