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").

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 (astronomy)

In the field of astronomy the term chord typically refers to a line crossing an object which is formed during an occultation event. By taking accurate measurements of the start and end times of the event, in conjunction with the known location of the observer and the object's orbit, the length of the chord can be determined giving an indication of the size of the occulting object. By combining observations made from several different locations, multiple chords crossing the occulting object can be determined giving a more accurate shape and size model. This technique of using multiple observers during the same event has been used to derive more sophisticated shape models for asteroids, whose shape can be highly irregular. A notable example of this occurred in 2002 when the asteroid 345 Tercidina underwent a stellar occultation of a very bright star as seen from Europe. During this event a team of at least 105 observers recorded 75 chords across the asteroid's surface allowing for a very accurate size and shape determination.

Chordal graph

In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have at most three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree. They are sometimes also called rigid circuit graphs or triangulated graphs.

Chordal graphs are a subset of the perfect graphs. They may be recognized in polynomial time, and several problems that are hard on other classes of graphs such as graph coloring may be solved in polynomial time when the input is chordal. The treewidth of an arbitrary graph may be characterized by the size of the cliques in the chordal graphs that contain it.

Perfect elimination and efficient recognition

Music

Music is an art form and cultural activity whose medium is sound and silence. The common elements of music are pitch (which governs melody and harmony), rhythm (and its associated concepts tempo, meter, and articulation), dynamics (loudness and softness), and the sonic qualities of timbre and texture (which are sometimes termed the "color" of a musical sound). Different styles or types of music may emphasize, de-emphasize or omit some of these elements. Music is performed with a vast range of instruments and with vocal techniques ranging from singing to rapping, and there are solely instrumental pieces, solely vocal pieces and pieces that combine singing and instruments. The word derives from Greek μουσική (mousike; "art of the Muses"). In its most general form, the activities describing music as an art form include the production of works of music (songs, tunes, symphonies, and so on), the criticism of music, the study of the history of music, and the aesthetic examination of music. Ancient Greek and Indian philosophers defined music as tones ordered horizontally as melodies and vertically as harmonies. Common sayings such as "the harmony of the spheres" and "it is music to my ears" point to the notion that music is often ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, saying, for example, "There is no noise, only sound."

Music (Erick Sermon and Marvin Gaye song)

"Music" is a 2001 hit single by Erick Sermon featuring archived vocals from Marvin Gaye.

The song was thought of by Sermon after buying a copy of Gaye's Midnight Love and the Sexual Healing Sessions album, which overlook some of the original album's earlier mixes. After listening to an outtake of Gaye's 1982 album track, "Turn On Some Music" (titled "I've Got My Music" in its initial version), Sermon decided to mix the vocals (done in a cappella) and add it into his own song. The result was similar to Natalie Cole's interpolation of her father, jazz great Nat "King" Cole's hit, "Unforgettable" revisioned as a duet. The hip hop and soul duet featuring the two veteran performers was released as the leading song of the soundtrack to the Martin Lawrence & Danny DeVito comedy, "What's the Worst That Could Happen?" The song became a runaway success rising to #2 on Billboard's R&B chart and was #1 on the rap charts. It also registered at #21 pop giving Sermon his highest-charted single on the pop charts as a solo artist and giving Gaye his first posthumous hit in 10 years following 1991's R&B-charted single, "My Last Chance" also bringing Gaye his 41st top 40 pop hit. There is also a version that's played on Adult R&B stations that removes Erick Sermon's rap verses. The song was featured in the 2011 Matthew McConaughey film The Lincoln Lawyer.

Musical Symbols (Unicode block)

Musical Symbols is a Unicode block containing characters for representing modern musical notation.

See also

References