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A chord in musical theory is three or more notes played simultaneously. Chords are named according to the notes of the scale that they contain.

The Triad

The most commonly used chords, that form the basis of western diatonic harmony are composed of triads: a root note, the third of a relevant scale, and the fifth. For example, an octave of the C major scale consists of the notes: C D E F G A B C.

http://meta.wikipedia.com/upload/c_maj.png Fig 1. The C major scale

The triad formed using the C note as the root would consist of C(root), E(third) and G(fifth), and these comprise a C major chord (the designation major denotes the fact that the E is four semitones (a major third) higher than the root note.

http://meta.wikipedia.com/upload/c_triad.png Fig 2. C, E and G - The C major triad

Using the same scale (and thus, implicitly, the key of C major) a chord may be constructed using the D as the root note. This would be D(root), F(third), A(fifth), which comprise the chord of D minor, since the third, F, is a minor third (three semitones) higher than the root.

Types of triads

As well as major and minor, there can also be augmented and diminished triads. Augmented triads are composed of a major 3rd but an augmented 5th (meaning the top note has been increased by one semitone.) Diminished triads have a minor 3rd and a diminished 5th (same as a minor triad, except the top note has been lowered by a semitone.) These rules summarise the type of triads encountered so far:

• Major triad: root, major 3rd, perfect 5th
• Minor triad: root, minor 3rd, perfect 5th
• Augmented triad: root, major 3rd, augmented 5th
• Diminished triad: root, minor 3rd, diminished 5th

Some chords constructed from the notes of the C major scale:

E G B -- E minor

F A C -- F major

G B D -- G major

A C E -- A minor

B D F -- B diminished

Naming

Triads are sometimes named using roman numerals after their position in the scale of the key of the piece. For example in the key of C major any triad with C as its root is named I. A triad beginning on a E (the third note of the scale of C major) would be named III etc... Written in lowercase next to the roman numeral of the triad is its particular inversion (a description of which notes have been moved up an octave.) A first inversion triad has an 'a' in its name (eg. the first inversion of chord V is Va.) A second inversion triad has a 'b', and a third inversion triad has a c.

Patterns with the type of chords found in major keys can be seen when using this naming scheme:

• In a major key, the major triads are: I, IV, V
• In a major key, the minor triads are: II, III, VI
• In a major key, the triad on VII is diminished

The dominant seventh

In geometry, a chord is a line segment whose endpoints both lie on a circle. The perpendicular bisector of any chord passes through the circle's center.