title: Rachel Uchitel

text: In late 2009, "The National Enquirer" published a story that alleged that Uchitel had had an affair with Tiger Woods at the Australian Masters, an allegation Uchitel denied to the Associated Press.


title: Rachel Uchitel

text: In 2010, actor David Boreanaz admitted to having an affair with Uchitel, who he claimed tried to blackmail him. At the time of the affair Boreanaz's wife was pregnant.


title: Rachel Uchitel

text: On October 2, 2011 she married insurance underwriter and former Penn State fullback Matt Hahn. In May 2012, Uchitel gave birth to a daughter. Hahn filed for divorce from Uchitel in 2013. The divorce was finalized in January 2014.


title: Late capitalism

text: Late capitalism, late-stage capitalism, or end-stage capitalism is a term first used in print by German economist Werner Sombart around the turn of the 20th century. In the late 2010s, the term began to be used in the United States and Canada to refer to perceived absurdities, contradictions, crises, injustices, inequality, and exploitation created by modern business development.


title: Late capitalism

text: Later capitalism refers to the historical epoch since 1940, including the post–World War II economic expansion called the "golden age of capitalism". The expression already existed for a long time in continental Europe, before it gained popularity in the English-speaking world through the English translation of Ernest Mandel's book "Late Capitalism", published in 1975.


title: Late capitalism

text: The German original edition of Mandel's work was subtitled in "an attempt at an explanation", meaning that Mandel tried to provide an orthodox Marxist explanation of the post-war epoch in terms of Marx's theory of the capitalist mode of production. Mandel suggested that important qualitative changes occurred within the capitalist system during and after World War II and that there are limits to capitalist development.


title: Late capitalism

text: The term "late capitalism" (Spätkapitalismus) was first used by Werner Sombart in his magnum opus "Der Moderne Kapitalismus", which was published from 1902 through 1927, and subsequent writings; Sombart divided capitalism into different stages: (1) proto-capitalist society from the early middle ages up to 1500 AD, (2) early capitalism in 1500–1800, (3) the heyday of capitalism ("Hochkapitalismus") from 1800 to the first World War, and (4) late capitalism since then. Sombart's work was never translated into English, but historians sometimes do refer to "late bourgeois society" in contrast to "early bourgeois society" in the 17th and 18th century, or "classical bourgeois society" in the 19th and early 20th century.


title: Late capitalism

text: Vladimir Lenin famously declared that there are no "absolutely hopeless situations" for capitalism. The Communist International stated that with the first World War, a new world epoch of wars and revolutions had opened, and it defined state monopoly capitalism as the highest and final stage of capitalism.


title: Late capitalism

text: The term "late capitalism" began to be used by socialists in continental Europe towards the end of the 1930s and in the 1940s, when many economists believed capitalism was doomed.


title: Late capitalism

text: At the end of World War II, many economists, including Joseph Schumpeter and Paul Samuelson, believed the end of capitalism could be near, in that the economic problems might be insurmountable.


title: Late capitalism

text: The term was used in the 1960s in Germany and Austria, by Western Marxists writing in the tradition of the Frankfurt School and Austromarxism.


title: Late capitalism

text: Leo Michielsen and Andre Gorz popularized the term "neo-capitalism" in France and Belgium, with new analyses of the new post-war capitalism. Jacques Derrida preferred "neo-capitalism" to "post-" or "late-capitalism".


title: Late capitalism

text: Theodor Adorno preferred "late capitalism" over "industrial society," which was the theme of the 16th Congress of German Sociologists in 1968.


title: Late capitalism

text: In 1971, Leo Kofler published a book called "Technologische Rationalität im Spätkapitalismus" (Technological Rationality in Late Capitalism).


title: Late capitalism

text: Claus Offe published his essay "Spätkapitalismus – Versuch einer Begriffsbestimmung" (Late capitalism – an attempt at a conceptual definition) in 1972.


title: Late capitalism

text: In 1973, Jürgen Habermas published his "Legitimationsprobleme im Spätkapitalismus" (Legitimacy problems in late capitalism).


title: Late capitalism

text: Immanuel Wallerstein believed that capitalism was in the process of being replaced by another world system. The American literary critic and cultural theorist Frederic Jameson thought Rudolf Hilferding's term "the latest stage of capitalism" ("jüngster Kapitalismus") perhaps more prudent and less prophetic-sounding but Jameson often used "late capitalism" in his writings.


title: Late capitalism

text: Hegel's theme of "the end of history" was rekindled by Kojève in his "Introduction to the Reading of Hegel". The "end of history" is discussed by Francis Fukuyama in the sense that liberal democracy is the ultimate form of society, which cannot be surpassed by anything that is superior to it, because there does not and cannot exist anything superior.


title: Late capitalism

text: In modern usage, late capitalism often refers to a new mix of high-tech advances, the concentration of (speculative) financial capital, post-Fordism, and a growing income inequality.


title: Late capitalism

text: According to the Marxist economist Ernest Mandel, who popularised the term with his 1972 PhD dissertation, late-stage capitalism will be dominated by the machinations—or perhaps better, fluidities—of financial capital; and also by the increasing commodification and industrialisation of ever more inclusive sectors of human life. Mandel believed that "[f]ar from representing a 'post-industrial society', late capitalism [...] constitutes "generalized universal industrialization" for the first time in history".


title: Late capitalism

text: Up to the mid-1960s, Mandel preferred to use the term "neo-capitalism", which was most often used by intellectuals in Belgium and France around that time. This term drew attention to new characterististics of capitalism, but at the time ultra-leftist Marxists objected to it, because, according to them, it might suggest that capitalism was no longer capitalism, and it might lead to reformist errors rather than the overthrow of capitalism.


title: Late capitalism

text: In his work "Late Capitalism", Mandel distinguished three periods in the development of the capitalist mode of production.


title: Late capitalism

text: In the tradition of the orthodox Marxists, Mandel tried to characterize the nature of the modern epoch as a whole, with reference to the main laws of motion of capitalism specified by Marx. Mandel's aim was to explain the unexpected revival of capitalism after World War II, contrary to leftist prognostications, and the long economic boom which showed the fastest economic growth ever seen in human history. His work has produced a new interest in the theory of long waves in economic development.


title: Late capitalism

text: Fredric Jameson borrowed Mandel's vision as a basis for his widely cited "Postmodernism, or, the Cultural Logic of Late Capitalism." Jameson's postmodernity involves a new mode of cultural production (developments in literature, film, fine art, video, social theory, etc.) which differs markedly from the preceding era of Modernism, particularly in its treatment of subject position, temporality and narrative.


title: Late capitalism

text: In the modernist era, the dominant ideology was that society could be re-engineered on the basis of scientific and technical knowledge, and on the basis of a popular consensus about the meaning of progress. From the second half of the 20th century, however, modernism was gradually eclipsed by postmodernism, which is skeptical about social engineering and features a lack of consensus about the meaning of progress. In the wake of rapid technological and social change, all the old certainties have broken down. This begins to destabilize every part of life, making almost everything malleable, changeable, transient and impermanent.


title: Late capitalism

text: Jameson argues that "every position on postmodernism today — whether apologia or stigmatization — is also..."necessarily" an implicitly or explicitly political stance on the nature of multinational capitalism today". A section of Jameson's analysis has been reproduced on the Marxists Internet Archive. Jameson regards the late capitalist stage as a new and previously unparalleled development with a global reach — whether defined as a multinational or informational capitalism. At the same time, late capitalism diverges from Marx's prognosis for the final stage of capitalism.


title: Late capitalism

text: According to a 2017 article in "The Atlantic", the term "late capitalism" is again in vogue to describe modern business culture, although with a semantic change or an ironic twist. "Late capitalism" has become a catch-all term for various phenomena that express capitalism's distortions of human life and psyche, which is often used in critique and satire. This usage also conveys a sense that contemporary capitalism cannot go on like it does forever, because the problems created by business are getting too large and unmanageable.


title: Late capitalism

text: The phrase “late stage capitalism” is used commonly as a critique of the allegedly fascistic qualities that emerge in the later stages of capitalism. Capitalism to many may seem to be free of this exploitation if not taken to the extremes of “late capitalism”. A competing viewpoint is that “Capitalism, in its orthodoxy, is a system that relies on authoritative, controlling, and exploitative relationships, most notably between that of capitalists and workers”, and that this is not something that emerges out of a devolving system but rather is present in the framework of the system itself.


title: Late capitalism

text: A character in Thomas Pynchon's 2013 novel "Bleeding Edge" states "late capitalism is a pyramid racket on a global scale... getting the suckers to believe it's all gonna go on forever."


title: Late capitalism

text: Cyberpunk films such as "Blade Runner" (1982) explore potential consequences of late stage capitalism.


title: Demographics of South Africa

text: The population of South Africa is about 58.8 million people of diverse origins, cultures, languages, and religions. The South African National Census of 2022 was the most recent census held; the next will be in 2032.


title: Demographics of South Africa

text: In 2011, Statistics South Africa counted 2.1 million foreigners in total. Reports suggest that is an underestimation. The real figure may be as high as five million, including some three million Zimbabweans.


title: Demographics of South Africa

text: Bantustan demographics were removed from South African census data during Apartheid and for this reason official figures on the national population of the country during that period will be inaccurate.


title: Demographics of South Africa

text: According to the 2019 revision of the United Nations Secretariat's "World Population Prospects", South Africa's total population was 55,386,000 in 2015, compared to only 13,628,000 in 1950. In 2015, 29.3% of the people were children under the age of 15, 65.7% were between 15 and 64 years of age, and 5.0% were 65 or older. All population estimates are rounded to the nearest thousand.


title: Demographics of South Africa

text: The following statistics are obtained from the mid-year population estimates published by Statistics South Africa:


title: Demographics of South Africa

text: The Population Department of the United Nations prepared the following estimates. (Natural increase or decrease over a time period is the difference between that period's live births and deaths, before accounting for inward or outward migration.)


title: Demographics of South Africa

text: Statistics South Africa asks people to describe themselves in the census in terms of five racial population groups. The 2011 census figures for these groups were Black African at 80.2%, White at 8.4%, Coloured at 8.8%, Indian/Asian at 2.5%, and Other/Unspecified at 0.5%.


title: Demographics of South Africa

text: The white percentage of the population has sharply declined. The first census in South Africa in 1911 showed that whites made up 22% of the population. This declined to 16% in 1980, 8.9% in 2011 and 7.65% in 2022.Coloured South Africans replaced Whites as the largest minority group around 2010.


title: Demographics of South Africa

text: South Africa has eleven official languages: isiZulu 22.7%, isiXhosa 16%, Afrikaans 13.5%, English 9.6%, Sepedi 9.1%, Setswana 8%, Sesotho 7.6%, Xitsonga 4.5%, siSwati 2.5%, Tshivenda 2.4% and isiNdebele 2.1%.


title: Demographics of South Africa

text: In this regard, it is third only to Bolivia and India in number. While all the languages are formally equal, some languages are spoken more than others. According to the 2011 census, the three most spoken first languages are Zulu (22.7%), Xhosa (16.0%), and Afrikaans (13.5%). Despite the fact that English is recognised as the language of commerce and science, it ranked fourth, and was spoken by only 9.6% of South Africans as a first language in 2011.


title: Demographics of South Africa

text: The country also recognises several unofficial languages, including Sekholokoe, Fanagalo, Khwe, Lobedu, Nama, Northern Ndebele, Phuthi, San and South African Sign Language. These unofficial languages may be used in certain official uses in limited areas where it has been determined that these languages are prevalent. Nevertheless, their populations are not such that they require nationwide recognition.


title: Demographics of South Africa

text: Many of the "unofficial languages" of the San and Khoikhoi people contain regional dialects stretching northwards into Namibia and Botswana, and elsewhere. These people, who are a physically distinct population from other Africans, have their own cultural identity based on their hunter-gatherer societies. They have been marginalised to a great extent, and many of their languages are in danger of becoming extinct.


title: Demographics of South Africa

text: Many white South Africans also speak other European languages, such as Portuguese (also spoken by black Angolans and Mozambicans), German, and Greek, while some Indians and other Asians in South Africa speak South Asian languages, such as Tamil, Hindi, Gujarati, Urdu and Telugu. Although many South Africans are of Huguenot (French) origin, South African French is spoken by fewer than 10,000 individuals country-wide. Congolese French is also spoken in South Africa by migrants.


title: Demographics of South Africa

text: The primary sign language of deaf South Africans is South African Sign Language. Other sign languages among indigenous peoples are also used.


title: Demographics of South Africa

text: In 2011, the first language was Zulu for 28.1% of South African residents, Xhosa for 19.8%, Northern Sotho for 11.2%, Tswana for 9.7%, Sesotho for 9.3%, Tsonga for 5.5%, siSwati for 3.1%, Venda for 2.9%, English for 2.8%, Southern Ndebele for 2.6%, Afrikaans for 1.5%, while 3.4% had another first language.


title: Demographics of South Africa

text: Among whites, Afrikaans was the first language for 59.1% of the population, compared to 35.0% for English. Other languages accounted for the remaining 5.9%.


title: Demographics of South Africa

text: According to the 2001 national census, Christians accounted for 79.7% of the population. This includes Protestant (36.6%), Zionist Christian (11.1%), Pentecostal/Charismatic (8.2%), Roman Catholic (7.1%), Methodist (6.8%), Dutch Reformed (6.7%), Anglican (3.8%); members of other Christian churches accounted for another 36% of the population. Muslims accounted for 1.5% of the population, Other 2.3%, and 1.4% were Unspecified and None 15.1%.


title: Demographics of South Africa

text: African Indigenous Churches made up the largest of the Christian groups. Some believe that many people claiming no affiliation with any organised religion adhered to traditional indigenous religions. Many people have syncretic religious practices combining Christian and indigenous influences.


title: Demographics of South Africa

text: Muslims are largely found among the Coloured and Indian ethnic groups. They have been joined by black or white South African converts as well as immigrants from other parts of Africa. South African Muslims claim that their faith is the fastest-growing religion of conversion in the country, with the number of black Muslims growing sixfold, from 12,000 in 1991 to 74,700 in 2004


title: Demographics of South Africa

text: The Hindu population has its roots in the British colonial period, but later waves of immigration from India have also contributed to it. Most Hindus are of South Asian origin, but there are many who come from mixed racial stock. Some are converts due to the efforts of ISKCON.


title: Demographics of South Africa

text: 87.9% of Black residents are Christian, 9.5% have no religion, 0.2% are Muslim, 0.0% are Jewish, 1.22% are Hindu and 2.3% have other or undetermined beliefs.


title: Demographics of South Africa

text: 71.8% of White residents are Christian, 23.8% have no religion, 0.2% are Muslim, 1.4% are Jewish, and 0.0% are Hindu. 2.7% have other or undetermined beliefs.


title: Demographics of South Africa

text: note: widespread ongoing transmission of a respiratory illness caused by the novel coronavirus (COVID-19) is occurring throughout South Africa; as of 6 June 2022, South Africa has reported a total of 3,968,205 cases of COVID-19 or 6,690.7 cumulative cases of COVID-19 per 100,000 population with a total of 101,317 cumulative deaths or a rate of 170.83 cumulative deaths per 100,000 population; as of 6 June 2022, 36.33% of the population has received at least one dose of COVID-19 vaccine


title: Demographics of South Africa

text: South Africa hosts a sizeable refugee and asylum seeker population. According to the "World Refugee Survey 2008", published by the U.S. Committee for Refugees and Immigrants, this population numbered approximately 144,700 in 2007. Groups of refugees and asylum seekers numbering over 10,000 included people from Zimbabwe (48,400), the Democratic Republic of the Congo (24,800), and Somalia (12,900). These populations mainly lived in Johannesburg, Pretoria, Durban, Cape Town, and Port Elizabeth. Many refugees have now also started to work and live in rural areas in provinces such as Mpumalanga and KwaZulu-Natal.


title: Demographics of South Africa

text: Statistics SA assumes in some of their calculations that there are fewer than 2 million immigrants in South Africa. Other institutions, like the police and Médecins Sans Frontières place estimate the figure at 4 million.


title: Demographics of South Africa

text: Immigration assumptions by Statistics South Africa to South Africa based on race. Negative numbers represent net migration from South Africa to other countries.


title: Demographics of South Africa

text: "Urban areas contain about two-thirds of the population; many of these consist of huge informal or squatter settlements."


title: Arithmetic progression

text: An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.


title: Arithmetic progression

text: If the initial term of an arithmetic progression is formula_1 and the common difference of successive members is formula_2, then the formula_3-th term of the sequence (formula_4) is given by:


title: Arithmetic progression

text: A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.


title: Arithmetic progression

text: The sum of the members of a finite arithmetic progression is called an arithmetic series. For example, consider the sum:


title: Arithmetic progression

text: This sum can be found quickly by taking the number "n" of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 2 + 14 = 16), and dividing by 2:


title: Arithmetic progression

text: The product of the members of a finite arithmetic progression with an initial element "a", common differences "d", and "n" elements in total is determined in a closed expression


title: Arithmetic progression

text: where formula_22 denotes the Gamma function. The formula is not valid when formula_23 is negative or zero.


title: Arithmetic progression

text: This is a generalization from the fact that the product of the progression formula_24 is given by the factorial formula_25 and that the product


title: Arithmetic progression

text: Taking the example formula_42, the product of the terms of the arithmetic progression given by formula_43 up to the 50th term is


title: Arithmetic progression

text: formula_49 is the common difference between terms. The formula is very similar to the standard deviation of a discrete uniform distribution.


title: Arithmetic progression

text: The intersection of any two doubly infinite arithmetic progressions is either empty or another arithmetic progression, which can be found using the Chinese remainder theorem. If each pair of progressions in a family of doubly infinite arithmetic progressions have a non-empty intersection, then there exists a number common to all of them; that is, infinite arithmetic progressions form a Helly family. However, the intersection of infinitely many infinite arithmetic progressions might be a single number rather than itself being an infinite progression.


title: Arithmetic progression

text: According to an anecdote of uncertain reliability, young Carl Friedrich Gauss in primary school reinvented this method to compute the sum of the integers from 1 through 100, by multiplying pairs of numbers in the sum by the values of each pair . However, regardless of the truth of this story, Gauss was not the first to discover this formula, and some find it likely that its origin goes back to the Pythagoreans in the 5th century BC. Similar rules were known in antiquity to Archimedes, Hypsicles and Diophantus; in China to Zhang Qiujian; in India to Aryabhata, Brahmagupta and Bhaskara II; and in medieval Europe to Alcuin, Dicuil, Fibonacci, Sacrobosco


title: Bryce Hall

text: Bryce Michael Hall (born August 14, 1999) is an American social media personality known for his TikTok and YouTube videos. , his TikTok account has 21.8 million followers, and his YouTube channel has 3 million subscribers.


title: Bryce Hall

text: Hall started his social media career on YouNow at the age of 15. He originally started live streaming in an effort to make friends after being bullied. In late 2014, he started gaining traction on the social media platforms Vine and Musical.ly, accumulating over 30,000 followers on Vine before it was shut down at the end of 2016.


title: Bryce Hall

text: In 2018, Hall moved from his home in Maryland to Los Angeles to pursue his career. In 2019, he was one of the social-media celebrities featured in the documentary "Jawline", which detailed his career beginnings and his legal scandals with his former manager, Michael Weist.


title: Bryce Hall

text: In January 2020, Hall and five other social media personalities moved into the Sway House, a Bel Air mansion owned by the talent management company TalentX Entertainment. There, they committed to creating viral content for multiple social media platforms, especially TikTok. In February 2021, TalentX and Sway House co-founder Michael Gruen confirmed that the Sway House had been discontinued.


title: Bryce Hall

text: In April 2022, it was reported that Hall would star in "Skill House", a horror film written and directed by Josh Stolberg and financed by Ryan Kavanaugh's Proxima Studios.


title: Bryce Hall

text: Before his match against Austin McBroom, in an interview, Bryce Hall claimed that he had participated in "over 40 street fights." Hall claims that he has yet to lose in any street fight.


title: Bryce Hall

text: Hall and YouTuber Austin McBroom began fighting on Twitter and a match was booked between them. On March 18, 2021, the undercard of the match was turned into a new event called YouTubers vs. TikTokers, with Hall representing the TikTok side. At the press conference for the event, a fight between McBroom and Hall broke out on stage. On June 12, 2021, McBroom beat Hall by TKO. Hall would say in the post-interview, "I'm not a fighter, I never claimed to be a fighter." Later on a Keemstar interview Hall stated he meant to say he isn't a boxer.


title: Bryce Hall

text: Hall moved to Los Angeles, California in 2018, later becoming the creator of the Sway House. In 2020, Hall dated TikToker Addison Rae. They broke up the following year.


title: Bryce Hall

text: In June 2020, his tweet about "straight TikTok" and hetero-phobia created controversy. Critics alleged Hall had mocked the LGBT community. He deleted the tweet minutes later and issued an apology to the public of Twitter.


title: Bryce Hall

text: In 2017, Hall falsely accused his former manager Michael Weist of sexual assault. On November 1, 2017, Hall tweeted out accusing Weist of hacking his Twitter account, and he also claimed that Weist touched him inappropriately, writing ""Managers who touch their clients in ways they don't wanna be touched hide the truth by hacking their Twitter accounts."" In Hulu's "Jawline," Weist is shown replying to a text about suing Hall by stating that he would sue his former client for $5 million. Weist filed a lawsuit against Hall for defamation. The case was settled outside of court, and Hall publicly apologized to Weist, stating ""I made some harsh statements about Michael and regret making those statements, including any suggestion of sexual assault. I am sorry for what happened and I am glad it is over.""


title: Bryce Hall

text: On August 19, 2020, Mayor of Los Angeles Eric Garcetti authorized the Los Angeles Department of Water and Power to shut off Hall's home utility services for violating the city's social distancing measures against the COVID-19 pandemic, which include a ban on house parties with large gatherings, which Hall allegedly violated with a celebration of his 21st birthday after several warnings from the Los Angeles Police Department to cease his parties. On August 28, he was charged by the Los Angeles City Attorney with a misdemeanor violating the Safer L.A. health order and the city's “Party House Ordinance”.


title: Bryce Hall

text: On May 25, 2020, Hall, along with fellow Tik Tok star Jaden Hossler, was arrested in Lee County, Texas on drug charges. He was charged with a misdemeanor for possession of marijuana, and posted $5,000 bail the same day.


title: Bryce Hall

text: In October 2020, footage obtained by TMZ showed Hall and some of his friends in an altercation with an employee of the Cinco restaurant in Los Angeles. Several months later in April 2021, the restaurant co-owner, Hernan Fernando sued Hall for "battery; assault; intentional infliction of emotional distress; and engaging in acts of violence motivated by race, national origin, citizenship, immigration status and primary language."


title: Interval (music)

text: 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.


title: Interval (music)

text: In Western music, intervals are most commonly differences between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. 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.


title: Interval (music)

text: 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.


title: Interval (music)

text: In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.). Examples include the minor third or perfect fifth. These names identify not only the difference in semitones between the upper and lower notes but also how the interval is spelled. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G and G–A.


title: Interval (music)

text: The size of an interval (also known as its width or height) can be represented using two alternative and equivalently valid methods, each appropriate to a different context: frequency ratios or cents.


title: Interval (music)

text: The size of an interval between two notes may be measured by the ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (unison), 2:1 (octave), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). Intervals with small-integer ratios are often called "just intervals", or "pure intervals".


title: Interval (music)

text: Most commonly, however, musical instruments are nowadays tuned using a different tuning system, called 12-tone equal temperament. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, although it is very close to the size of the corresponding just intervals. For instance, an equal-tempered fifth has a frequency ratio of 2:1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2). For a comparison between the size of intervals in different tuning systems, see .


title: Interval (music)

text: The standard system for comparing interval sizes is with cents. The cent is a logarithmic unit of measurement. If frequency is expressed in a logarithmic scale, and along that scale the distance between a given frequency and its double (also called octave) is divided into 1200 equal parts, each of these parts is one cent. In twelve-tone equal temperament (12-TET), a tuning system in which all semitones have the same size, the size of one semitone is exactly 100 cents. Hence, in 12-TET the cent can be also defined as one hundredth of a semitone.


title: Interval (music)

text: The table shows the most widely used conventional names for the intervals between the notes of a chromatic scale. A perfect unison (also known as perfect prime) is an interval formed by two identical notes. Its size is zero cents. A semitone is any interval between two adjacent notes in a chromatic scale, a whole tone is an interval spanning two semitones (for example, a major second), and a tritone is an interval spanning three tones, or six semitones (for example, an augmented fourth). Rarely, the term ditone is also used to indicate an interval spanning two whole tones (for example, a major third), or more strictly as a synonym of major third.


title: Interval (music)

text: Intervals with different names may span the same number of semitones, and may even have the same width. For instance, the interval from D to F is a major third, while that from D to G is a diminished fourth. However, they both span 4 semitones. If the instrument is tuned so that the 12 notes of the chromatic scale are equally spaced (as in equal temperament), these intervals also have the same width. Namely, all semitones have a width of 100 cents, and all intervals spanning 4 semitones are 400 cents wide.


title: Interval (music)

text: The names listed here cannot be determined by counting semitones alone. The rules to determine them are explained below. Other names, determined with different naming conventions, are listed in a separate section. Intervals smaller than one semitone (commas or microtones) and larger than one octave (compound intervals) are introduced below.


title: Interval (music)

text: In Western music theory, an interval is named according to its "number" (also called "diatonic number") and "quality". For instance, "major third" (or M3) is an interval name, in which the term "major" (M) describes the quality of the interval, and "third" (3) indicates its number.


title: Interval (music)

text: The number of an interval is the number of letter names or staff positions (lines and spaces) it encompasses, including the positions of both notes forming the interval. For instance, the interval C–G is a fifth (denoted P5) because the notes from C to the G above it encompass five letter names (C, D, E, F, G) and occupy five consecutive staff positions, including the positions of C and G. The table and the figure above show intervals with numbers ranging from 1 (e.g., P1) to 8 (e.g., P8). Intervals with larger numbers are called compound intervals.


title: Interval (music)

text: There is a one-to-one correspondence between staff positions and diatonic-scale degrees (the notes of diatonic scale).


title: Interval (music)

text: This means that interval numbers can also be determined by counting diatonic scale degrees, rather than staff positions, provided that the two notes that form the interval are drawn from a diatonic scale. Namely, C–G is a fifth because in any diatonic scale that contains C and G, the sequence from C to G includes five notes. For instance, in the A-major diatonic scale, the five notes are C–D–E–F–G (see figure). This is not true for all kinds of scales. For instance, in a chromatic scale, the notes from C to G are eight (C–C–D–D–E–F–F–G). This is the reason interval numbers are also called "diatonic numbers", and this convention is called "diatonic numbering".


title: Interval (music)

text: If one adds any accidentals to the notes that form an interval, by definition the notes do not change their staff positions. As a consequence, any interval has the same interval number as the corresponding natural interval, formed by the same notes without accidentals. For instance, the intervals C–G (spanning 8 semitones) and C–G (spanning 6 semitones) are fifths, like the corresponding natural interval C–G (7 semitones).


title: Interval (music)

text: Notice that interval numbers represent an inclusive count of encompassed staff positions or note names, not the difference between the endpoints. In other words, one starts counting the lower pitch as one, not zero. For that reason, the interval C–C, a perfect unison, is called a prime (meaning "1"), even though there is no difference between the endpoints. Continuing, the interval C–D is a second, but D is only one staff position, or diatonic-scale degree, above C. Similarly, C–E is a third, but E is only two staff positions above C, and so on. As a consequence, joining two intervals always yields an interval number one less than their sum. For instance, the intervals C–E and E–G are thirds, but joined together they form a fifth (C–G), not a sixth. Similarly, a stack of three thirds, such as C–E, E–G, and G–B, is a seventh (C–B), not a ninth.


title: Interval (music)

text: The name of any interval is further qualified using the terms perfect (P), major (M), minor (m), augmented (A), and diminished (d). This is called its "interval quality". It is possible to have doubly diminished and doubly augmented intervals, but these are quite rare, as they occur only in chromatic contexts. The quality of a compound interval is the quality of the simple interval on which it is based. Some other qualifiers like "neutral", "subminor", and "supermajor" are used for non-diatonic intervals.


title: Interval (music)

text: although in Western classical music the perfect fourth was sometimes regarded as a less than perfect consonance, when its function was contrapuntal. Conversely, minor, major, augmented or diminished intervals are typically considered less consonant, and were traditionally classified as mediocre consonances, imperfect consonances, or dissonances.


title: Interval (music)

text: Within a diatonic scale all unisons (P1) and octaves (P8) are perfect. Most fourths and fifths are also perfect (P4 and P5), with five and seven semitones respectively. One occurrence of a fourth is augmented (A4) and one fifth is diminished (d5), both spanning six semitones. For instance, in a C-major scale, the A4 is between F and B, and the d5 is between B and F (see table).


title: Interval (music)

text: By definition, the inversion of a perfect interval is also perfect. Since the inversion does not change the pitch class of the two notes, it hardly affects their level of consonance (matching of their harmonics). Conversely, other kinds of intervals have the opposite quality with respect to their inversion. The inversion of a major interval is a minor interval, the inversion of an augmented interval is a diminished interval.


title: Interval (music)

text: As shown in the table, a diatonic scale defines seven intervals for each interval number, each starting from a different note (seven unisons, seven seconds, etc.). The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves, the diatonic intervals with a given interval number always occur in two sizes, which differ by one semitone. For example, six of the fifths span seven semitones. The other one spans six semitones. Four of the thirds span three semitones, the others four. If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise, the larger version is called major, the smaller one minor. For instance, since a 7-semitone fifth is a perfect interval (P5), the 6-semitone fifth is called "diminished fifth" (d5). Conversely, since neither kind of third is perfect, the larger one is called "major third" (M3), the smaller one "minor third" (m3).


title: Interval (music)

text: Within a diatonic scale, unisons and octaves are always qualified as perfect, fourths as either perfect or augmented, fifths as perfect or diminished, and all the other intervals (seconds, thirds, sixths, sevenths) as major or minor.


title: Interval (music)

text: Augmented intervals are wider by one semitone than perfect or major intervals, while having the same interval number (i.e., encompassing the same number of staff positions): they are wider by a chromatic semitone. Diminished intervals, on the other hand, are narrower by one semitone than perfect or minor intervals of the same interval number: they are narrower by a chromatic semitone. For instance, an augmented third such as C–E spans five semitones, exceeding a major third (C–E) by one semitone, while a diminished third such as C–E spans two semitones, falling short of a minor third (C–E) by one semitone.


title: Interval (music)

text: The augmented fourth (A4) and the diminished fifth (d5) are the only augmented and diminished intervals that appear in diatonic scales (see table).


title: Interval (music)

text: Neither the number, nor the quality of an interval can be determined by counting semitones alone. As explained above, the number of staff positions must be taken into account as well.


title: Interval (music)

text: For example, as shown in the table below, there are four semitones between A and B, between A and C, between A and D, and between A and E, but


title: Interval (music)

text: Intervals are often abbreviated with a P for perfect, m for minor, M for major, d for diminished, A for augmented, followed by the interval number. The indications M and P are often omitted. The octave is P8, and a unison is usually referred to simply as "a unison" but can be labeled P1. The tritone, an augmented fourth or diminished fifth is often TT. The interval qualities may be also abbreviated with perf, min, maj, dim, aug. Examples:


title: Interval (music)

text: A simple interval (i.e., an interval smaller than or equal to an octave) may be inverted by raising the lower pitch an octave or lowering the upper pitch an octave. For example, the fourth from a lower C to a higher F may be inverted to make a fifth, from a lower F to a higher C.


title: Interval (music)

text: For example, the interval from C to the E above it is a minor third. By the two rules just given, the interval from E to the C above it must be a major sixth.


title: Interval (music)

text: Since compound intervals are larger than an octave, "the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded."


title: Interval (music)

text: For intervals identified by their ratio, the inversion is determined by reversing the ratio and multiplying the ratio by 2 until it is greater than 1. For example, the inversion of a 5:4 ratio is an 8:5 ratio.


title: Interval (music)

text: For intervals identified by an integer number of semitones, the inversion is obtained by subtracting that number from 12.


title: Interval (music)

text: Since an interval class is the lower number selected among the interval integer and its inversion, interval classes cannot be inverted.


title: Interval (music)

text: The table above depicts the 56 diatonic intervals formed by the notes of the C major scale (a diatonic scale). Notice that these intervals, as well as any other diatonic interval, can be also formed by the notes of a chromatic scale.


title: Interval (music)

text: The distinction between diatonic and chromatic intervals is controversial, as it is based on the definition of diatonic scale, which is variable in the literature. For example, the interval B–E (a diminished fourth, occurring in the harmonic C-minor scale) is considered diatonic if the harmonic minor scales are considered diatonic as well. Otherwise, it is considered chromatic. For further details, see the main article.


title: Interval (music)

text: By a commonly used definition of diatonic scale (which excludes the harmonic minor and melodic minor scales), all perfect, major and minor intervals are diatonic. Conversely, no augmented or diminished interval is diatonic, except for the augmented fourth and diminished fifth.


title: Interval (music)

text: The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called "diatonic to C major". All other intervals are called "chromatic to C major". For instance, the perfect fifth A–E is chromatic to C major, because A and E are not contained in the C major scale. However, it is diatonic to others, such as the A major scale.


title: Interval (music)

text: Consonance and dissonance are relative terms that refer to the stability, or state of repose, of particular musical effects. Dissonant intervals are those that cause tension and desire to be "resolved" to consonant intervals.


title: Interval (music)

text: A simple interval is an interval spanning at most one octave (see Main intervals above). Intervals spanning more than one octave are called compound intervals, as they can be obtained by adding one or more octaves to a simple interval (see below for details).


title: Interval (music)

text: is a linear interval between two consecutive notes of a scale. Any larger interval is called a "skip" (also called a "leap"), or "disjunct motion". In the diatonic scale, a step is either a minor second (sometimes also called "half step") or major second (sometimes also called "whole step"), with all intervals of a minor third or larger being skips.


title: Interval (music)

text: More generally, a step is a smaller or narrower interval in a musical line, and a skip is a wider or larger interval, where the categorization of intervals into steps and skips is determined by the tuning system and the pitch space used.


title: Interval (music)

text: Melodic motion in which the interval between any two consecutive pitches is no more than a step, or, less strictly, where skips are rare, is called "stepwise" or "conjunct" melodic motion, as opposed to "skipwise" or "disjunct" melodic motions, characterized by frequent skips.


title: Interval (music)

text: Two intervals are considered "enharmonic", or "enharmonically equivalent", if they both contain the same pitches spelled in different ways; that is, if the notes in the two intervals are themselves enharmonically equivalent. Enharmonic intervals span the same number of semitones.


title: Interval (music)

text: For example, the four intervals listed in the table below are all enharmonically equivalent, because the notes F and G indicate the same pitch, and the same is true for A and B. All these intervals span four semitones.


title: Interval (music)

text: When played as isolated chords on a piano keyboard, these intervals are indistinguishable to the ear, because they are all played with the same two keys. However, in a musical context, the diatonic function of the notes these intervals incorporate is very different.


title: Interval (music)

text: The discussion above assumes the use of the prevalent tuning system, 12-tone equal temperament ("12-TET"). But in other historic meantone temperaments, the pitches of pairs of notes such as F and G may not necessarily coincide. These two notes are enharmonic in 12-TET, but may not be so in another tuning system. In such cases, the intervals they form would also not be enharmonic. For example, in quarter-comma meantone, all four intervals shown in the example above would be different.


title: Interval (music)

text: There are also a number of minute intervals not found in the chromatic scale or labeled with a diatonic function, which have names of their own. They may be described as microtones, and some of them can be also classified as commas, as they describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes. In the following list, the interval sizes in cents are approximate.


title: Interval (music)

text: A compound interval is an interval spanning more than one octave. Conversely, intervals spanning at most one octave are called simple intervals (see Main intervals below).


title: Interval (music)

text: In general, a compound interval may be defined by a sequence or "stack" of two or more simple intervals of any kind. For instance, a major tenth (two staff positions above one octave), also called "compound major third", spans one octave plus one major third.


title: Interval (music)

text: Any compound interval can be always decomposed into one or more octaves plus one simple interval. For instance, a major seventeenth can be decomposed into two octaves and one major third, and this is the reason why it is called a compound major third, even when it is built by adding up four fifths.


title: Interval (music)

text: The diatonic number "DN" of a compound interval formed from "n" simple intervals with diatonic numbers "DN", "DN", ..., "DN", is determined by:


title: Interval (music)

text: The quality of a compound interval is determined by the quality of the simple interval on which it is based. For instance, a compound major third is a major tenth (1+(8−1)+(3−1) = 10), or a major seventeenth (1+(8−1)+(8−1)+(3−1) = 17), and a compound perfect fifth is a perfect twelfth (1+(8−1)+(5−1) = 12) or a perfect nineteenth (1+(8−1)+(8−1)+(5−1) = 19). Notice that two octaves are a fifteenth, not a sixteenth (1+(8−1)+(8−1) = 15). Similarly, three octaves are a twenty-second (1+3×(8−1) = 22), and so on.


title: Interval (music)

text: It is also worth mentioning here the major seventeenth (28 semitones)—an interval larger than two octaves that can be considered a multiple of a perfect fifth (7 semitones) as it can be decomposed into four perfect fifths (7 × 4 = 28 semitones), or two octaves plus a major third (12 + 12 + 4 = 28 semitones). Intervals larger than a major seventeenth seldom come up, most often being referred to by their compound names, for example "two octaves plus a fifth" rather than "a 19th".


title: Interval (music)

text: Chords are sets of three or more notes. They are typically defined as the combination of intervals starting from a common note called the root of the chord. For instance a major triad is a chord containing three notes defined by the root and two intervals (major third and perfect fifth). Sometimes even a single interval (dyad) is considered a chord. Chords are classified based on the quality and number of the intervals that define them.


title: Interval (music)

text: The symbols used for chord quality are similar to those used for interval quality (see above). In addition, + or aug is used for augmented, ° or dim for diminished, for half diminished, and dom for dominant (the symbol − alone is not used for diminished).


title: Interval (music)

text: The main rules to decode chord "names or symbols" are summarized below. Further details are given at Rules to decode chord names and symbols.


title: Interval (music)

text: The table shows the intervals contained in some of the main chords (component intervals), and some of the symbols used to denote them. The interval qualities or numbers in boldface font can be deduced from chord name or symbol by applying rule 1. In symbol examples, C is used as chord root.


title: Interval (music)

text: In this table, the interval widths used in four different tuning systems are compared. To facilitate comparison, just intervals as provided by 5-limit tuning (see symmetric scale n.1) are shown in bold font, and the values in cents are rounded to integers. Notice that in each of the non-equal tuning systems, by definition the width of "each" type of interval (including the semitone) changes depending on the note that starts the interval. This is the art of just intonation. In equal temperament, the intervals are never precisely in tune with each other. This is the price of using equidistant intervals in a 12-tone scale. For simplicity, for some types of interval the table shows only one value (the most often observed one).


title: Interval (music)

text: In -comma meantone, by definition 11 perfect fifths have a size of approximately 697 cents (700 − "ε" cents, where "ε" ≈ 3.42 cents); since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of about 738 cents (700 + 11"ε", the wolf fifth or diminished sixth); 8 major thirds have size about 386 cents (400 − 4"ε"), 4 have size about 427 cents (400 + 8"ε", actually diminished fourths), and their average size is 400 cents. In short, similar differences in width are observed for all interval types, except for unisons and octaves, and they are all multiples of ε (the difference between the -comma meantone fifth and the average fifth). A more detailed analysis is provided at -comma meantone Size of intervals. Note that -comma meantone was designed to produce just major thirds, but only 8 of them are just (5:4, about 386 cents).


title: Interval (music)

text: The Pythagorean tuning is characterized by smaller differences because they are multiples of a smaller "ε" ("ε" ≈ 1.96 cents, the difference between the Pythagorean fifth and the average fifth). Notice that here the fifth is wider than 700 cents, while in most meantone temperaments, including -comma meantone, it is tempered to a size smaller than 700. A more detailed analysis is provided at .


title: Interval (music)

text: The 5-limit tuning system uses just tones and semitones as building blocks, rather than a stack of perfect fifths, and this leads to even more varied intervals throughout the scale (each kind of interval has three or four different sizes). A more detailed analysis is provided at . Note that 5-limit tuning was designed to maximize the number of just intervals, but even in this system some intervals are not just (e.g., 3 fifths, 5 major thirds and 6 minor thirds are not just; also, 3 major and 3 minor thirds are wolf intervals).


title: Interval (music)

text: The above-mentioned symmetric scale 1, defined in the 5-limit tuning system, is not the only method to obtain just intonation. It is possible to construct juster intervals or just intervals closer to the equal-tempered equivalents, but most of the ones listed above have been used historically in equivalent contexts. In particular, the asymmetric version of the 5-limit tuning scale provides a juster value for the minor seventh (9:5, rather than 16:9). Moreover, the tritone (augmented fourth or diminished fifth), could have other just ratios; for instance, 7:5 (about 583 cents) or 17:12 (about 603 cents) are possible alternatives for the augmented fourth (the latter is fairly common, as it is closer to the equal-tempered value of 600 cents). The 7:4 interval (about 969 cents), also known as the harmonic seventh, has been a contentious issue throughout the history of music theory; it is 31 cents flatter than an equal-tempered minor seventh. For further details about reference ratios, see .


title: Interval (music)

text: In the diatonic system, every interval has one or more "enharmonic equivalents", such as augmented second for minor third.


title: Interval (music)

text: Although intervals are usually designated in relation to their lower note, David Cope and Hindemith both suggest the concept of interval root. To determine an interval's root, one locates its nearest approximation in the harmonic series. The root of a perfect fourth, then, is its "top" note because it is an octave of the fundamental in the hypothetical harmonic series. The bottom note of every odd diatonically numbered intervals are the roots, as are the tops of all even numbered intervals. The root of a collection of intervals or a chord is thus determined by the interval root of its strongest interval.


title: Interval (music)

text: As to its usefulness, Cope provides the example of the final tonic chord of some popular music being traditionally analyzable as a "submediant six-five chord" (added sixth chords by popular terminology), or a first inversion seventh chord (possibly the dominant of the mediant V/iii). According to the interval root of the strongest interval of the chord (in first inversion, CEGA), the perfect fifth (C–G), is the bottom C, the tonic.


title: Interval (music)

text: Interval cycles, "unfold [i.e., repeat] a single recurrent interval in a series that closes with a return to the initial pitch class", and are notated by George Perle using the letter "C", for cycle, with an interval-class integer to distinguish the interval. Thus the diminished-seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle.


title: Interval (music)

text: As shown below, some of the above-mentioned intervals have alternative names, and some of them take a specific alternative name in Pythagorean tuning, five-limit tuning, or meantone temperament tuning systems such as quarter-comma meantone. All the intervals with prefix "sesqui-" are justly tuned, and their frequency ratio, shown in the table, is a superparticular number (or epimoric ratio). The same is true for the octave.


title: Interval (music)

text: Typically, a comma is a diminished second, but this is not always true (for more details, see Alternative definitions of comma). For instance, in Pythagorean tuning the diminished second is a descending interval (524288:531441, or about −23.5 cents), and the Pythagorean comma is its opposite (531441:524288, or about 23.5 cents). 5-limit tuning defines four kinds of comma, three of which meet the definition of diminished second, and hence are listed in the table below. The fourth one, called syntonic comma (81:80) can neither be regarded as a diminished second, nor as its opposite. See Diminished seconds in 5-limit tuning for further details.


title: Interval (music)

text: Additionally, some cultures around the world have their own names for intervals found in their music. For instance, 22 kinds of intervals, called shrutis, are canonically defined in Indian classical music.


title: Interval (music)

text: Up to the end of the 18th century, Latin was used as an official language throughout Europe for scientific and music textbooks. In music, many English terms are derived from Latin. For instance, semitone is from Latin "".


title: Interval (music)

text: The prefix semi- is typically used herein to mean "shorter", rather than "half". Namely, a semitonus, semiditonus, semidiatessaron, semidiapente, semihexachordum, semiheptachordum, or semidiapason, is shorter by one semitone than the corresponding whole interval. For instance, a semiditonus (3 semitones, or about 300 cents) is not half of a ditonus (4 semitones, or about 400 cents), but a ditonus shortened by one semitone. Moreover, in Pythagorean tuning (the most commonly used tuning system up to the 16th century), a semitritonus (d5) is smaller than a tritonus (A4) by one Pythagorean comma (about a quarter of a semitone).


title: Interval (music)

text: Intervals in non-diatonic scales can be named using analogs of the diatonic interval names, by using a diatonic interval of similar size and distinguishing it by varying the quality, or by adding other modifiers. For example, the just interval 7/6 may be referred to as a "subminor third", since it is ~267 cents wide, which is narrower than a minor third (300 cents in 12-TET, ~316 cents for the just interval 6/5), or as the "septimal minor third", since it is a 7-limit interval. These names refer just to the individual interval's size, and the interval number need not correspond to the number of scale degrees of a (heptatonic) scale. This naming is particularly common in just intonation and microtonal scales.


title: Interval (music)

text: The most common of these extended qualities are a neutral interval, in between a minor and major interval; and subminor and supermajor intervals, respectively narrower than a minor or wider than a major interval. The exact size of such intervals depends on the tuning system, but they often vary from the diatonic interval sizes by about a quarter tone (50 cents, half a chromatic step). For example, the neutral second, the characteristic interval of Arabic music, in 24-TET is 150 cents, exactly halfway between a minor second and major second. Combined, these yield the progression "diminished, subminor, minor, neutral, major, supermajor, augmented" for seconds, thirds, sixths, and sevenths. This naming convention can be extended to unisons, fourths, fifths, and octaves with "sub" and "super", yielding the progression "diminished, sub, perfect, super, augmented". This allows one to name all intervals in 24-TET or 31-TET, the latter of which was used by Adriaan Fokker. Various further extensions are used in Xenharmonic music.


title: Interval (music)

text: In post-tonal or atonal theory, originally developed for equal-tempered European classical music written using the twelve-tone technique or serialism, integer notation is often used, most prominently in musical set theory. In this system, intervals are named according to the number of half steps, from 0 to 11, the largest interval class being 6.


title: Interval (music)

text: In atonal or musical set theory, there are numerous types of intervals, the first being the ordered pitch interval, the distance between two pitches upward or downward. For instance, the interval from C upward to G is 7, and the interval from G downward to C is −7. One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, somewhat similar to the interval of tonal theory.


title: Interval (music)

text: The interval between pitch classes may be measured with ordered and unordered pitch-class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. For unordered pitch-class intervals, see interval class.


title: Interval (music)

text: In diatonic set theory, specific and generic intervals are distinguished. Specific intervals are the interval class or number of semitones between scale steps or collection members, and generic intervals are the number of diatonic scale steps (or staff positions) between notes of a collection or scale.


title: Interval (music)

text: Notice that staff positions, when used to determine the conventional interval number (second, third, fourth, etc.), are counted including the position of the lower note of the interval, while generic interval numbers are counted excluding that position. Thus, generic interval numbers are smaller by 1, with respect to the conventional interval numbers.


title: Interval (music)

text: The term "interval" can also be generalized to other music elements besides pitch. David Lewin's "Generalized Musical Intervals and Transformations" uses interval as a generic measure of distance between time points, timbres, or more abstract musical phenomena.


title: Interval (music)

text: For example, an interval between two bell-like sounds, which have no pitch salience, is still perceptible. When two tones have similar acoustic spectra (sets of partials), the interval is just the distance of the shift of a tone spectrum along the frequency axis, so linking to pitches as reference points is not necessary. The same principle naturally applies to pitched tones (with similar harmonic spectra), which means that intervals can be perceived "directly" without pitch recognition. This explains in particular the predominance of interval hearing over absolute pitch hearing.


title: University of Glasgow

text: The University of Glasgow (abbreviated as Glas. in post-nominals; ) is a public research university in Glasgow, Scotland. Founded by papal bull in , it is the fourth-oldest university in the English-speaking world and one of Scotland's four ancient universities. Along with the universities of Edinburgh, Aberdeen, and St Andrews, the university was part of the Scottish Enlightenment during the 18th century.


title: University of Glasgow

text: In common with universities of the pre-modern era, Glasgow originally educated students primarily from wealthy backgrounds; however, it became a pioneer in British higher education in the 19th century by also providing for the needs of students from the growing urban and commercial middle class. Glasgow University served all of these students by preparing them for professions: law, medicine, civil service, teaching, and the church. It also trained smaller but growing numbers for careers in science and engineering. The annual income of the institution for 2020–21 was £809.4 million of which £173.3 million was from research grants and contracts, with an expenditure of £693.1 million. It is a member of Universitas 21, the Russell Group and the Guild of European Research-Intensive Universities.


title: University of Glasgow

text: The university was originally located in the city's High Street; since 1870, its main campus has been at Gilmorehill in the City's West End. Additionally, a number of university buildings are located elsewhere, such as the Veterinary School in Bearsden, and the Crichton Campus in Dumfries.


title: University of Glasgow

text: High educational standards, high entry standards (3rd highest in the UK) and a strong international research reputation have made the university a competitive destination for students worldwide. Glasgow is a World Top 100 university so that the institution is positioned at the top 1% of world universities. More specifically, the University of Glasgow ranked 53rd and 67th globally in the 2020 CWTS Leiden and 2020 QS World University Ranking respectively, as well as placing nationally among the top 10 UK universities. According to the Research Excellence Framework (REF) 2014, 81% of the research achievements were rated as "internationally excellent" and achieved the 10th position on research volume in the United Kingdom. The university was awarded the "2020 THE University of the Year" in recognition of its contribution to reparative justice.


title: University of Glasgow

text: The alumni of the University of Glasgow include some of the major figures of modern history, including James Wilson, a signatory of the United States Declaration of Independence, 3 Prime Ministers of the United Kingdom (William Lamb, Henry Campbell-Bannerman and Bonar Law), 2 Scottish First Ministers (Nicola Sturgeon and Donald Dewar), economist Adam Smith, philosopher Francis Hutcheson, engineer James Watt, physicist Lord Kelvin, surgeon Joseph Lister along with 8 Nobel Prize laureates and numerous Olympic gold medallists, including the current chancellor, Dame Katherine Granger.


title: University of Glasgow

text: The University of Glasgow was founded in 1451 by a charter or papal bull from Pope Nicholas V, at the suggestion of King James II, giving Bishop William Turnbull, a graduate of the University of St Andrews, permission to add a university to the city's Cathedral. It is the second-oldest university in Scotland after St Andrews and the fourth-oldest in the English-speaking world. The universities of St Andrews, Glasgow, and Aberdeen were ecclesiastical foundations, while Edinburgh was a civic foundation. As one of the ancient universities of the United Kingdom, Glasgow is one of only eight institutions to award undergraduate master's degrees in certain disciplines.


title: University of Glasgow

text: The university has been without its original Bull since the mid-sixteenth century. In 1560, during the political unrest accompanying the Scottish Reformation, the then chancellor, Archbishop James Beaton, a supporter of the Marian cause, fled to France. He took with him, for safe-keeping, many of the archives and valuables of the cathedral and the university, including the Mace and the Bull. Although the Mace was sent back in 1590, the archives were not. Principal Dr. James Fall told the Parliamentary Commissioners of Visitation on 28 August 1690, that he had seen the Bull at the Scots College in Paris, together with the many charters granted to the university by the monarchs of Scotland from James II to Mary, Queen of Scots. The university enquired of these documents in 1738 but was informed by Thomas Innes and the superiors of the Scots College that the original records of the foundation of the university were not to be found. If they had not been lost by this time, they certainly went astray during the French Revolution when the Scots College was under threat. Its records and valuables were moved for safe-keeping out of the city of Paris. The Bull remains the authority by which the university awards degrees.


title: University of Glasgow

text: Teaching at the university began in the Chapter House of Glasgow Cathedral, subsequently moving to nearby Rottenrow, in a building known as the "Auld Pedagogy". The university was given of land belonging to the Black Friars (Dominicans) on High Street by Mary, Queen of Scots, in 1563. By the late 17th century its building centred on two courtyards surrounded by walled gardens, with a clock tower, which was one of the notable features of Glasgow's skyline—reaching in height—and a chapel adapted from the church of the former Dominican (Blackfriars) friary. Remnants of this Scottish Renaissance building, mainly parts of the main façade, were transferred to the Gilmorehill campus and renamed as the "Pearce Lodge", after Sir William Pearce, the shipbuilding magnate who funded its preservation. The Lion and Unicorn Staircase was also transferred from the old college site and is now attached to the Main Building.


title: University of Glasgow

text: John Anderson, while professor of natural philosophy at the university, and with some opposition from his colleagues, pioneered vocational education for working men and women during the Industrial Revolution. To continue this work in his will, he founded Anderson's College, which was associated with the university before merging with other institutions to become the University of Strathclyde in 1964.


title: University of Glasgow

text: In October 2014, the university court voted for the university to become the first academic institution in Europe to divest from the fossil fuel industry.


title: University of Glasgow

text: The university is currently spread over a few campuses. The main one is the Gilmorehill campus, in Hillhead. As well as this there is the Garscube Estate in Bearsden, housing the Veterinary School, Observatory, ship model basin and much of the university's sports facilities, the Dental School in the city center, the section of Mental Health and Well Being at Gartnavel Royal Hospital on Great Western Road, the Teaching and Learning Centre at the Queen Elizabeth University Hospital and the Crichton Campus in Dumfries (operated jointly by the University of Glasgow, the University of the West of Scotland and the Open University).


title: University of Glasgow

text: The Imaging Centre of Excellence (ICE) was opened at the Queen Elizabeth University Hospital on 29 March 2017, including a Clinical Innovation Zone spanning of collaboration space for researchers and industry.


title: University of Glasgow

text: The university's initial accommodation including Glasgow University Library was part of the complex of religious buildings in the precincts of Glasgow Cathedral. In 1460, the university received a grant of land from James, Lord Hamilton, on the east side of the High Street, immediately north of the Blackfriars Church, on which it had its home for the next four hundred years. In the mid-seventeenth century, the Hamilton Building was replaced with a very grand two-court building with a decorated west front facing the High Street, called the 'Nova Erectio', or New Building. This foundation is widely considered to have been one of the finest 17th-century buildings in Scotland. Decorated fragments from it, including a complete exterior stairway, were rescued and built into its 19th-century replacement. In Sir Walter Scott's best-selling 1817 novel "Rob Roy", set at the time of the Jacobite rising of 1715, the lead character fights a duel in the New Building grounds before the contest is broken up by Rob Roy MacGregor.


title: University of Glasgow

text: Over the following centuries, the university's size and scope continued to expand. In 1757 it built the Macfarlane Observatory and later Scotland's first public museum, the Hunterian. It was a center of the Scottish Enlightenment and subsequently of the Industrial Revolution, and its expansion in the High Street was constrained. The area around the university declined as well-off residents moved westwards with the expansion of the city and overcrowding of the immediate area by less well-off residents. It was this rapid slumming of the area that was a chief catalyst of the university's migration westward.


title: University of Glasgow

text: In 1870, the university moved to a (then greenfield) site on Gilmorehill in the West End of the city, around west of its previous location, enclosed by a large meander of the River Kelvin. The original site on the High Street was sold to the City of Glasgow Union Railway and replaced by the college goods yard. The new-build campus was designed by Sir George Gilbert Scott in the Gothic revival style. The largest of these buildings echoed, on a far grander scale, the original High Street campus's twin-quadrangle layout, and may have been inspired by Ypres' late-medieval cloth hall; Gilmorehill, in turn, inspired the design of the Clocktower complex of buildings for the new University of Otago in New Zealand. In 1879, Gilbert Scott's son, Oldrid, completed this original vision by building an open undercroft forming two quadrangles, above which is his grand Bute Hall (used for examinations and graduation ceremonies), named after its donor, John Crichton-Stuart, 3rd Marquess of Bute. Oldrid also later added a spire to the building's signature gothic bell tower in 1887, bringing it to a total height of some . The local Bishopbriggs blond sandstone cladding and Gothic design of the building's exterior belie the modernity of its Victorian construction; Scott's building is structured upon what was then a cutting-edge riveted iron frame construction, supporting a lightweight wooden-beam roof. The building also forms the second-largest example of Gothic revival architecture in Britain, after the Palace of Westminster. An illustration of the Main Building previously featured on the reverse side of £100 notes issued by Clydesdale Bank.


title: University of Glasgow

text: The university's Hunterian Museum resides in the Main Building, and the related Hunterian Gallery is housed in buildings adjacent to the University Library. The latter includes "The Mackintosh House", a rebuilt terraced house designed by, and furnished after, architect Charles Rennie Mackintosh.


title: University of Glasgow

text: Even these enlarged premises could not contain the expanding university, which quickly spread across much of Gilmorehill. The 1930s saw the construction of the award-winning round Reading Room (it is now a category-A listed building) and an aggressive program of house purchases, in which the university (fearing the surrounding district of Hillhead was running out of suitable building land) acquired several terraces of Victorian houses and joined them together internally. The departments of Psychology, Computing Science, and most of the Arts Faculty continue to be housed in these terraces.


title: University of Glasgow

text: More buildings were built to the west of the Main Building, developing the land between University Avenue and the River Kelvin with natural science buildings and the faculty of medicine. The medical school spread into neighboring Partick and joined with the Western Infirmary. At the eastern flank of the Main Building, the James Watt Engineering Building was completed in 1959. The growth and prosperity of the city, which had originally forced the university's relocation to Hillhead, again proved problematic when more real estate was required. The school of veterinary medicine, which was founded in 1862, moved to a new campus in the leafy surrounds of Garscube Estate, around west of the main campus, in 1954. The university later moved its sports ground and associated facilities to Garscube and also built student halls of residence in both Garscube and Maryhill.


title: University of Glasgow

text: The growth of tertiary education, as a result of the Robbins Report in the 1960s, led the university to build numerous modern buildings across Hillhead, including several brutalist concrete blocks: the Mathematics building; the Boyd Orr Building and the Adam Smith building (housing the Faculty of Law, Business and Social Sciences, named after university graduate Adam Smith). Other additions around this time, including the new glass-lined Glasgow University Library, Rankine Building for Civil Engineering (named for Macquorn Rankine), and the amber-brick Gregory Building (housing the Geology department), were more in keeping with Gilmorehill's leafy suburban architecture. The erection of these buildings in the late 1960s, however, involved the demolition of a large number of houses in Ashton Road and rerouting the west end of University Avenue to its current position. To cater to the expanding student population, a new refectory, known as the Hub, was opened adjacent to the library in 1966. The Glasgow University Union also had an extension completed in 1965 and the new Queen Margaret Union building opened in 1969.


title: University of Glasgow

text: In October 2001 the century-old Bower Building (previously home to the university's botany department) was gutted by fire. The interior and roof of the building were largely destroyed, though the main façade remained intact. After a £10.8 million refit, the building re-opened in November 2004.


title: University of Glasgow

text: The Wolfson Medical School Building, with its award-winning glass-fronted atrium, opened in 2002, and in 2003, the St Andrews Building was opened, housing the what is now the School of Education. It is sited a short walk from Gilmorehill, in the Woodlands area of the city on the site of the former Queens College, which had in turn been bought by Glasgow Caledonian University, from whom the university acquired the site. It replaced the St Andrews Campus in Bearsden. The university also procured the former Hillhead Congregational Church, converting it into a lecture theatre in 2005. The Sir Alwyn Williams building, designed by Reiach and Hall, was completed at Lilybank Terrace in 2007, housing the School of Computing Science.


title: University of Glasgow

text: In September 2016 in partnership with Glasgow City Council, Glasgow Life and the National Library of Scotland the transformed Kelvin Hall has been brought into new public use including in Phase I the Hunterian Collections and Study Centre.


title: University of Glasgow

text: The university is investing £1 billion to expand its campus now that it has acquired what was formerly known as the Western Infirmary.


title: University of Glasgow

text: The University Chapel was constructed as a memorial to the 755 sons of the university who had died in the First World War. Designed by Sir John Burnet, it was completed in 1929 and dedicated on 4 October. Tablets on the wall behind the Communion Table list the names of those who died, while other tablets besides the stalls record the 405 members of the university community who gave their lives in the Second World War. Most of the windows are the work of Douglas Strachan, although some have been added over the years, including those on the South Wall, created by Alan Younger.


title: University of Glasgow

text: Daily services are held in the chapel during term-time, as well as seasonal events. Before Christmas, there is a Service of Nine Lessons and Carols on the last Sunday of term, and a Watchnight service on Christmas Eve. Graduates, students, members of staff, and the children of members of staff are entitled to be married in the chapel, which is also used for baptisms and funerals. Civil marriages and civil partnerships may be blessed in the chapel, although under UK law may not be performed there.


title: University of Glasgow

text: The current chaplain of the university is the Reverend Stuart MacQuarrie, and the university appoints honorary chaplains of other denominations.


title: University of Glasgow

text: The University Library, situated on Hillhead Street opposite the Main Building, is one of the oldest and largest libraries in Europe. Situated over 12 floors, it hosts more than three million books and journals, as well as providing access to an extensive range of electronic resources including over 51,900 electronic journals. It also houses sections for periodicals, microfilms, special collections and rare materials. Open between 7 a.m. and 2 a.m., 361 days of the year, the library provides a resource not only for the academic community.


title: University of Glasgow

text: In addition to the main library, subject libraries also exist for Medicine, Chemistry, Dental Medicine, Veterinary Medicine, Education, Law, History of Art, and the faculty of Social Sciences, which are held in branch libraries around the campus. In 2007, a state-of-the-art section to house the library's collection of historic photographs was opened, funded by the Wolfson Foundation.


title: University of Glasgow

text: The Archives of the University of Glasgow is the central place of deposit for the records of the university, created and accumulated since its foundation in 1451.


title: University of Glasgow

text: The university opened the Crichton campus in Dumfries, Dumfries and Galloway during the 1980s. It was designed to meet the needs for tertiary education in an area far from major cities and is operated jointly by the University of Glasgow, the University of the West of Scotland and the Open University. It offers a modular undergraduate curriculum, leading to one of a small number of liberal arts degrees, as well as providing the region's only access to postgraduate study.


title: University of Glasgow

text: As well as these teaching campuses the university has halls of residence in and around the North-West of the city, accommodating a total of approximately 3,500 students. These include the Murano Street halls in Maryhill; Wolfson halls on the Garscube Estate; Queen Margaret halls, in Kelvinside; Cairncross House and Kelvinhaugh Gate, in Yorkhill. In recent years, Dalrymple House and Horslethill halls in Dowanhill, Reith halls in North Kelvinside and the Maclay halls in Park Circus (near Kelvingrove Park), have closed and been sold, as the development value of such property increased.


title: University of Glasgow

text: The Stevenson Building on Gilmorehill opened in 1961 and provides students with the use of a fitness suite, squash courts, sauna, and six-lane, 25-metre swimming pool. The university also has a large sports complex on the Garscube Estate, besides their Wolfson Halls and Vet School. This is a new facility, replacing the previous "Westerlands" sports ground in the Anniesland area of the city. The university also has use of half of the East Boathouse situated at Glasgow Green on the River Clyde where Glasgow University Boat Club train.


title: University of Glasgow

text: In common with the other ancient universities of Scotland the university's constitution is laid out in the Universities (Scotland) Acts. These Acts create a tripartite structure of bodies: the University Court (governing body), the Academic Senate (academic affairs), and the General Council (advisory). There is also a clear separation between governance and executive administration.


title: University of Glasgow

text: The university's constitution, academic regulations, and appointments are described in the university calendar, while other aspects of its story and constitution are detailed in a separate "history" document.


title: University of Glasgow

text: There are several officers of the university. The role of each involves the management of the operations of Glasgow.


title: University of Glasgow

text: The Chancellor is the titular head of the university and President of the General Council. They award all degrees, although this duty is generally carried out by the Vice-Chancellor, appointed by them.


title: University of Glasgow

text: The current Chancellor is Dame Katherine Grainger, a former rower who is Britain's most decorated female Olympian, the current chair of UK Sport, and former Chancellor of Oxford Brookes University. She is an alumna of the university, with a Master of Philosophy (MPhil) in Medical Law and Medical Ethics. She is the first woman to hold the office in the university.


title: University of Glasgow

text: All students at the university are eligible to vote in the election of the Rector (officially styled "Lord Rector"), who holds office for a three-year term and chairs the University Court. In the past, this position has been a largely honorary and ceremonial one, and has been held by political figures including William Gladstone, Benjamin Disraeli, Bonar Law, Robert Peel, Raymond Poincaré, Arthur Balfour, Charles Kennedy and 1970s union activist Jimmy Reid, and latterly by celebrities such as TV presenters Arthur Montford and Johnny Ball, musician Pat Kane, and actors Richard Wilson, Ross Kemp and Greg Hemphill. In 2004, for the first time in its history, the university was left without a Rector as no nominations were received. When the elections were run in December, Mordechai Vanunu was chosen for the post, even though he was unable to attend due to restrictions placed upon him by the Israeli government. In 2014, Edward Snowden, an American computer specialist, a former Central Intelligence Agency (CIA) employee, and former National Security Agency (NSA) contractor—who came to international attention when he disclosed a large number of classified NSA documents to several media outlets—was elected. In 2017, Aamer Anwar a Scottish lawyer and former student of the university was elected rector until 2020 when rector elections had to be postponed due to the COVID-19 pandemic. On April 21, 2021, Rita Rae, Lady Rae a Scottish lawyer, judge and former Senator of the College of Justice was appointed Rector after a decisive victory.


title: University of Glasgow

text: Day-to-day management of the university is undertaken by the University Principal (who is also Vice-Chancellor). The current principal is Sir Anton Muscatelli who replaced Sir Muir Russell in October 2009.


title: University of Glasgow

text: There are also several Vice-Principals, each with a specific remit. They, along with the Clerk of Senate, play a major role in the day-to-day management of the university.


title: University of Glasgow

text: The governing body of the university is the University Court, which is responsible for contractual matters, employing staff, and all other matters relating to finance and administration. The Court takes decisions about the deployment of resources as well as formulating strategic plans for the university. The Court is chaired by the Rector, who is elected by all the matriculated students at the university. The University Secretary is the Head of University Services and assists the Principal in day-to-day management. The current University Secretary is David Duncan.


title: University of Glasgow

text: The Academic Senate (or University Senate) is the body which is responsible for the management of academic affairs, and which recommends the conferment of degrees by the Chancellor. Membership of the Senate comprises all Professors of the university, as well as elected academic members, representatives of the Student's Representative Council, the Secretary of Court and directors of university services (e.g. Library). The President of the Senate is the principal.


title: University of Glasgow

text: The Clerk of Senate, who has a status equivalent to that of a Vice-Principal and is a member of the Senior Management Group, has responsibility for regulation of the university's academic policy, such as dealing with plagiarism and the conduct of examinations. Notable Clerks of Senate have included the chemist, Joseph Black; John Anderson, father of the University of Strathclyde; and the economist, John Millar.


title: University of Glasgow

text: There are also a number of committees of both the Court and Senate that make important decisions and investigate matters referred to them. As well as these bodies there is a General Council made up of the university graduates that is involved in the running of the university. The graduates also elect the Chancellor of the university.


title: University of Glasgow

text: At the university's foundation in 1451, there were four original faculties: Arts, Divinity, Law, and Medicine. The Faculty of Divinity became a constituent school of the Faculty of Arts in 2002, while the Faculty of Law was changed in 1984 into the Faculty of Law and Financial Studies, and in 2005 became the Faculty of Law, Business and Social Sciences. Although one of the original faculties established, teaching in the Faculty of Medicine did not begin formally until 1714, with the revival of the Chair in the Practice of Medicine. The Faculty of Science was formed in 1893 from Chairs removed from the Faculties of Arts and Medicine, and subsequently divided in 2000 to form the three Faculties of Biomedical and Life Sciences, Computing Science, Mathematics and Statistics (now Information and Mathematical Sciences) and Physical Sciences. The Faculty of Social Sciences was formed from Chairs in the Faculty of Arts in 1977, and merged to form the Faculty of Law, Business and Social Sciences in 2005, the two having operated as a single 'resource unit' since 2002. The Faculty of Engineering was formally established in 1923, although engineering had been taught at the university since 1840 when Queen Victoria founded the UK's first Chair of Engineering. Through a concordat ratified in 1913, Royal Technical College (later Royal College of Science and Technology and now University of Strathclyde) students received Glasgow degrees in applied sciences, particularly engineering. It was in 1769 when James Watt's engineering at Glasgow led to a stable steam engine and, subsequently, the Industrial Revolution. The Faculty of Veterinary Medicine was established in 1862 as the independent Glasgow Veterinary College, being subsumed into the university in 1949 and gaining independent Faculty status in 1969. The Faculty of Education was formed when the university merged with St Andrew's College of Education in 1999.


title: University of Glasgow

text: On 1 August 2010, the former faculties of the university were removed and replaced by a system of four larger Colleges, intended to encourage interdisciplinary research and make the university more competitive. This structure was similar to that at other universities, including the University of Edinburgh.


title: University of Glasgow

text: The university generates a total income of over £450 million per year, amongst the top 10 in the UK. The university is a member of the Russell Group of research-led British universities and was a founding member of the organisation, Universitas 21, an international grouping of universities dedicated to setting worldwide standards for higher education. The university currently has fifteen Regius Professorships, more than in any other UK university.


title: University of Glasgow

text: In the QS World University Rankings Glasgow climbed from 59th overall in 2011 to 54th in 2012, then to 51st in 2013.


title: University of Glasgow

text: Glasgow places within the top 20 in the UK and 3rd in Scotland for the employability of its graduates as ranked by recruiters from the UK's major companies.


title: University of Glasgow

text: In the 2008 Research Assessment Exercise (RAE), almost 70% of research carried out at the university was in the top two categories (88% in the top three categories). Eighteen subject areas were rated top ten in the UK, whilst fourteen subject areas were rated the best in Scotland. The 2008 Times RAE table ranks according to an 'average' score across all departments, of which Glasgow posted an average of 2.6/4. The overall average placed Glasgow as the thirty-third-highest of all UK universities, perhaps reflecting the broadness of the university's activities. In terms of research 'power', however, Glasgow placed fourteenth in the UK and second in Scotland.


title: University of Glasgow

text: As of , the university had undergraduate and postgraduate students. Glasgow has a large (for the UK) proportion of "home" students, with almost 40 per cent of the student body coming from the West of Scotland. In the 2016–17 academic year, the university had a domicile breakdown of 71:11:18 of UK:EU:non-EU students, respectively, with a female-to-male ratio of 59:41.


title: University of Glasgow

text: For undergraduate entry, course requirements range from A*A*A* (for second year entry) to BBB (for minimum requirements for Primary Teaching) in A-levels. Glasgow had the 23rd highest average entry qualification for undergraduates of any UK university in 2015, with new students averaging 420 UCAS points, equivalent to ABBbb in A-level grades.


title: University of Glasgow

text: Scottish and EU students, with the exception of students from the Channel Islands, England, Northern Ireland and Wales, do not pay tuition fees. As the number of places available for Scottish and EU students are capped by the Scottish Government, students applying from the rest of the UK and outside of the European Union have a higher likelihood of an offer. For most courses, with the exceptions of Medicine, Dentistry, Veterinary Medicine and Law, the university guarantees unconditional offers to applicants who have achieved AAAA or AAABB in one sitting at Scottish Highers. The other components of the applicant's UCAS form (such as predicted grades and the personal statement) are only taken into account if the applicant has not achieved these grades.


title: University of Glasgow

text: The University of Glasgow was the first university in Europe to divest from fossil fuel companies in October 2014. The 12-month campaign was led by the Glasgow University Climate Action Society and involved over 1,300 students.


title: University of Glasgow

text: Unlike other universities in Scotland, Glasgow does not have a single students' association; instead, there exist a number of bodies concerned with the representation, welfare, and entertainment of its students. Due to the university's retention of its separate male and female students' unions, which since 1980 have admitted both sexes as full members, there are two independent students' unions, as well as a sports association and the students' representative council. None of these are affiliated to the National Union of Students: membership has been rejected on a number of occasions, most recently in November 2006, on both economic and political grounds. A student-run "No to NUS" campaign won a campuswide referendum with more than 90% of the vote.


title: University of Glasgow

text: The university has an eclectic body of clubs and societies, including sports teams, political and religious groups, and gaming societies.


title: University of Glasgow

text: Glasgow University Students' Representative Council is the legal representative body for students, as recognized by the Universities (Scotland) Act 1889. The SRC is responsible for representing students' interests to the management of the university, to local and national government, and for health and welfare issues. Under the Universities (Scotland) Acts, all students of the university automatically become members of the SRC; however, they are entitled to opt-out of this. Members of the SRC sit on various committees throughout the university, from the departmental level to the Senate and Court.


title: University of Glasgow

text: The SRC organizes Media Week, RAG (Raising And Giving) Week, and Welfare Week, as well as funding some 130 clubs and societies.


title: University of Glasgow

text: In addition to the Students' Representative Council, students are commonly members of one of the university's two students' unions, the Glasgow University Union (GUU) and the Queen Margaret Union (QMU). Unlike many other student unions in the UK, membership to either GUU or QMU is not automatic and students must apply, for free, to become a member of either. Students are also permitted to be a member of both. These are largely social and cultural institutions, providing their members with facilities for debating, dining, recreation, socializing, and drinking, and both have a number of meeting rooms available for rental to members. Postgraduate students, mature students and staff were previously able to join the Hetherington Research Club; however, large debts led to the club being closed in February 2010. However, in February 2011, students gained access to the old HRC building, situated at 13 University Gardens (Hetherington House) and "reopened" it as the Free Hetherington, a social centre for learning and lectures, as well as protesting the shutting down of the club. Attempts to evict this occupation resulted in complaints of heavy-handed policing and much controversy on campus.


title: University of Glasgow

text: The separate unions exist due to the university's previous male-only status; the GUU was founded before the admission of women, while the QMU was originally the union of Queen Margaret College, a women-only college which merged with the university in 1892. Their continued separate existence is due largely to their individual atmospheres. The GUU's focus is mainly towards people involved in sports and debates (as among its founders were the Athletic Association and Dialectic Society), the QMU is one of Glasgow's music venues, and has played host to Nirvana, Red Hot Chili Peppers, Biffy Clyro and Franz Ferdinand.


title: University of Glasgow

text: In 1955, the GUU won the Observer Mace, now the John Smith Memorial Mace, named after the deceased GUU debater and former leader of the British Labour Party. The GUU has since won the mace debating championship fourteen more times, more than any other university. The GUU has also won the World Universities Debating Championships five times, more than any other university or club in the series' history.


title: University of Glasgow

text: Sporting affairs are regulated by the Glasgow University Sports Association (GUSA) (previously the Glasgow University Athletics Club) which works closely with the Sport and Recreation Service. There are a large number of varied clubs, including Squash, Gaelic Football, Basketball, Cycling, Football, Hockey, Netball, Martial Arts and Rowing, who regularly compete in BUCS competitions. Students who join one of the sports clubs affiliated with the university must also join GUSA. However, there are also regular classes and drop-in sessions for various sports which are non-competitive and available to all university gym members.


title: University of Glasgow

text: The community of mature students—that is those students aged 21 or over—are served by the Mature Students' Association located at 62 Oakfield Avenue. The MSA aims are to provide all mature students with facilities for recreation and study. Throughout the year, the MSA also organizes social events and peer support for the wide range of subjects studied by the university's mature students.