by Danlee Mitchell and Jack Logan, Ph.D.

The word harmony refers to (1) the procedure by which chords of music are constructed and (2) the system by which one chord follows another chord in time.
A chord may be defined as a combination of three or more different tones conceived as a related unit and sounding at the same moment in time or arpeggiated. An arpeggio is a rapid alternation of chord tones each occurring with one following the other in time.
Although harmony is non-existent in many world musics, it is found extensively in the music of the West where it has gained complexity with the passage of time. Harmony is said to give the effect of "depth" to a melodic line and forms the accompaniment material to melody in a homophonic texture.
Many world cultures employ only melody in their music. Western music began as a melodic music only. It was not until the Renaissance period that harmony was introduced as a basic element in the music of the West. As a basic element of music, harmony continued to evolve in complexity until the beginning of the 20th century in the West. Although harmony is not an effective conveyer of abstract "idea", it is a very powerful and efficient element that contributes to goal-oriented motion in music.
Chords exist in a scale-tonal infrastructure. Certain chords project a quality of instability and tension and are known as dissonant chords while other chords project a quality of stability and repose and are known as consonant chords. A series of successive chords in time is known as a chord progression.
Chords require at least three (3) different tones in their structure. A three-tone chord is a triad. Chords may contain as few as three tones and as many as seven or more. However, three- four- and five-tone chords are most common. A commonly structured four-tone chord is a and a commonly structured five-tone chord is a 9th chord. More elaborate chords are 11th chords (six-tone chords) and 13th chords (seven-tone chords).
One "property" of harmony is "vertical profile" which adds sonic "depth" to music. The effect of three or more different tones sounding at the same moment in time creates the sense of greater mass and intensity of sound as compared to the effect of the sound of a single note.
Chords are constructed from low to high tones. The lowest tone of a chord is known as the root and all other chord tones are built higher in pitch from this tone. Harmony occupies the sonic "space" below melody.
Another "property" of harmony is "harmonic saturation". Minor harmonic saturation occurs when a few chords occur in a passage of music while major harmonic saturation occurs when many chords occur in a musical passage. Low harmonic saturation creates a serene and calm emotional mood while high harmonic saturation creates a sense of great intensity and expectation.
Harmony functions as accompaniment to melody. One very important aspect of harmonic accompaniment is the bass line or lowest harmonic component. A bass line is composed primarily of chord tones and is written in a quasi-linear fashion much like the melody line. In this context the bass line becomes a line of counterpoint (a secondary horizontal line) to the more important upper melodic material.
Like melody, harmony is also constructed from the raw materials of scale tones and, as a result, has "scale infrastructure" and tonal attributes of the major-minor tonal system. A chord may be built on each scale degree (tone) of the equal-tempered scales of Western music. Each scale degree may serve as the root of a chord to be built on that particular scale degree. In Western harmonic practice chords are built by using alternating scale degrees above the lowest tone. In the design of Western scales the distance (interval) between alternating scale degrees is known as a third. The interval between adjacent scale degrees is known as a second. Therefore, Western harmony is built by ascending intervals of thirds and is known as tertian harmony.
In the scales of Western music there are seven different general interval distances (2nds, 3rds, 4ths, 5ths, 6ths, 7ths, octaves) and four different specific interval qualities - major, minor, diminished, augmented. There are two specific qualities of third intervals - major 3rd and minor 3rd, and, because of this, there are four different triad qualities - major, minor, diminished, augmented. Because of the two different third interval qualities, there are many different qualities of 7th, 9th, 11th, and 13th chords none of which will be discussed in this general survey.
The reader may see that the terms "major," "minor," "diminished," "augmented" have been given double-duty as specific interval quality and triad quality. The terms "major" and "minor" are actually given triple-duty because they serve also as mode names. The author apologizes for this hodge-podge of interchangeable and double-duty terms but the language of "common practice" Western music is a hodge-podge of words with multiple meanings and any efforts are unlikely to be successful changing this nomenclature.
Chord quality is closely connected to emotional "mood" in music. The "mood quality" of the four triad sizes might be described as: major equals confident, triumphant; minor equals somber, pensive; diminished equals tense, restless, introverted; augmented equals energetic, restless, extroverted. This type of musical "psycho-analysis" is very subjective and serves here only as a general guide to an introductory understanding of music.
Since there are seven basic tones per scale in the Western system, each tone of the scale may produce simple triads or more extended 7th, 9th, 11th or 13th chords. These chords collectively are known as extended harmony. When harmony first appeared in the music of the West during the Renaissance, it was of uniformly simpler triadic construction. Western harmony became more complex during the next 350 years and reached a high degree of sophistication by the beginning of the 20th century.
Of the collection of triads found on the various scale degrees (tones) of the major and minor mode, certain triads have a higher function than others. Harmony, like melody, is subject to the gravitational forces of the major-minor tonal system. The effect of certain triads in a scale is said to be "restful and stable". This condition of any chord, interval or tone in music is known as consonance. The effect of other triads is said to be "active and unstable". This condition of any chord, interval or tone in music is known as dissonance. When chords change from one to the next, the term progression is used. Stable (consonant) chords attract unstable (dissonant) chords. When a less-stable chord "progresses" toward a more-stable chord, the term resolution is used. The dissonance-consonance (unstable-stable) concept in the music of the West is quasi-subjective and is the result of five-hundred years of cultural conditioning.
As there are specific names and symbols for scale degrees as individual notes, so too are there names and symbols for the chords whose roots occur on these notes. Each chord is represented by a proper name and a Roman number as follows: