Basics
A chord may be built upon any note of a musical scale, therefore a seven-note scale allows seven basic chords, each degree of the scale becoming the "root" of its own chord. A chord built upon the note A is an A chord of some type (major/minor/diminished, etc.) The harmonic function of any particular chord depends on the context of the particular chord progression in which it is found. (See Diatonic function)
The diatonic harmonization of any major scale results in three major triads. They are based on the first, fourth, and fifth scale degrees (the tonic, subdominant and dominant – see three-chord song). These three triads include, and therefore can harmonize, every note of that scale.
The same scale also provides three relative minor chords, one related to each of the three major chords. These are based upon the sixth, second and third degrees of the major scale and stand in the same relationship to one another as do the three majors, so that they may be viewed as the first, fourth and fifth degrees of the relative minor key. Separate from these six common chords there is one degree of the scale, the seventh, that results in a diminished chord.
In addition, extra notes may be added to any chord. If these notes are also selected from the original scale the harmony remains diatonic. If new chromatic intervals are introduced then a change of scale or modulation occurs, which may bring the sense of a change of tonal center. This in turn may lead to a resolution back to the original key, so that the entire sequence of chords helps create an extended musical form.
Although all this allows for a large number of possible progressions (depending upon the length of the progression), in practice, progressions are often limited to a few bars' length and certain progressions are favored above others: there is a certain amount of fashion in this and a chord progression may even define an entire genre.
In western classical notation, chords built on the scale are numbered with Roman numerals. A D chord will be figured I in the key of D, for example, but IV in the key of A. Minor chords are signified by lower case Roman, so that D minor in the key of C would be written ii. Other forms of chord notation have been devised, from figured bass to the chord chart. These usually allow or even require a certain amount of improvisation.
Read more about this topic: Chord Progression