(Musical) - A chord is a set of notes, usually played at the same time, that form a particular harmonic relationship with each other. The most basic chord is the triad.

Chords (in western music) are usually built by stacking thirds. This means that from the root of the chord, you add minor or major thirds (usually, depending on the scale). The triad is generally the root (first), third and fifth of a scale. So if you have C major - the notes of the scale are C D E F G A B, and to build a major triad you take the root (C) and add the third (E), and the fifth (G), which is also a third above E. For a more in depth discussion - read triad.

The triad can be extended by adding more thirds on top. For instance, if you take a C major triad (C, E, G) and add a B (a third above G), you have a major 7th chord (Cmaj7 or CM7), so called because the notes come from the C major scale. Similarly, if you take the A minor triad (A C E), and add a G, you get a minor 7th chord (Am7 or A-7).

Extensions to all the seventh chord can be created by adding more thirds. For example, adding a B to the above mentioned Am7 chord yields Am9 (B being the ninth of A). Adding a further D (a third above B) yields Am11, and adding an Fon top of that yields Am13.

The simplest way to see this is by looking at the A minor (natural) scale, and writing it in two octaves. Then thirds are seen as 'every other note':

A B C D E F G A B C D E F G. Thus, using any scale, you can easily build a triad, a seventh chord, and add tensions. Of course, not all tensions are available.

The chord of an arc is a straight line joining two points of the arc. A chord divides a circle into segments (qv. sector). The formula for the chord of an arc is:

c = 2r × sin(theta/2)

Where c is the chord length, r is the radius of the arc, and theta is the angle (from the centre of a circle described by the arc) between the two chord ends.

Prove it!

1. Draw a circle.
2. Draw two lines from the centre to the edge. Mark them r1 and r2.
3. Mark the angle between these lines theta.
4. Draw a line between the points where these lines meet the edge. Label it c.
5. Draw a line, perpendicular to c, and passing through the centre of the circle. Mark it b
6. We now note that the angles between b and c are right, so the triangle formed by b,r1 and half of c is right.
7. Pulling out our trigonometry (sin theta = o/a), we get sin (theta/2) = (c/2) / r1
8. Rearranging gives us (c/2) = r1 × sin (theta/2)
9. And leads us to c = 2r × sin(theta/2) QED

An interesting point we can find from this is the chord lengths of hexagons, which can be shown to be identical to the radius of the circle. This means that a hexagon can be drawn with only the aid of a straight edge and a pair of compasses.

Chord (?), n. [L chorda a gut, a string made of a gut, Gr. . In the sense of a string or small rope, in general, it is written cord. See Cord.]

1.

The string of a musical instrument.

Milton.

2. Mus.

A combination of tones simultaneously performed, producing more or less perfect harmony, as, the common chord.

3. Geom.

A right line uniting the extremities of the arc of a circle or curve.

4. Anat.

A cord. See Cord, n., 4.

5. Engin.

The upper or lower part of a truss, usually horizontal, resisting compression or tension.

Accidental, Common, and Vocal chords. See under Accidental, Common, and Vocal. -- Chord of an arch. See Illust. of Arch. -- Chord of curvature, a chord drawn from any point of a curve, in the circle of curvature for that point. -- Scale of chords. See Scale.

Chord, v. t. [imp. & p. p. Chorded; p. pr. & vb. n. Chording.]

To provide with musical chords or strings; to string; to tune.

When Jubal struck the chorded shell. Dryden.

Even the solitary old pine tree chords his harp. Beecher.

Chord, v. i. Mus.

To accord; to harmonize together; as, this note chords with that.

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