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• 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.
• In reference to aircraft, chord refers to the distance between the front and back of a wing, referred to as the leading and trailing edges, measured in the direction of the normal airflow. The term chord was selected due to the curved nature of the wings surface.
• In musical theory a chord is two or more pitches sounded simultaneously. Chords are named according to the notes of the scale that they contain.

The remainder of this article is about the musical chord.

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. These four are referred to collectively as the quality of the chord. For instance a triad built on top of a root D in the key of C would be said to have a minor quality.

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

Each note has a function within the chord, the note the chord is built on is called the root of the chord, the second note a third above it is called the third of the chord, and the third note a third above the second note is called the fifth of the chord. This is true of all triads, regardless of key, inversion, or quality. For example, in an F chord, F is always the root, A (sharp, natural or flat) is always the third, and C(sharp, natural, or flat) is always the fifth.

Tonal music relies upon a key to indicate the natural relationships between the major and minor chords that result from the natural diatonic relationships. For instance, in any major key, the quality of a chord built on the fifth note of the scale will be major. This is because of the constant relationship between the tonal intervals of major scale. Chords are notated by the scale degree of their root, although there are many different conventions for indicating the quality and inversion of the chord. For Example, since the first scale degree of the C major scale is the note C, a triad built on top of the note C would be called the one chord, which might be notated 1, I, or even C in which case the assumption would be made that the key signature of the particular piece of music in question would indicate to the musician what function a C major triad was playing, and that any special functioning of the chord outside of it's normal diatonic function would be inferred due to context.

Chords are also said to have a function in their diatonic scale, which relates to the expected resolution of each chord within a key. The strongest form of motion has root movement by fifth, which is the characteristic sound used as finality in most music of the baroque and classical periods, and is also exploited to modulate a piece of music into a different key. The chord function for a major scale is as follows:

• The I, III and VI chord are said to have a Tonic Function, due to the fact that they have a stable sound and do not have a tendency to resolve. When a chord progression resolves to a III or IV chord, it is called a Tonic Substitution, because the stable III or VI chord is being used as a substitute for the expected I chord.

• The VII and the V chord are said to have a Dominant Function, and they have a strong tendency to resolve to other chords. The five down a perfect fifth to the I chord and the VII chord up a minor second to the I chord, due to the expected resolution of the tritone, or the highly unstable diminished fifth which is present in a diatonic VII chord.

• The II and IV chord's have Subdominant Function, partially due to the fact that they are a fifth away from the Dominant chords of a key, and partially because in their own Tonic keys, their respective Dominant chords are built on the root notes of the stable Tonic function I and VI. They are also referred to as Dominant Preparation chords, and are used to approach a Dominant function chord. The progression IV-V-I, (subdominant, dominant, tonic) is by far the most common chord progression in all of music, and can be found in an astonishingly wide variety of styles, forms, and genres.

The spellings of the diatonic triads of the C major scale are given in the following table, along with their quality, name, and function"

I -- C E G -- major -- C major -- tonic

ii -- D F A -- minor -- D minor -- subdominant

iii -- E G B -- minor -- E minor -- tonic

IV -- F A C -- major -- F major -- subdominant

V -- G B D -- major -- G major -- dominant

vi -- A C E -- minor -- A minor -- tonic

vii dim-- B D F -- dim. -- B dim -- dominant

There is another type of chord function, Subdominant Minor, which is reserved for non-diatonic chords, or chords that do not occur naturally in the diatonic key, and will be dealt with separately under the heading Modal Interchange.

Inverted Triads

Triads are said to be inverted when a note other than the root is the lowest note played. There are three types of inversions, or positions, for triads.

• Root position is when the chord is played in ascending thirds with it's root note in the bass.

• First Inversion when the chord consists of a major or minor sixth and a major or minor third, and the third of the chord is in the bass

• Second Inversion when the chord consists of a perfect or, less common, augmented or diminished 4th, and a major or minor sixth, with the fifth of the chord in the bass.

Various compositional techniques in classical music have made use of inversion for a variety of interesting effects.

Naming and Chord Notation

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.

Possibly more common is the use of figured bass as a means of notating chord inversions, particularly in music from the baroque period. Figured bass uses a combination of Roman Numerals and Arabic Numerals to indicate the function of the chord (given by the roman numeral) and the chord's inversion (given by the arabic figured bass). For instance, a first inversion chord would have the designation 6/3 since there is a note a sixth and a third above the bass note. Common practice shortens this to just the 6 since it is the characteristic interval of the inversion.

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

Another common form of notation makes use of lower case roman numerals to denote minor chords, so the chords would be written I, ii, iii, IV, V, vi, vii dim.

There are a number of ways that a diminished chord can be notated, the most common being the use of a small superscript circle, or the abbreviation dim. being written next to the chord.

Also common is the use of a minus sign to indicate minor chords. Using this system, the triads of the major scale would be written: I, II-, III-, IV, V, VI-, and VII dim. The superscript circle is also occasionally used to indicate a diminished chord in this system.

Seventh Chords

The dominant seventh