By Matt Boynick

The combining of notes simultaneously, to produce chords, and their successive use to produce chord progressions.
Different eras of Western music (harmony is much more highly developed in Western music than in any other) have held different ideas as to what kinds of harmony are acceptable or good. In the Middle Ages, the concept of harmony concerns combinations of two notes. In the Renaissance, three-note harmony became the norm and the triad had become the main unit of harmony (a three-note chord built up in 3rds). This remained the basic element in Western harmony until the 20th century, even when harmony was composed in four parts or more. From the beginning of the Baroque era (circa 1600), harmony was widely understood as the chords with which a melody was accompanied (as the practice of basso continuo, or figured bass, implies). The study of harmony also dictates acceptable relationships between successive chords. For example, if one chord is a dissonance, that dissonance needs to be resolved in the next chord (even though that next chord may itself incorporate another dissonance). In triadic harmony, the root of each chord - not necessarily the same as its bass - is the note in that chord from which the other notes can be derived in a series of rising 3rds. Thus the triad C-E-G has C as its root; but it may be heard with E as the lowest note.
In medieval and early Renaissance music, even a full major triad was felt inappropriate for the last chord of a piece, which normally would embody the final note (in more than one octave) and the 5th above it. In the period 1600-1900, full triads are usual for concluding chords; but in the 20th century, composers have treated dissonance more freely and have not felt it necessary to resolve chords that in earlier eras would be considered dissonant. During the 19th century, much more chromatic alteration of notes was being used, particularly by Wagner, and in the early 20th the principles of triadic harmony were under attack: from such composers as Bart?k who (inspired by the folk music of the area from which he came) was constructing chords based on the interval of a 4th; by Schonberg, using first atonal and then 12-note methods of composition; and Stravinsky, who, though his music was predominantly tonal, left dissonances unresolved to tease the ear.
Harmony cannot be dissociated from the rhythmic aspects of music. In particular, the use of dissonance and consonance can generate, by the tensions it creates, a powerful forward momentum. Harmony can also provide punctuation marks in the form of cadences - simple, readily recognizable chord progressions that mark a natural end to a phrase in a stereotyped way. Harmony is sometimes seen as the 'opposite' to counterpoint, because it primarily operates vertically whereas counterpoint seems to operate horizontally. The two are not opposed: most contrapuntal writing, particularly of the 1600-1900 period, is governed by harmonic progression while, equally, harmony is concerned with the movement of individual voices.