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File:Pitch class on C.png

All Cs possible on a piano (except C₈, available on grand)  Play (help·info).

In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position."^[1] Thus, using scientific pitch notation, the pitch class "C" is the set

{C_n : n is an integer} = {..., C_-2, C_-1, C₀, C₁, C₂, C₃ ...};

although there is no formal limit to this sequence on either end, only a limited number of these pitches will actually be audible to the human ear. Pitch class is important because human pitch-perception is periodic: pitches belonging to the same pitch class are perceived as having a similar "quality" or "color", a property called octave equivalence.

Psychologists refer to the quality of a pitch as its "chroma". A "chroma" is an attribute of pitches, just like hue is an attribute of color. A "pitch class" is a set of all pitches sharing the same chroma, just like "the set of all white things" is the collection of all white objects.^{[citation needed]}

Note that in standard Western equal temperament, distinct spellings can refer to the same sounding object: B♯₃, C₄, and D₄ all refer to the same pitch, hence share the same chroma, and therefore belong to the same pitch class; a phenomenon called enharmonic equivalence.

Integer notation[link]

To avoid the problem of enharmonic spellings, theorists typically represent pitch classes using numbers beginning from zero, with each successively larger integer representing a pitch class a semitone higher than the preceding one. Because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero. This cyclical system is referred to as modular arithmetic and, in the usual case of chromatic twelve-tone scales, pitch-class numbering is regarded as "mod 12"—that is, the twelfth member is identical to the first. One can map a pitch's fundamental frequency Failed to parse (Missing texvc executable; please see math/README to configure.): f

(measured in hertz) to a real number Failed to parse (Missing texvc executable; please see math/README to configure.):  p 
using the equation

Failed to parse (Missing texvc executable; please see math/README to configure.): p = 69 + 12\log_2 {(f/440)}

This creates a linear pitch space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C is assigned the number 60. Indeed, the mapping from pitch to real numbers defined in this manner forms the basis of the MIDI Tuning Standard, which uses the real numbers from 0 to 127 to represent the pitches C_-1 to G₉. To represent pitch classes, we need to identify or "glue together" all pitches belonging to the same pitch class—i.e. all numbers p and p + 12. The result is a circular quotient space that musicians call pitch class space and mathematicians call R/12Z. Points in this space can be labelled using real numbers in the range 0 ≤ x < 12. These numbers provide numerical alternatives to the letter names of elementary music theory:

0 = C, 1 = C♯/D♭, 2 = D, 2.5 = "D quarter tone sharp", 3 = D♯/E♭,

and so on. In this system, pitch classes represented by integers are classes of twelve-tone equal temperament (assuming standard concert A).

To avoid confusing 10 with 1 and 0, some theorists assign pitch classes 10 and 11 the letters "t" (after "ten") and "e" (after "eleven"), respectively (or A and B, as in the writings of Allen Forte and Robert Morris).

Integer notation.

In music, integer notation is the translation of pitch classes and/or interval classes into whole numbers.^[2] Thus C=0, C#=1 ... A#=10, B=11, with "10" and "11" substituted by "t" and "e" in some sources.^[2] This allows the most economical presentation of information regarding post-tonal materials.^[2]

In the integer model of pitch, all pitch classes and intervals between pitch classes are designated using the numbers 0 through 11. It is not used to notate music for performance, but is a common analytical and compositional tool when working with chromatic music, including twelve tone, serial, or otherwise atonal music.

Pitch classes can be notated in this way by assigning the number 0 to some note—C natural by convention^{[citation needed]}—and assigning consecutive integers to consecutive semitones; so if 0 is C natural, 1 is C sharp, 2 is D natural and so on up to 11, which is B natural. The C above this is not 12, but 0 again (12-12=0). Thus arithmetic modulo 12 is used to represent octave equivalence. One advantage of this system is that it ignores the "spelling" of notes (B sharp, C natural and D double-flat are all 0) according to their diatonic functionality.

There are a few disadvantages with integer notation. First, theorists have traditionally used the same integers to indicate elements of different tuning systems. Thus, the numbers 0, 1, 2, ... 5, are used to notate pitch classes in 6-tone equal temperament. This means that the meaning of a given integer changes with the underlying tuning system: "1" can refer to C♯ in 12-tone equal temperament, but D in 6-tone equal temperament.

Also, the same numbers are used to represent both pitches and intervals. For example, the number 4 serves both as a label for the pitch class E (if C=0) and as a label for the distance between the pitch classes D and F♯. (In much the same way, the term "10 degrees" can function as a label both for a temperature, and for the distance between two temperatures.) Only one of these labelings is sensitive to the (arbitrary) choice of pitch class 0. For example, if one makes a different choice about which pitch class is labeled 0, then the pitch class E will no longer be labelled "4." However, the distance between D and F♯ will still be assigned the number 4. The late music theorist David Lewin was particularly sensitive to the confusions that this can cause^{[example needed]}, and both this and the above may be viewed as disadvantages.

Other ways to label pitch classes[link]

Pitch class

Pitch class	Tonal counterparts
0	C (also B♯, D)
1	C♯, D♭ (also B)
2	D (also C, E)
3	D♯, E♭ (also F)
4	E (also D, F♭)
5	F (also E♯, G)
6	F♯, G♭ (also E)
7	G (also F, A)
8	G♯, A♭
9	A (also G, B)
10, t or A	A♯, B♭ (also C)
11, e or B	B (also A, C♭)

The system described above is flexible enough to describe any pitch class in any tuning system: for example, one can use the numbers {0, 2.4, 4.8, 7.2, 9.6} to refer to the five-tone scale that divides the octave evenly. However, in some contexts, it is convenient to use alternative labeling systems. For example, in just intonation, we may express pitches in terms of positive rational numbers p/q, expressed by reference to a 1 (often written "1/1"), which represents a fixed pitch. If a and b are two positive rational numbers, they belong to the same pitch class if and only if

Failed to parse (Missing texvc executable; please see math/README to configure.): a/b = 2^n\,

for some integer n. Therefore, we can represent pitch classes in this system using ratios p/q where neither p nor q is divisible by 2, that is, as ratios of odd integers. Alternatively, we can represent just intonation pitch classes by reducing to the octave, Failed to parse (Missing texvc executable; please see math/README to configure.): 1 \le p/q < 2 .

It is also very common to label pitch classes with reference to some scale. For example, one can label the pitch classes of n-tone equal temperament using the integers 0 to n-1. In much the same way, one could label the pitch classes of the C major scale, C-D-E-F-G-A-B using the numbers from 0 to 6. This system has two advantages over the continuous labeling system described above. First, it eliminates any suggestion that there is something natural about a 12-fold division of the octave. Second, it avoids pitch-class universes with unwieldy decimal expansions when considered relative to 12; for example, in the continuous system, the pitch-classes of 19-tet are labeled 0.63158..., 1.26316..., etc. Labeling these pitch classes {0, 1, 2, 3 ..., 18} simplifies the arithmetic used in pitch-class set manipulations.

The disadvantage of the scale-based system is that it assigns an infinite number of different names to chords that sound identical. For example, in twelve-tone equal-temperament the C major triad is notated {0, 4, 7}. In twenty-four-tone equal-temperament, this same triad is labeled {0, 8, 14}. Moreover, the scale-based system appears to suggest that different tuning systems use steps of the same size ("1") but have octaves of differing size ("12" in 12-tone equal-temperament, "19" in 19-tone equal temperament, and so on), whereas in fact the opposite is true: different tuning systems divide the same octave into different-sized steps.

In general, it is often more useful to use the traditional integer system when one is working within a single temperament; when one is comparing chords in different temperaments, the continuous system can be more useful.

See also[link]

• Pitch circularity
• Pitch interval
• Tone row

Sources[link]

Further reading[link]

• Purwins, Hendrik (2005). "Profiles of Pitch Classes: Circularity of Relative Pitch and Key—Experiments, Models, Computational Music Analysis, and Perspectives". Ph.D. Thesis. Berlin: Technische Universität Berlin.
• Rahn, John (1980). Basic Atonal Theory. New York: Longman; London and Toronto: Prentice Hall International. ISBN 0-02-873160-3. Reprinted 1987, New York: Schirmer Books; London: Collier Macmillan.
• Schuijer, Michiel (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts. Eastman Studies in Music 60. Rochester, NY: University of Rochester Press. ISBN 978-1-58046-270-9.

This biographical article needs additional citations for verification. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately, especially if potentially libelous or harmful. (July 2009)

Cal Thomas.

John Calvin "Cal" Thomas^[1] (born 1942) is an American syndicated columnist, pundit, author and radio commentator.

Life and career[link]

Thomas was born in 1942 in Washington, D.C.. He attended the American University for his undergraduate education. During the 1960s and early 1970s he worked as a reporter at NBC News. His column, which began in 1984, is syndicated by Tribune Media Services.^[2] Thomas joined Fox News as a political contributor in 1997. He is a panelist on Fox News Watch, a Fox News Channel program criticizing the media, and until September 2005 hosted After Hours with Cal Thomas on the same network. He also gives a daily radio commentary, which is heard on more than 300 stations.

Thomas has written extensively about political issues and he supports, among other things, many American positions related to Israel.

He has written 10 books, including Blinded By Might, that discussed, among other things, the role of the Moral Majority in American politics of the 1980s. Thomas was vice president of the Moral Majority from 1980 to 1985. He is an evangelical Christian.

A study at Hamilton College indicated Thomas as the least accurate prognosticator among 26 notable pundits.^[3]

Criticism of Dutch government policy[link]

In 2004, Cal Thomas was the target of a Google bomb attack, where the phrase "ignorant asshole" was linked to his website.^[4] This Googlebomb was triggered by a segment on his After Hours show regarding the Netherlands' policy on euthanasia. It soon became an attack on the Netherlands' drug policy, prostitution, and the nation's immigration policy. In a follow-up, Thomas rejoined "Thanks to our Dutch viewers for watching and for caring enough to write. Keep watching. Maybe you'll see some things you do like."

Criticism of Islam[link]

In his article "Mumbai Explained", published in the Chicago Tribune, Thomas writes that "no new [Mosques] should be built" in Western countries following the Mumbai terrorist attacks. He further claimed that Muslim immigration posed a danger to the UK and United States.^[5]

Criticism of homosexuality[link]

After Bill Clinton became the first sitting United States president to address a gay rights organization, the Human Rights Campaign,^[6] Thomas published a column^[7] in November 1997 opposing homosexuality, in which he said:

God designed norms for behavior that are in our best interests. When we act outside those norms—such as for premarital sex, adultery, or homosexual sex—we cause physical, emotional, and spiritual damage to ourselves and to our wider culture. The unpleasant consequences of divorce and sexually transmitted diseases are not the result of intolerant bigots seeking to denigrate others. They are the result of violating God's standards, which were made for our benefit.

— Cal Thomas, Immutable Morals

Thomas published a similar column^[8] on October 16, 2009, after Barack Obama became the second sitting United States president to address the Human Rights Campaign.^[6] Thomas said:

We will get more of what we tolerate. Sexual behavior is an important cultural and moral issue. Mr. Obama won the election with just 52 percent of the popular vote and a margin of 7 percent over Sen. John McCain. This should not be seen as a mandate for him and his administration to make over America in a secular and liberal image. Neither should it be seen as an invitation to give blanket approval to homosexuality, considered by some to be against the best interests of the people who practice it as well as the nations that accept it.

— Cal Thomas, Don't Ask, Tell or Legitimize

Bibliography[link]

• 2008, "Mumbai Explained" Cal Thomas Chicago Tribune/Daily Yomiuri
• 2007, Common Ground: How to Stop the Partisan War That Is Destroying America with Bob Beckel (ISBN 978-0-06-123634-1)
• 2001, The Wit & Wisdom of Cal Thomas (ISBN 1-58660-299-3)
• 1999, Blinded by Might with Ed Dobson (ISBN 0-310-22650-3)
• 1994, The Things That Matter Most (ISBN 0-06-017083-2)
• 1988, The Death of Ethics in America (ISBN 0-8499-0638-5)

See also[link]

Biography portal

• List of newspaper columnists

References[link]

External links[link]

• Cal Thomas Website
• Cal Thomas at Townhall.com
• Cal Thomas at the Internet Movie Database Retrieved on 2008-01-17
• Booknotes interview with Thomas on The Things That Matter Most, July 10, 1994.

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Adam Levine
Levine during a press conference in Singapore in 2011
Background information
Birth name	Adam Noah Levine
Born	(1979-03-18) March 18, 1979 (age 33) Los Angeles, California, U.S.
Genres	Alternative rock, funk rock, pop rock, soul, rhythm and blues
Occupations	Musician, singer-songwriter
Instruments	Vocals, guitar, bass, piano
Years active	1994–present
Labels	A&M Octone
Associated acts	Maroon 5, Kara's Flowers, Kanye West, Wiz Khalifa, Natasha Bedingfield, Ying Yang Twins, Alicia Keys, K'naan, Rihanna, Slash, Gym Class Heroes, Christina Aguilera
Website	www.maroon5.com

Adam Noah Levine^[1] (born March 18, 1979) is an American singer-songwriter and musician, best known as the front man and guitarist for the pop rock band Maroon 5. He is also a coach on the American talent show The Voice.

Early life[link]

Levine was born in Los Angeles to Fred and Patsy (née Noah) Levine. His uncle is journalist and author Timothy Noah.^[2] He has a brother, Michael, and a sister, Julia.^[3] When he was six years old, he made the winning shot of his local YMCA championship basketball game (on a team his father coached) with no time left on the clock. He has said that the incident changed his life and gave him the confidence to be successful.^[4][5]

Levine attended French Woods Festival of the Performing Arts Camp (Hancock, NY) with best friend Jesse Carmichael, guitar player of the band known at that time as Kara's Flowers. He graduated from Brentwood School in 1997.

Levine has Jewish ancestry on both sides of his family (his father and maternal grandfather were Jewish), and considers himself Jewish, though according to The Jewish Chronicle, who interviewed Levine, he "has rejected formal religious practice for a more generalized, spiritual way of life". He chose not to have a Bar Mitzvah as a child.^[6]

Original band Kara's Flowers[link]

Having met at Brentwood School in Los Angeles, the band released their first album titled The Fourth World in 1997 as high school seniors. That same year the band appeared on an episode of Beverly Hills, 90210. The album had little success, and its only single, "Soap Disco", failed commercially. Disappointed with the results of their album, the band members went their separate ways.^[7]

Levine and Carmichael left Los Angeles for New York. This was the first time the two Los Angeles natives were exposed to a completely different music scene, a cultural awakening for the young men.^[8] On MTV News, in 2002, Levine said, "That's when I started waking up to the whole hip hop, R&B thing. We had friends named Chaos and shit. It was not Brentwood High."^[9]

Maroon 5 and mainstream success[link]

During this time, Levine worked a two-week stint as a waiter at Johnny Rockets.^[10] After dropping out of Five Towns College, Levine and Jesse reunited with Mickey and Ryan, but added former Square guitarist, James Valentine in 2001. Renaming the band Maroon 5, Levine and his friends began to compile all of their newfound musical influences into their music. While Levine was working as a writer's assistant on the television show "Judging Amy," he spent time writing the lyrics about his ex-girlfriend, Jane. Those lyrics became the album "Songs About Jane."^[10]

Other work[link]

Levine (right) with bandmate Jesse Carmichael in 2007

Levine has collaborated with various musical acts. In 2005, Levine was featured on the Ying Yang Twins song "Live Again". He appeared on Kanye West's Late Registration album, on the third single, "Heard 'Em Say".^[11] He is also featured in the song "Wild Horses" on Alicia Keys' third album Alicia Keys: MTV Unplugged. Over the next year, he co-wrote the track "Say It Again" on Natasha Bedingfield's album N.B.. He also performed the background vocals on this song. Most recently, Levine offered his vocals on Gym Class Heroes' newest album in the song "Stereo Hearts".

Levine has made four notable comic appearances on television. During 2007, he appeared on the 33rd season premiere of Saturday Night Live in an SNL Digital Short called Iran So Far with Andy Samberg, Fred Armisen and Jake Gyllenhaal. Levine played himself while singing a humorous bridge to a "love song" for Mahmoud Ahmadinejad. In 2008, he appeared on Comedy Central's "Night Of Too Many Stars". Levine also had a cameo on Jimmy Kimmel Live for the night of stars and endorsed Barack Obama in the 2008 Presidential Election.

In October 2008, Levine collaborated with First Act to create the First Act 222 Guitar, fashioned to Levine's specifications. The guitar was made available for purchase at Target retail stores.^[12]

Levine has stated in various interviews that he does not plan on continuing in Maroon 5 forever, and may stop after the tour for Maroon 5's third album.^[13][14] In 2009, he recorded "Gotten", a song for Slash's first solo album Slash released in April 2010. "Gotten" was premiered at amazon.com on March 29, 2010.^[15] Levine is also featured as a singer for his band's song "She Will be Loved" in the music rhythm game Band Hero. In February 2010, he was among approximately 80 musicians who sang on the charity-single remake of "We Are the World" called "We Are the World 25 for Haiti".^{[citation needed]}

Levine is one of the contestant judges and coach mentors on the singing TV show, The Voice.^[16] The winner of the first season, Javier Colon, was on Levine's team. Levine also returned as a coach for Season 2 of The Voice. His team consisted of Mathai (singer), Pip (singer), Tony Lucca, Katrina Parker, Karla Davis, and Kim Yarbrough. Levine will appear in the second season of American Horror Story.^[17]

Personal life[link]

Levine's ex-girlfriend Jane is the inspiration behind the name of the band's debut album Songs About Jane. In a 2004 interview, he claimed that she had not contacted him despite the success of the album.^[18]

In September 2010, Levine said on the Howard Stern Show he had been dating Russian Sports Illustrated swimsuit and Victoria's Secret model Anne Vyalitsyna seriously for about eight months. The couple met when Maroon 5 performed at the 2010 Sports Illustrated Swimsuit Issue release party in Las Vegas.^[19] In April 2012, Levine and Vyalitsyna announced that they had split.^[20]

Levine stripped naked for testicular cancer awareness for a centerfold in Cosmopolitan UK's February 2011 issue.^[21]

During Levine's teenage years, he was medically diagnosed with Attention Deficit Hyperactivity Disorder. In 2011, he launched an educational campaign to raise awareness of ADHD, titled "Own It".^[22]

Levine, whose brother is openly gay, is an outspoken supporter of LGBT rights.^[23] In 2011, he made a video^[24] on Maroon 5's official YouTube account in support of the It Gets Better Project. In January 2012, he announced that Maroon 5 had changed the location of their post-Grammy Awards show because of the "unnamed Los Angeles restaurant's backing of Proposition 8".^[23]

Discography[link]

As a featured artist[link]

Other charted songs[link]

Guest appearances[link]

Further reading[link]

• Kimpel, Dan (2006), How They Made It: True Stories of How Music's Biggest Stars Went from Start to Stardom!. Location unknown:Hal Leonard Corporation. ISBN 0-634-07642-6

References[link]

External links[link]

Wikiquote has a collection of quotations related to: Adam Levine

• Adam Levine at the Internet Movie Database
• "y’know – interviews with the famous". C.B.Liddell. February 10, 2008. http://yknow-interviews.blogspot.com/2008/02/adam-levine-maroon-5.html.