Interval (music)

In music theory, an interval is the difference between two pitches. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

In Western music, intervals are most commonly differences between notes of a diatonic scale. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C♯ and D♭. Intervals can be arbitrarily small, and even imperceptible to the human ear.

In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio.

Interval (graph theory)

In graph theory, an interval I(h) in a directed graph is a maximal, single entry subgraph in which h is the only entry to I(h) and all closed paths in I(h) contain h. Intervals were described in 1976 by F. E. Allen and J. Cooke. Interval graphs are integral to some algorithms used in compilers, specifically data flow analyses.

The following algorithm finds all the intervals in a graph consisting of vertices N and the entry vertex n₀, and with the functions pred(n) and succ(n) which return the list of predecessors and successors of a given node n, respectively.

The algorithm effectively partitions the graph into its intervals.

Each interval can in turn be replaced with a single node, while all edges between nodes in different intervals in the original graph become edges between their corresponding nodes in the new graph. This new graph is called an interval derived graph. The process of creating derived graphs can be repeated until the resulting graph can't be reduced further. If the final graph consists of a single node, then the original graph is said to be reducible.

Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0 and 1, as well as all numbers between them. Other examples of intervals are the set of all real numbers , the set of all negative real numbers, and the empty set.

Real intervals play an important role in the theory of integration, because they are the simplest sets whose "size" or "measure" or "length" is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.

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 (short story)

"Music" is a short story by Russian American author Vladimir Nabokov originally published in Russian in 1932.

Summary

The story uses third-person narration and tells the story of Victor, a self-conscious man for whom "music he did not know... could be likened to the patter of a conversation in a strange tongue." When Victor arrives at a party, he finds the other guests listening with varying degrees of engagement to a man named Wolfe play the piano. As Victor does not know the song being played, he loses interest. He catches a glimpse of his ex-wife at the party, but cannot look at her. He laments the fact that now he must "start all over" the long task of forgetting her (in a flashback, it's revealed that she left him for another, who may or may not be at the party). Throughout the entire story, Victor views the music as a structure that has him encaged in an awkward situation with his ex-wife; it had seemed to him "a narrow dungeon" until it ends, thus giving his ex-wife the opportunity to leave, which she does. Victor then realizes that the music was not a dungeon, but actually "incredible bliss, a magic glass dome that had embraced and imprisoned him and her," and which allowed him to "breathe the same air as she." After she leaves, another party-goer comments to Victor that he looked immune to the music and that he didn't think such a thing possible. His own inanity is revealed when Victor asks him what was played and he cannot tell whether it was Beethoven's Kreutzer Sonata or Tekla Bądarzewska-Baranowska's rather easy piece, Maiden's Prayer.

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.