Thecent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, to check intonation, or to compare the sizes of comparable intervals in different tuning systems. For humans, a single cent is too small to be perceived between successive notes.
Alexander John Ellis' paper On the Musical Scales of Various Nations,[1] published by the Journal of the Society of Arts in 1885, officially introduced the cent system to be used in exploring, by comparing and contrasting, musical scales of various nations. The cent system had already been defined in his History of Musical Pitch, where Ellis writes: "If we supposed that, between each pair of adjacent notes, forming an equal semitone [...], 99 other notes were interposed, making exactly equal intervals with each other, we should divide the octave into 1200 equal hundrecths [sic] of an equal semitone, or cents as they may be briefly called."[4]
Ellis defined the pitch of a musical note in his 1880 work History of Musical Pitch[5] to be "the number of double or complete vibrations, backwards and forwards, made in each second by a particle of air while the note is heard".[6] He later defined musical pitch to be "the pitch, or V [for "double vibrations"] of any named musical note which determines the pitch of all the other notes in a particular system of tunings."[7] He notes that these notes, when sounded in succession, form the scale of the instrument, and an interval between any two notes is measured by "the ratio of the smaller pitch number to the larger, or by the fraction formed by dividing the larger by the smaller".[8] Absolute and relative pitches were also defined based on these ratios.[8]
Ellis noted that "the object of the tuner is to make the interval [...] between any two notes answering to any two adjacent finger keys throughout the instrument precisely the same. The result is called equal temperament or tuning, and is the system at present used throughout Europe.[9] He further gives calculations to approximate the measure of a ratio in cents, adding that "it is, as a general rule, unnecessary to go beyond the nearest whole number of cents."[10]
Ellis presents applications of the cent system in this paper on musical scales of various nations, which include: (I. Heptatonic scales) Ancient Greece and Modern Europe,[11] Persia, Arabia, Syria and Scottish Highlands,[12] India,[13] Singapore,[14] Burmah[15] and Siam,;[16] (II. Pentatonic scales) South Pacific, [17] Western Africa,[18] Java,[19] China[20] and Japan.[21] And he reaches the conclusion that "the Musical Scale is not one, not 'natural,' nor even founded necessarily on the laws of the constitution of musical sound, so beautifully worked out by Helmholtz, but very diverse, very artificial, and very capricious".[22]
When listening to pitches with vibrato, there is evidence that humans perceive the mean frequency as the center of the pitch.[27] One study of modern performances of Schubert's Ave Maria found that vibrato span typically ranged between 34 cents and 123 cents with a mean of 71 cents and noted higher variation in Verdi's opera arias.[28]
Normal adults are able to recognize pitch differences of as small as 25 cents very reliably. Adults with amusia, however, have trouble recognizing differences of less than 100 cents and sometimes have trouble with these or larger intervals.[29]
The representation of musical intervals by logarithms is almost as old as logarithms themselves. Logarithms had been invented by Lord Napier in 1614.[30] As early as 1647, Juan Caramuel y Lobkowitz (1606-1682) in a letter to Athanasius Kircher described the usage of base-2 logarithms in music.[31] In this base, the octave is represented by 1, the semitone by 1/12, etc.
Joseph Sauveur, in his Principes d'acoustique et de musique of 1701, proposed the usage of base-10 logarithms, probably because tables were available. He made use of logarithms computed with three decimals. The base-10 logarithm of 2 is equal to approximately 0.301, which Sauveur multiplies by 1000 to obtain 301 units in the octave. In order to work on more manageable units, he suggests to take 7/301 to obtain units of 1/43 octave.[b] The octave therefore is divided in 43 parts, named "merides", themselves divided in 7 parts, the "heptamerides". Sauveur also imagined the possibility to further divide each heptameride in 10, but does not really make use of such microscopic units.[32]
Flix Savart (1791-1841) took over Sauveur's system, without limiting the number of decimals of the logarithm of 2, so that the value of his unit varies according to sources. With five decimals, the base-10 logarithm of 2 is 0.30103, giving 301.03 savarts in the octave.[33] This value often is rounded to 1/301 or to 1/300 octave.[34][35]
Early in the 19th century, Gaspard de Prony proposed a logarithmic unit of base 2 12 \displaystyle \sqrt[12]2 , where the unit corresponds to a semitone in equal temperament.[36] Alexander John Ellis in 1880 describes a large number of pitch standards that he noted or calculated, indicating in pronys with two decimals, i.e. with a precision to the 1/100 of a semitone,[37] the interval that separated them from a theoretical pitch of 370 Hz, taken as point of reference.[38]
The following audio files play various intervals. In each case the first note played is middle C. The next note is sharper than C by the assigned value in cents. Finally, the two notes are played simultaneously.
Curtis James Jackson III (born July 6, 1975),[3] known professionally as 50 Cent,[n 1] is an American rapper, actor, television producer, and businessman. Born in South Jamaica, a neighborhood of Queens, Jackson began pursuing a musical career in 1996. In 1999-2000, he recorded his "debut" album Power of the Dollar for Columbia Records; however, he was struck by nine bullets during a shooting in May 2000, causing its release to be cancelled and Jackson to be dropped from the label. His 2002 mixtape, Guess Who's Back? was discovered by Detroit rapper Eminem, who signed Jackson to his label Shady Records, an imprint of Dr. Dre's Aftermath Entertainment and Interscope Records that same year.[5][6]
Jackson has sold over 30 million albums worldwide and won several awards, including a Grammy Award, a Primetime Emmy Award, thirteen Billboard Music Awards, six World Music Awards, three American Music Awards and four BET Awards.[8] In his acting career, Jackson first starred in the semi-autobiographical film Get Rich or Die Tryin' (2005), which was critically panned. He was also cast in the war film Home of the Brave (2006), and the crime thriller Righteous Kill (2008). Billboard ranked Jackson as 17th on their "50 Greatest Rappers" list in 2023,[9] and named him the sixth top artist of the 2000s decade.[10] Rolling Stone ranked Get Rich or Die Tryin' and "In da Club" in its lists of the "100 Best Albums of the 2000s" and "100 Best Songs of the 2000s" at numbers 37 and 13, respectively.[11][12]
Jackson was born in the borough of Queens, New York City, and raised in its South Jamaica neighborhood[3] by his mother Sabrina. Sabrina, a drug dealer, raised Jackson until she died in a fire when Jackson was eight years old.[13][14] Jackson revealed in an interview that his mother was a lesbian.[15][16] After his mother's death and his father's departure, Jackson was raised by his grandparents.[17]
He began boxing at about age 11, and when he was 14, a neighbor opened a boxing gym for local youth. "When I wasn't killing time in school, I was sparring in the gym or selling crack on the strip," Jackson remembered.[18] He sold crack during primary school.[19] "I was competitive in the ring and hip-hop is competitive too ... I think rappers condition themselves like boxers, so they all kind of feel like they're the champ."[20]
At age 12, Jackson began dealing narcotics when his grandparents thought he was in after-school programs,[21] and brought guns and drug money to school. In the tenth grade, he was caught by metal detectors at Andrew Jackson High School: "I was embarrassed that I got arrested like that ... After I got arrested I stopped hiding it. I was telling my grandmother [openly], 'I sell drugs.'"[22]
On June 29, 1994, Jackson was arrested for selling four vials of cocaine to an undercover police officer. He was arrested again three weeks later, when police searched his home and found heroin, ten ounces of crack cocaine, and a starting pistol. Although Jackson was sentenced to three to nine years in prison, he served six months in a boot camp and earned his GED. He has said that he did not use cocaine himself.[17][23][24] Jackson adopted the nickname "50 Cent" as a metaphor for change.[25] The name was inspired by Kelvin Martin, a 1980s Brooklyn robber known as "50 Cent"; Jackson chose it "because it says everything I want it to say. I'm the same kind of person 50 Cent was. I provide for myself by any means."[26]
Jackson began rapping in a friend's basement, where he used turntables to record over instrumentals.[27] In 1996, a friend introduced him to Jam Master Jay of Run-DMC, who was establishing Jam Master Jay Records. Jay taught him how to count bars, write choruses, structure songs, and make records.[28][29] Jackson's first appearance was on "React" with Onyx, for their 1998 album Shut 'Em Down. He credited Jam Master Jay for improving his ability to write hooks,[20] and Jay produced Jackson's first (unreleased) album.[14] In 1999, after Jackson left Jam Master Jay, the platinum-selling producers Trackmasters signed him to Columbia Records. They sent him to an upstate New York studio, where he produced 36 songs in two weeks;[13] 18 were included on his 2000 album, Power of the Dollar.[30] Jackson founded Hollow Point Entertainment with former G-Unit member Bang 'Em Smurf.[31][32]
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