Harmony

Harmony is the use and study of pitch simultaneity, and therefore chords, actual or implied, in music. The study of harmony in Western Music may often refer to the study of harmonic progressions, the movement from one pitch simultaneity to another, and the structural principles that govern such progressions. In Western Art Music, harmony often refers to the "vertical" aspects of music, distinguished from ideas of melodic line, or the "horizontal" aspect. For this reason, considerations of counterpoint or polyphony are often distinguished from those of harmony, nevertheless contrapuntal writing of the common practice period of western music, is often conceived and defined in terms of underlying harmonic motion.

Origin of term, and history of use
The term harmony originates in the Greek harmonía, meaning "joint, agreement, concord". In Ancient Greek music, the term was used to define the combination of contrasted elements: a higher and lower note.

Historical rules of harmony
Some traditions of music performance, composition, and theory have specific rules of harmony. These rules are often held to be based on 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 strongly imply harmony with only one melodic line. Many pieces from the baroque period for solo string instruments, such as Bach's Sonatas and partitas for solo violin, convey subtle harmony through inference rather than full chordal structures; see below:



Types of harmony
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.

Other types of harmony are based upon the intervals used in constructing the chords used in that harmony. Most chords used in "western" music are based on "tertial" harmony, or chords built with the interval of thirds. In the chord C Major7, C-E is a major third; E-G is a minor third; and G to B is a major third. Other types of harmony consist of quartal harmony and quintal harmony.

Intervals
An interval is the relationship between two separate musical pitches. For example, in the common tune "Twinkle Twinkle Little Star", the first two notes (the first "twinkle") and the second two notes (the second "twinkle") are at the interval of one fifth. What this means is that if the first two notes were the pitch "C", the second two notes would be the pitch "G"--four scale notes, or seven chromatic notes (one fifth), above it.

Here is a table to common intervals:

To put it simply, the combination of notes to make intervals creates harmony. A chord is harmony, for example. In a C chord, there are three notes: C, E, and G. The note "C" is the root tone, with the notes "E" and "G" providing harmony.

In the musical scale, there are twelve pitches. Each pitch is referred to as a "degree" of the scale. In actuality, there are no names for each degree-there is no real "C" or "E-flat" or "A". Nature did not name the pitches. The only inherent quality that these degrees have is their harmonic relationship to each other. The names A, B, C, D, E, F, and G are intransigent. The intervals, however, are not. Here is an example:

As you can see there, no note always corresponds to a certain degree of the scale. The "root", or 1st-degree note, can be any of the 12 notes of the scale. All the other notes fall into place. So, when C is the root note, the fourth degree is F. But when D is the root note, the fourth degree is G. So while the note names are intransigent, the intervals are not in layman's terms: a "fourth" (four-step interval) is always a fourth, no matter what the root note is. The great power of this fact is that any song can be played or sung in any key-it will be the same song, as long as the intervals are kept the same.

Tensions
There are certain basic harmonies. A basic chord consists of three notes: the root, the third above the root, and the fifth above the root (which happens to be the minor third above the third above the root). So, in a C chord, the notes are C, E, and G. In an A-flat chord, the notes are Ab, C, and Eb. In many types of music, notably baroque and jazz, basic chords are often augmented with "tensions". A tension is a degree of the scale which, in a given key, hits a dissonant interval. For more on what that means, see the article on Consonance and dissonance. The most basic, common example of a tension is a "seventh" (actually a minor, or flat seventh)--so named because it is the seventh degree of the scale in a given key. While the actual degree is a flat seventh, the nomenclature is simply "seventh". So, in a C7 chord, the notes are C, E, G, and Bb. Other common dissonant tensions include ninths and elevenths. In jazz, chords can become very complex with several tensions.

Typically, a dissonant chord (chord with a tension) will "resolve" to a consonant chord.

Part harmonies
There are four basic "parts" in classical music-soprano, alto, tenor, and bass.

Note: there can be more than one example of those parts in a given song, and there are also more parts. These are just the basic ones.

The four parts combine to form a chord. Speaking in the most general, basic, quintessential terms, the parts function in this manner:

Bass - root note of chord (1st degree) Tenor and Alto - provide harmonies corresponding to the 3rd and 5th degrees of the scale; the Alto line usually sounds a third below the soprano Soprano - melody line; usually provides all tensions

Please note that that is the most impossibly basic and distilled example of 4-part harmony. There is a nearly infinite number of alternate harmonic permutations.