Chord

Chord may refer to:

Chord (geometry)

A chord of a circle is a straight line segment whose endpoints both lie on the circle. A secant line, or just secant, is the infinite line extension of a chord. More generally, a chord is a line segment joining two points on any curve, for instance an ellipse. A chord that passes through a circle's center point is the circle's diameter.

Chords of a circle

Among properties of chords of a circle are the following:

The area that a circular chord "cuts off" is called a circular segment.

Chord is from the Latin chorda meaning bowstring.

Chords of an ellipse

The midpoints of a set of parallel chords of an ellipse are collinear.

Chords in trigonometry

Chords were used extensively in the early development of trigonometry. The first known trigonometric table, compiled by Hipparchus, tabulated the value of the chord function for every 7.5 degrees. In the second century AD, Ptolemy of Alexandria compiled a more extensive table of chords in his book on astronomy, giving the value of the chord for angles ranging from 1/2 degree to 180 degrees by increments of half a degree. The circle was of diameter 120, and the chord lengths are accurate to two base-60 digits after the integer part.

Chord (music)

A chord, in music, is any harmonic set of three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords (these involve the notes of the chord played one after the other, rather than at the same time) may, for many practical and theoretical purposes, constitute chords. Chords and sequences of chords are frequently used in modern Western, West African and Oceanian music, whereas they are absent from the music of many other parts of the world.

In tonal Western classical music, the most frequently encountered chords are triads, so called because they consist of three distinct notes: the root note, a third above the root and a fifth interval above the root. Further notes may be added to give tetrads such as seventh chords (the most commonly encountered example being the dominant seventh chord) and added tone chords, as well as extended chords and tone clusters. Triads commonly found in the Western classical tradition are major and minor chords, with augmented and diminished chords appearing less often. The descriptions major, minor, augmented, and diminished are referred to collectively as chordal quality. Chords are also commonly classified by their root note—for instance, a C major triad consists of the pitch classes C, E, and G. A chord retains its identity if the notes are stacked in a different way vertically; however, if a chord has a note other than the root note as the lowest note, the chord is said to be in an inversion (this is also called an "inverted chord").