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Harmony is the art of using pitch simultaneity (or chords, actual or implied) in music. It is sometimes referred to as the "vertical" aspect of music, with melody being the "horizontal" aspect. Very often, harmony is a result of several melodic lines or motifs being played at once, creating counterpoint and called polyphony.
The word harmony comes from the Greek ἁρμονία harmonía meaning "a fastening or join". The concept of harmony dates as far back as Pythagoras.
Harmony is based on harmonics and resonances. Notes may be considered to be in harmony with each other when some of the harmonics of each note, especially the louder harmonics (which are often the lower ones), share the same frequency (with a small margin of error). Some traditions of music performance, compositionA musical composition is a piece of original music designed for repeated performance (as opposed to strictly improvisational music, in which each performance is unique). The music may be preserved in memory, or through a written system of notation. Compos, and theoryMusic theory is a set of systems for analyzing, classifying, and composing music and the elements of music. Narrowly it may be defined as the description in words of elements of music, and the interrelationship between the notation of music and performanc have specific rules of harmony, typically amounting to a simplified description of harmonics and resonances, which will be more or less appropriate depending on the instrumentA musical instrument is a device that has been constructed or modified with the purpose of making music. In principle, anything that somehow produces sound can serve as a musical instrument, but the expression is reserved generally to items that have that(s) to which they are applied.
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 baroqueBaroque music is Western classical music from the Baroque era, after the Renaissance music era and before the Classical music era proper. This roughly covers the time period from Claudio Monteverdi (1567-1643) through Johann Sebastian Bach (1685-1750). period for solo string instrumentA string instrument (also "stringed instrument") is a musical instrument that produces sound by means of vibrating strings. In the Hornbostel-Sachs scheme of musical instrument classification, used in organology, they are called chordophones. Sound producs for example, in which chords are very rare, but which nonetheless convey a full sense of harmony.
For much of the history of western classical musicThis article is about the broad genre of classical music in the Western musical tradition. For the period of music in the 18th century see Classical music era, for articles on classical music of non-Western cultures, see: List of classical music tradition, including the common practice periodIn music the Common Practice Period is a long period in western musical history spanning from before the classical era proper to today, dated, on the outside, as 1600-1900. It is most commonly contrasted with contemporary music. Common practice music shar, the conventions and rules of harmony were strictly enforced, often by the controlling influence of the Roman Catholic ChurchThe Roman Catholic Church (often called simply the Catholic Church, but see Catholicism for other meanings of the term "Catholic Church") is a worldwide body of Christians in full communion with the Pope, the Bishop of Rome, and subscribing to the beliefs, while folk music and non-Western music also developed often widely different notions of harmony. Church music was controlled by the churches in the Baroque and Classical periods, and music which had harmonies considered too dissonant were frowned upon. However, there was a general trend from the classical period to the 20th century in western classical music for harmony to become more advanced, with composers breaking many of the conventions which were once considered "rules".
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 tonalite 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 subcordinate. Interval cycles create symmetrical harmonies, such as frequently in the music of Alban Berg, George Perle, Arnold Schoenberg, Bela Bartok, and Edgard Varese's Density 21.5.Together Tonality and Chord (music) contain much information on harmony.