The word harmony comes from the Greek ἁρμονία harmonía meaning "a fastening or join". The concept of harmony dates as far back as Pythagoras.
Some traditions of music performance, composition, and theory have specific rules of harmony. These rules are often held to be based on a natural properties such as Pythagorean tuning's low whole number ratios ("harmoniousness" being inherent in the ratios either perceptually or in themselves) or harmonics and resonances ("harmoniousness" being inherent in the quality of sound), with the allowable pitches and harmonies gaining their beauty or simplicity from their closeness to those properties. Other traditions, such as the ban on parallel fifths, were simply matters of taste.
Although most harmony comes about as a result of two or more notes being sounded simultaneously, it is possible to create harmony with only one melodic line. There are many pieces from the baroque period for solo string instruments for example, in which chords are very rare, but which nonetheless convey a full sense of harmony.
For much of the common practice period of European classical music, there was a general trend for harmony to become more dissonant; chords considered daring in one generation become commonplace in the next.
Carl Dahlhaus (1990) distinguishes between coordinate and subordinate harmony. Subordinate harmony is the hierarchical tonality or tonal harmony well known today, while coordinate harmony is the older Medieval and Renaissance tonalité ancienne, "the term is meant to signify that sonorities are linked one after the other without giving rise to the impression of a goal-directed development. A first chord forms a "progression" with a second chord, and a second with a third. But the earlier chord progression is independent of the later one and vice versa." Coordinate harmony follows direct (adjacent) relationships rather than indirect as in subordinate. Interval cycles create symmetrical harmonies, such as frequently in the music of Alban Berg, George Perle, Arnold Schoenberg, Béla Bartók, and Edgard Varèse's Density 21.5.
Harmony may also be distinguished as centrifugal or centripetal harmony, harmony which leads away from or to the tonic, respectively. For example, music of the classical era is more often centrifugal, while the ragtime progression is centripetal. (van der Merwe 1989)
Music theory | Music history | Harmony
Harmonie | Harmonia | Harmonie | Harmonik | Armonía | Harmoniscienco | Harmonie | 화성 (음악) | Armonia (musica) | הרמוניה | Harmonieleer | 和声 | Harmonika (muzyka) | Harmonia | Harmony | Harmonija | Harmonia | Harmoni | 和声