18 Steps
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18 Steps
''18 Steps'' is an EP by rock artist Trey Anastasio. It was released in 2006 on Rubber Jungle Records. It was included as a bonus with pre-orders of ''Bar 17'' from his official website. The disc contains nine new songs, which are outtakes from ''Bar 17''. Like the tracks on ''Bar 17'', the tunes featured on ''18 Steps'' were recorded over roughly a three-year period, from the spring of 2003 to the summer of 2006. ''18 Steps'' can be found in select independent record stores, online auctions, and is still available for download via LivePhish. Album cover David Steinberg (aka "Zzyzx") contributed the mathematical expression for the cover. He briefly explains it on Tom Marshall's podcasepisode 4 and mentions it includes stirling numbers, phi Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet. In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated ...
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Trey Anastasio
Ernest Joseph "Trey" Anastasio III (born September 30, 1964) is an American guitarist, singer, and songwriter, best known as the lead guitarist of the rock band Phish, which he co-founded in 1983. He is credited by name as composer of 152 Phish original songs, 141 of them as a solo credit, in addition to 41 credits attributed to the band as a whole. In addition to his work with Phish, Anastasio has released 11 solo albums, and been part of several side projects including the Trey Anastasio Band, Oysterhead, Ghosts of the Forest, Phil Lesh and Friends, and Surrender to the Air. He has performed his own compositions with the New York Philharmonic, the Los Angeles Philharmonic, the Baltimore Symphony Orchestra, the Atlanta Symphony Orchestra, the National Symphony Orchestra, and many others. With Amanda Green, he wrote the score for the Broadway musical ''Hands on a Hardbody (musical), Hands on a Hardbody''. In 2013, they were nominated for a Tony Award for Best Original Score at t ...
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United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territories, nine Minor Outlying Islands, and 326 Indian reservations. The United States is also in free association with three Pacific Island sovereign states: the Federated States of Micronesia, the Marshall Islands, and the Republic of Palau. It is the world's third-largest country by both land and total area. It shares land borders with Canada to its north and with Mexico to its south and has maritime borders with the Bahamas, Cuba, Russia, and other nations. With a population of over 333 million, it is the most populous country in the Americas and the third most populous in the world. The national capital of the United States is Washington, D.C. and its most populous city and principal financial center is New York City. Paleo-Americ ...
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Rock Music
Rock music is a broad genre of popular music that originated as " rock and roll" in the United States in the late 1940s and early 1950s, developing into a range of different styles in the mid-1960s and later, particularly in the United States and United Kingdom.W. E. Studwell and D. F. Lonergan, ''The Classic Rock and Roll Reader: Rock Music from its Beginnings to the mid-1970s'' (Abingdon: Routledge, 1999), p.xi It has its roots in 1940s and 1950s rock and roll, a style that drew directly from the blues and rhythm and blues genres of African-American music and from country music. Rock also drew strongly from a number of other genres such as electric blues and folk, and incorporated influences from jazz, classical, and other musical styles. For instrumentation, rock has centered on the electric guitar, usually as part of a rock group with electric bass guitar, drums, and one or more singers. Usually, rock is song-based music with a time signature using a verse–chorus form, ...
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Rubber Jungle Records
Rubber Jungle Records is an independent record label created by Phish frontman Trey Anastasio. It was started by Anastasio to release his album ''One Man's Trash''. The label released Anastasio's ''The Horseshoe Curve'' on July 24, 2007, and the live album '' Original Boardwalk Style'' on June 10, 2008. See also * List of record labels File:Alvinoreyguitarboogie.jpg File:AmMusicBunk78.jpg File:Bingola1011b.jpg Lists of record labels cover record labels, brands or trademarks associated with marketing of music recordings and music videos. The lists are organized alphabetically, b ... References Record labels established in 1998 American independent record labels Rock record labels Vanity record labels Companies based in Burlington, Vermont {{US-independent-record-label-stub ...
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Bryce Goggin
Bryce Goggin is an American record producer and sound engineer. His career began in the early 1990s, working at Baby Monster Studios. He first received note for mixing the album ''Crooked Rain, Crooked Rain'' by Pavement. He has since worked with a number of musicians including The Apples in Stereo, Luna, Swans, Evan Dando, Sean Lennon, Sebadoh, Come, Spacehog, Ramones, The Morning Glories, Band of Susans, Grand Avenue, Phish, Akron Family, The Spring Standards, Lucibel Crater, Skeleton Key, Bettie Serveert, and cabaret pop group Antony and the Johnsons Antony and the Johnsons is an American music group presenting the work of Anohni and her collaborators. Career British experimental musician David Tibet of Current 93 heard a demo and offered to release Anohni's music through his Durtro label .... In 2013, he mixed "This Tree" by Leah Coloff, one of the first releases in interactive Gralbum format. He won an Independent Music Award, along with Kenny Siegal and Brian Gelt ...
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Bar 17
''Bar 17'' is Trey Anastasio's fifth solo studio album. It was the first release from his newly formed record label, Rubber Jungle Records. Work began on ''Bar 17'' shortly after the breakup of Phish, but had to temporarily suspend the project due to the absence of producer Bryce Goggin. During the long hiatus in the middle of the album's production, Anastasio flew to Atlanta to record his 2005 album '' Shine'', which was very pop-oriented and different from Anastasio's normal musical style. ''Bar 17'' contains songs written over roughly three years by Anastasio, from the spring of 2003 to the spring of 2006. The album features contributions by a greatly varied cast of musicians including Phish bandmates Mike Gordon and Jon Fishman as well as the Benevento/Russo Duo and John Medeski. The album credits a total of 42 musicians as performing on various tracks. The first single released from the album is ''Dragonfly'', recorded with Mike Gordon and the Benevento/Russo Duo. Unlik ...
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Live In New York City 12-31-05
''Live in New York City 12-31-05'' is an EP by Trey Anastasio that was bundled with select CD copies of ''Shine'' at Tower Records during 2006. The disc features tracks from a live concert at Madison Square Garden in New York City on New Year's Eve 2005, where Anastasio and his band opened for The Black Crowes The Black Crowes are an American rock band formed in Atlanta, Georgia, in 1984. Their discography includes eight studio albums, four live albums and several charting singles. The band was signed to Def American Recordings in 1989 by producer Geo .... Track listing # Sand - 11:03 # Tuesday - 7:22 # Plasma - 5:11 # Money, Love and Change - 20:33 # Come As Melody - 6:55 {{Trey Anastasio 2006 EPs Trey Anastasio EPs 2006 live albums Live EPs Albums recorded at Madison Square Garden ...
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Tom Marshall (singer)
Tom Marshall is an American lyricist, keyboardist and singer-songwriter best known for his association with Trey Anastasio and the rock band Phish. He has been the primary external lyricist for Phish during their career (1983–2004, 2009–present), with songwriting credits for more than 95 originals. In addition to his songwriting work, Marshall also fronts the rock band Amfibian and hosts the Phish podcast ''Under the Scales''. Marshall is the co-founder of Osiris, a podcast network in partnership with Jambase. Personal life Marshall attended Princeton Day School in New Jersey with Anastasio. The duo began writing songs together as early as the eighth grade (the reggae tune "Makisupa Policeman" is often regarded as the duo's first collaboration and the very first Phish original song). Other early collaborations include ''Bivouac Jaun'', a project recorded by Marshall, Anastasio, and their friend Marc Daubert (who occasionally played percussion with Phish in 1984 and wrote t ...
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Stirling Numbers Of The First Kind
In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to their number of cycles (counting fixed points as cycles of length one). The Stirling numbers of the first and second kind can be understood as inverses of one another when viewed as triangular matrices. This article is devoted to specifics of Stirling numbers of the first kind. Identities linking the two kinds appear in the article on Stirling numbers in general. Definitions The original definition of Stirling numbers of the first kind was algebraic: they are the coefficients s(n,k) in the expansion of the falling factorial :(x)_n = x(x-1)(x-2)\cdots(x-n+1) into powers of the variable x: :(x)_n = \sum_^n s(n,k) x^k, For example, (x)_3 = x(x-1)(x - 2) = 1x^3 - 3x^2 + 2x, leading to the values s(3, 3) = 1, s(3, 2) = -3, and s(3, 1) = 2. Subsequently, it was discovered that th ...
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Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( or \phi) denotes the golden ratio. The constant \varphi satisfies the quadratic equation \varphi^2 = \varphi + 1 and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of \varphi—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural object ...
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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance. For a long time, the idea that such a potentially infinite summation could produce a finite result was considered paradoxical. This paradox was resolved using the concept of a limit during the 17th century. Zeno's paradox of Achilles and the tortoise illustrates this counterintuitive property of infinite sums: Achilles runs after a tortoise, but when he reaches the position of the tortoise at the beginning of ...
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2006 EPs
6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number. In mathematics Six is the smallest positive integer which is neither a square number nor a prime number; it is the second smallest composite number, behind 4; its proper divisors are , and . Since 6 equals the sum of its proper divisors, it is a perfect number; 6 is the smallest of the perfect numbers. It is also the smallest Granville number, or \mathcal-perfect number. As a perfect number: *6 is related to the Mersenne prime 3, since . (The next perfect number is 28.) *6 is the only even perfect number that is not the sum of successive odd cubes. *6 is the root of the 6-aliquot tree, and is itself the aliquot sum of only one other number; the square number, . Six is the only number that is both the sum and the product of three consecutive positive numbers. Unrelated to 6's being a perfect number, a Golomb ruler of length 6 is a "perfect ruler". Six is a con ...
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