title: Music and mathematics

text: Without the boundaries of rhythmic structure – a fundamental equal and regular arrangement of pulse repetition, accent, phrase and duration – music would not be possible. Modern musical use of terms like meter and measure also reflects the historical importance of music, along with astronomy, in the development of counting, arithmetic and the exact measurement of time and periodicity that is fundamental to physics.


title: Music and mathematics

text: The elements of musical form often build strict proportions or hypermetric structures (powers of the numbers 2 and 3).


title: Music and mathematics

text: Musical form is the plan by which a short piece of music is extended. The term "plan" is also used in architecture, to which musical form is often compared. Like the architect, the composer must take into account the function for which the work is intended and the means available, practicing economy and making use of repetition and order. The common types of form known as binary and ternary ("twofold" and "threefold") once again demonstrate the importance of small integral values to the intelligibility and appeal of music.


title: Music and mathematics

text: A musical scale is a discrete set of pitches used in making or describing music. The most important scale in the Western tradition is the diatonic scale but many others have been used and proposed in various historical eras and parts of the world. Each pitch corresponds to a particular frequency, expressed in hertz (Hz), sometimes referred to as cycles per second (c.p.s.). A scale has an interval of repetition, normally the octave. The octave of any pitch refers to a frequency exactly twice that of the given pitch.


title: Music and mathematics

text: Succeeding superoctaves are pitches found at frequencies four, eight, sixteen times, and so on, of the fundamental frequency. Pitches at frequencies of half, a quarter, an eighth and so on of the fundamental are called suboctaves. There is no case in musical harmony where, if a given pitch be considered accordant, that its octaves are considered otherwise. Therefore, any note and its octaves will generally be found similarly named in musical systems (e.g. all will be called doh or A or Sa, as the case may be).


title: Music and mathematics

text: When expressed as a frequency bandwidth an octave A–A spans from 110 Hz to 220 Hz (span=110 Hz). The next octave will span from 220 Hz to 440 Hz (span=220 Hz). The third octave spans from 440 Hz to 880 Hz (span=440 Hz) and so on. Each successive octave spans twice the frequency range of the previous octave.


title: Music and mathematics

text: Because we are often interested in the relations or ratios between the pitches (known as intervals) rather than the precise pitches themselves in describing a scale, it is usual to refer to all the scale pitches in terms of their ratio from a particular pitch, which is given the value of one (often written 1/1), generally a note which functions as the tonic of the scale. For interval size comparison, cents are often used.


title: Music and mathematics

text: There are two main families of tuning systems: equal temperament and just tuning. Equal temperament scales are built by dividing an octave into intervals which are equal on a logarithmic scale, which results in perfectly evenly divided scales, but with ratios of frequencies which are irrational numbers. Just scales are built by multiplying frequencies by rational numbers, which results in simple ratios between frequencies, but with scale divisions that are uneven.


title: Music and mathematics

text: One major difference between equal temperament tunings and just tunings is differences in acoustical beat when two notes are sounded together, which affects the subjective experience of consonance and dissonance. Both of these systems, and the vast majority of music in general, have scales that repeat on the interval of every octave, which is defined as frequency ratio of 2:1. In other words, every time the frequency is doubled, the given scale repeats.


title: Music and mathematics

text: Below are Ogg Vorbis files demonstrating the difference between just intonation and equal temperament. You might need to play the samples several times before you can detect the difference.


title: Music and mathematics

text: 5-limit tuning, the most common form of just intonation, is a system of tuning using tones that are regular number harmonics of a single fundamental frequency. This was one of the scales Johannes Kepler presented in his Harmonices Mundi (1619) in connection with planetary motion. The same scale was given in transposed form by Scottish mathematician and musical theorist, Alexander Malcolm, in 1721 in his 'Treatise of Musick: Speculative, Practical and Historical', and by theorist Jose Wuerschmidt in the 20th century. A form of it is used in the music of northern India.


title: Music and mathematics

text: American composer Terry Riley also made use of the inverted form of it in his "Harp of New Albion". Just intonation gives superior results when there is little or no chord progression: voices and other instruments gravitate to just intonation whenever possible. However, it gives two different whole tone intervals (9:8 and 10:9) because a fixed tuned instrument, such as a piano, cannot change key. To calculate the frequency of a note in a scale given in terms of ratios, the frequency ratio is multiplied by the tonic frequency. For instance, with a tonic of A4 (A natural above middle C), the frequency is 440 Hz, and a justly tuned fifth above it (E5) is simply 440×(3:2) = 660 Hz.


title: Music and mathematics

text: Pythagorean tuning is tuning based only on the perfect consonances, the (perfect) octave, perfect fifth, and perfect fourth. Thus the major third is considered not a third but a ditone, literally "two tones", and is (9:8) = 81:64, rather than the independent and harmonic just 5:4 = 80:64 directly below. A whole tone is a secondary interval, being derived from two perfect fifths minus an octave, (3:2)/2 = 9:8.


title: Music and mathematics

text: The just major third, 5:4 and minor third, 6:5, are a syntonic comma, 81:80, apart from their Pythagorean equivalents 81:64 and 32:27 respectively. According to Carl , "the dependent third conforms to the Pythagorean, the independent third to the harmonic tuning of intervals."


title: Music and mathematics

text: Western common practice music usually cannot be played in just intonation but requires a systematically tempered scale. The tempering can involve either the irregularities of well temperament or be constructed as a regular temperament, either some form of equal temperament or some other regular meantone, but in all cases will involve the fundamental features of meantone temperament. For example, the root of chord ii, if tuned to a fifth above the dominant, would be a major whole tone (9:8) above the tonic. If tuned a just minor third (6:5) below a just subdominant degree of 4:3, however, the interval from the tonic would equal a minor whole tone (10:9). Meantone temperament reduces the difference between 9:8 and 10:9. Their ratio, (9:8)/(10:9) = 81:80, is treated as a unison. The interval 81:80, called the syntonic comma or comma of Didymus, is the key comma of meantone temperament.


title: Music and mathematics

text: In equal temperament, the octave is divided into equal parts on the logarithmic scale. While it is possible to construct equal temperament scale with any number of notes (for example, the 24-tone Arab tone system), the most common number is 12, which makes up the equal-temperament chromatic scale. In western music, a division into twelve intervals is commonly assumed unless it is specified otherwise.


title: Music and mathematics

text: For the chromatic scale, the octave is divided into twelve equal parts, each semitone (half-step) is an interval of the twelfth root of two so that twelve of these equal half steps add up to exactly an octave. With fretted instruments it is very useful to use equal temperament so that the frets align evenly across the strings. In the European music tradition, equal temperament was used for lute and guitar music far earlier than for other instruments, such as musical keyboards. Because of this historical force, twelve-tone equal temperament is now the dominant intonation system in the Western, and much of the non-Western, world.


title: Music and mathematics

text: Equally tempered scales have been used and instruments built using various other numbers of equal intervals. The 19 equal temperament, first proposed and used by Guillaume Costeley in the 16th century, uses 19 equally spaced tones, offering better major thirds and far better minor thirds than normal 12-semitone equal temperament at the cost of a flatter fifth. The overall effect is one of greater consonance. Twenty-four equal temperament, with twenty-four equally spaced tones, is widespread in the pedagogy and notation of Arabic music. However, in theory and practice, the intonation of Arabic music conforms to rational ratios, as opposed to the irrational ratios of equally tempered systems.


title: Music and mathematics

text: While any analog to the equally tempered quarter tone is entirely absent from Arabic intonation systems, analogs to a three-quarter tone, or neutral second, frequently occur. These neutral seconds, however, vary slightly in their ratios dependent on maqam, as well as geography. Indeed, Arabic music historian Habib Hassan Touma has written that "the breadth of deviation of this musical step is a crucial ingredient in the peculiar flavor of Arabian music. To temper the scale by dividing the octave into twenty-four quarter-tones of equal size would be to surrender one of the most characteristic elements of this musical culture."


title: Music and mathematics

text: 53 equal temperament arises from the near equality of 53 perfect fifths with 31 octaves, and was noted by Jing Fang and Nicholas Mercator.


title: Music and mathematics

text: Musical set theory uses the language of mathematical set theory in an elementary way to organize musical objects and describe their relationships. To analyze the structure of a piece of (typically atonal) music using musical set theory, one usually starts with a set of tones, which could form motives or chords. By applying simple operations such as transposition and inversion, one can discover deep structures in the music. Operations such as transposition and inversion are called isometries because they preserve the intervals between tones in a set.


title: Music and mathematics

text: Expanding on the methods of musical set theory, some theorists have used abstract algebra to analyze music. For example, the pitch classes in an equally tempered octave form an abelian group with 12 elements. It is possible to describe just intonation in terms of a free abelian group.


title: Music and mathematics

text: Transformational theory is a branch of music theory developed by David Lewin. The theory allows for great generality because it emphasizes transformations between musical objects, rather than the musical objects themselves.


title: Music and mathematics

text: Theorists have also proposed musical applications of more sophisticated algebraic concepts. The theory of regular temperaments has been extensively developed with a wide range of sophisticated mathematics, for example by associating each regular temperament with a rational point on a Grassmannian.


title: Music and mathematics

text: The chromatic scale has a free and transitive action of the cyclic group formula_1, with the action being defined via transposition of notes. So the chromatic scale can be thought of as a torsor for the group.


title: Music and mathematics

text: The mathematician and musicologist Guerino Mazzola has used category theory (topos theory) for a basis of music theory, which includes using topology as a basis for a theory of rhythm and motives, and differential geometry as a basis for a theory of musical phrasing, tempo, and intonation.


title: Ice cream sandwich

text: An ice cream sandwich is a frozen dessert consisting of ice cream between two biscuits, skins, wafers, or cookies. The ingredients are different around the world, with Ireland and Israel using wafers, and North America using chocolate cookies.


title: Ice cream sandwich

text: Within Australia, popular brands are "Giant Sandwich" (blue and pink wrapper), and "Monaco Bar" (gold and black metallic wrapper) in the Eastern provinces. Other brands include Streets "Cookie", "Maxibon" (with one-half ice cream sandwich) and "Maxibon Cookie", and "Pat and Stick's Homemade Range" (recognizable by its circular shape). Additional brands "Indulge" and "Feast" have also become popular.


title: Ice cream sandwich

text: Ice cream sandwiches were formerly known as a "cream between". One purchased a small block of ice cream wrapped in paper and placed it between two wafers.


title: Ice cream sandwich

text: In Germany, ice cream sandwiches are made with two wafers and the three flavour combination called "Fürst-Pückler-Eis", elsewhere known as Neapolitan ice cream. It is based on a recipe introduced in 1839 by the cook of a German nobleman, Prince Hermann Ludwig Heinrich von Pückler-Muskau.


title: Ice cream sandwich

text: The usual Iranian ice cream sandwich is called "bastani naani" () meaning "bread-ice cream", and is made with Iranian traditional ice cream between two wafers.


title: Ice cream sandwich

text: In Ireland they are known as "sliders" or an ice cream wafer, and they are usually served as vanilla ice cream sandwiched between two rectangular chocolate wafers. A "double nougat" is ice cream sandwiched between two nougat wafers. The wafers are not covered in chocolate, only the edges.


title: Ice cream sandwich

text: In Israel, ice cream sandwiches are commonly known as "kasata" (קסטה). Though the name comes from the Italian cassata, the dessert itself has little to do with Italian cassata, and usually consists of two thick biscuits holding a mix of block of vanilla and chocolate-flavoured ice cream.


title: Ice cream sandwich

text: The earliest mention of ice cream sandwiches in North America come in the year of 1899. Street vendors in New York recently sold slabs of ice cream between sheets of paper, called "hokey pokeys", until someone had the idea of using cookies instead. Photos from the Jersey Shore circa 1905 show ice cream sandwiches being sold at 1¢ each. The earliest US patent having to do with ice cream sandwiches (No. 1,387,613) is by Russell H. Proper for an "Ice Cream Sandwich Machine" in 1921. A Chipwich, where ice cream (usually vanilla) is sandwiched between two chocolate chip cookies, is also popular.


title: Ice cream sandwich

text: Local ice cream ("sorbetes") sellers/peddlers with their pushcarts that travel around cities sometimes offer ice cream sandwiches with pandesal as the bread.


title: Ice cream sandwich

text: Wafer ice cream is popular in Singapore. It is one of the types of "potong" (cut) ice cream, so named because the servings are sliced from a large bar of ice cream. Wafer ice cream consists of two wafers holding together a rectangular block of ice cream. Wafer ice cream evolved from the older 'ice potong' type, which is a rectangular prism of ice cream mounted on a wooden stick. Many customers complained that the ice potong would easily melt and fall off the stick, leading to the introduction of the wafers for better grip. Vendors are commonly found along Orchard Road and Chinatown and outside schools. A colloquial term for it is ""pia" ice cream", which translates to "biscuit ice cream" in the Hokkien dialect.


title: Ice cream sandwich

text: Common flavours offered include peppermint, chocolate chip, durian, ripple, red bean, yam, sweet corn, honeydew, and chocolate.


title: Ice cream sandwich

text: Wafer ice cream vendors also sell the same blocks of ice cream on slices of multicoloured bread, on cones or in cups instead of sandwiched between wafers.


title: Ice cream sandwich

text: "Itim Khanom Pang" (or "Icecream Khanom Pang"), literally bread ice cream, a street food in Thailand usually composed of longer rolls similar to hot dog buns a mix of scoops of coconut ice cream/sorbet (or vanilla) and chocolate-flavoured ice cream, with a selection of local toppings from traditionally salty or sweet sticky rice, salty crushed peanuts, and syrup-soaked chewy palm seeds to slivers of fresh or dried fruits. Then drizzled on top with evaporated milk, sweetened condensed milk or chocolate syrup.


title: Ice cream sandwich

text: In the United Kingdom, an ice cream wafer, consisting of a small block of ice cream between two rectangular wafer biscuits, was a popular alternative to a cone up until the 1980s. A "nougat wafer" was also available, consisting of a layer of mallow sandwiched between two wafers and coated with chocolate around the edges. Typically a vanilla block (or a layer of soft-serve) sandwiched between one plain wafer and one chocolate-covered nougat one. This is known as a single nougat" in Scotland, with a double nougat (pronounced nugget) having nougat wafers on both sides. Raspberry sauce is also a common topping. Nougat wafers came in double or triple varieties, depending on the number of nougat wafers in the construction.


title: Ice cream sandwich

text: In Uruguay, an ice cream sandwich ("sánguche helado") or triple sandwich ("sánguche triple") is typically a neapolitan ice cream ("helado triple") sandwich prepared with wafers such as the one in the image.


title: Ice cream sandwich

text: In Vietnam, an ice cream sandwich called ' is commonly sold on the street as a snack. It consists of scoops of ice cream stuffed inside a ', topped with crushed peanuts.


title: Jamal Lewis (footballer)

text: Jamal Piaras Lewis (born 25 January 1998) is a professional footballer who plays as a left back for Premier League club Newcastle United. Born and raised in England, he plays international football for Northern Ireland.


title: Jamal Lewis (footballer)

text: When he was young, Lewis was a talented athlete competing at national level for his age-group over 800m and 1500m. He represented England Schools in athletics and finished second in the English Schools' U17 cross-country in 2014.


title: Jamal Lewis (footballer)

text: Lewis started his football career as a youth player with his home-town club Luton Town, with whom he won the Aarau Masters, a European 5-a-side Under-11 Championship in 2009. He left Luton Town in 2013 to focus on his prospects as a national-level 800-metre runner.


title: Jamal Lewis (footballer)

text: During the 2016–17 season, he played for the Norwich U23 team. At the end of the 2016–17 season, Lewis signed a new contract until 2021. In December 2017, Lewis made his senior debut for Norwich City against Brentford, coming on as a substitute for Marco Stiepermann. On Boxing Day 2017, he made his first start for Norwich against Birmingham City. He scored his first senior goal in the 93rd minute of an FA Cup third round replay against Chelsea in January 2018.


title: Jamal Lewis (footballer)

text: Lewis was named the EFL Young Player of the Month for September 2018, and in October 2018, he was rewarded with a new long-term contract which ran until June 2023.


title: Jamal Lewis (footballer)

text: In March 2019 he was named in the 2018–19 PFA Championship Team of the Year, alongside team-mates Max Aarons and Teemu Pukki. Lewis made 28 appearances for Norwich City in the 2019–20 Premier League. In August 2020, Norwich rejected a £10 million bid from Liverpool for Lewis.


title: Jamal Lewis (footballer)

text: Though born in England, Lewis was eligible to play for Northern Ireland through his Belfast-born mother. He first represented the country in 2016, making three appearances for the U19 team. In June 2017, he was called up to the U21 team and made his U21 debut against Estonia.


title: Jamal Lewis (footballer)

text: In March 2018, he was called up to the Northern Ireland senior squad for the first time. He made his senior international debut in a 2–1 friendly win over South Korea on 24 March 2018.


title: Jamal Lewis (footballer)

text: On 9 October 2021, Lewis was sent off in the first half in an eventual 2–0 loss to Switzerland. His first yellow was for a rash challenge on Breel Embolo, but his second was for timewasting after he struggled to find a teammate from a throw-in. Manager Ian Baraclough said that the decision to send Lewis off was "diabolical" and it changed the course of the game.


title: Thomas G. Waites

text: Thomas G. Waites (born January 8, 1955) is an American actor and acting instructor born in Philadelphia, Pennsylvania. Waites runs an acting studio in New York City which is named for him. He has been a member of the Actors Studio since 1984.


title: Thomas G. Waites

text: Waites was born in Philadelphia, Pennsylvania, the son of Michael and Anne Waites. He completed grade school at Immaculate Conception and then high school at Bishop Egan in Fairless Hills, Pennsylvania. After one year at Bucks County Community College, he received a full scholarship for acting at the Juilliard School in New York City, where he studied as a member of the Drama Division's (1974–1977). He received a B.A. degree in Writing from The New School and a Master of Fine Arts in Playwriting from the University of Iowa.


title: Thomas G. Waites

text: When Waites was 21 years old, he was offered two movies simultaneously: "Snowbound", directed by Robert Young, and "Pity the Poor Soldier" (the title has subsequently changed), directed by Bill Jersey. Despite the fact that he was offered twice the money for "Snowbound", Waites chose "Pity the Poor Soldier" because it was in celebration of the centennial of the American Revolutionary War. Next Waites originated the role of Oliver Treefe in Simon Gray's world premiere of "Molly", at the First Annual Spoleto Festival in Charleston, S.C. After this highly acclaimed performance he returned to NYC to be cast in the Joan Micklin Silver-produced "On the Yard" (1978), co-starring John Heard. Subsequently, he was offered a three-picture option deal with Paramount Pictures. After very strong critical notices Waites auditioned for and got a part in Walter Hill's "The Warriors" (1979) playing the character Fox. After disputes with the director, he was fired from this film. Subsequently, when the studio asked him where he wanted his billing he told them to remove his name completely, a decision Waites regrets. He has since reconciled with Walter Hill. Three weeks after being fired from "The Warriors" Tom auditioned with Al Pacino, and was cast as Jeff McCullough in the Norman Jewison film "...And Justice for All" (1979). This began a long relationship with Pacino. The two worked together again in Shakespeare's "Richard III", with Waites playing Richmond, where he received strong notices again. After that, Waites originated the role of Mitchell in Alan Bowne's "Forty-Deuce" Off-Broadway at the Perry Street Theatre. In 1982, Waites competed with Matt Dillon and Kevin Bacon to land the role of Bobby in David Mamet's Pulitzer Prize-winning play, "American Buffalo". Kurt Russell and John Carpenter saw his performance and cast him as Windows in the film "The Thing" (1982). Waites was cast in the Broadway premiere of "Trafford Tanzi", a musical where he sang with Deborah Harry of Blondie fame. Next was "Pastorale", the Obie Award-winning play by Debra Eisenberg starring Judith Ivey and Christine Estabrook, playing the character of Steve.


title: Thomas G. Waites

text: It was during this time that Tom met his namesake and singer Tom Waits, who generously taught Tom the song "Jersey Girl" on the guitar. Out of deference to the musician Tom Waits, this is when Tom added the G. to his professional name to offset any confusion between the two talented artists. Tom Waits even played the bass drum on a demo tape of Thomas G. Waites' music. Tom G. Waites began writing music and formed a band called The Pushups, playing gigs around NYC in clubs such as CBGB's, Limelight, Traxs, The Bitter End and even opening for The Smithereens.


title: Thomas G. Waites

text: In 1983, Waits joined The Mirror Theater Ltd’s Mirror Repertory Company, performing in numerous repertory productions Off-Broadway at St. Peters Church throughout various seasons. His work with The Mirror included one of the highlights of Tom's career: working with Geraldine Page in Clifford Odets' "Paradise Lost" in the role of Kewpie, originated by Elia Kazan.


title: Thomas G. Waites

text: The reviews from this show and a recommendation by Al Pacino got Tom the part of Ralph in Clifford Odets' "Awake and Sing!" and Sing on Broadway with actress Frances McDormand and actor Harry Hamlin. Tom was then cast in the role of Broud in "The Clan of the Cave Bear" (1986) with Daryl Hannah and James Remar. Terrible critical notices and a cold reception from the public combined to make "Clan of the Cave Bear" a less than career-building move. It was at this point that he met his future wife, Lisa Greenberg, with whom he has two children: Samuel Jackson Waites and Michaela Kate Waites. Tom next played Otis Price the baby-stealer in ABC's "All My Children" for approximately 9 months, while performing Israel Horovitz's "North Shore Fish" at the WPA Theater in NYC alongside John Pankow, Christine Estabrook, Wendie Malick and Laura San Giacomo. Tom also made guest appearances in such popular television shows as "Kojak" (with Telly Savalas), "Miami Vice" and two episodes of "The Equalizer". Tom played the role of Rob in Howard Korder's "Search and Destroy" on Broadway alongside Griffin Dunne. Tom appeared as Smittie in the film "Light of Day" (1987) opposite Michael J. Fox and Joan Jett, and was then cast as Al Capone, competing with actors like Harvey Keitel, for the film "Gangland" (1987) with Scott Glenn.


title: Thomas G. Waites

text: Waites moved to Iowa City, Iowa, to pursue a career as a playwright. While in Iowa, Tom wrote a play called "Dark Laughter", based on the lives of William Faulkner and Dylan Thomas. The play was picked up by producer Barry Kemp, creator of the hit television series "Coach". The play was moved to the Marin Theatre Center in Mill Valley, California.


title: Thomas G. Waites

text: Tom next relocated to Los Angeles where he started the theatre company, TomCats. This is where he began his directing career. After two guest star appearances on "NYPD Blue" and some minor roles in small independent films and television shows, including a guest star in "Buffy the Vampire Slayer", "Mike Hammer, Private Eye" with Stacy Keach and "Sliders". At this time, Tom established himself as a top acting teacher. He opened the TGW Acting Studio in 2000 and his school continues to thrive today. He has coached such actors as Alfred Molina, Vinnie Pastore, Vinessa Shaw, Tim Guinee, Oliver Hudson and Jamie Harris. TGW Acting Studio was named the top school to study acting in New York City by Backstage in 2015. Tom directs and produces Off-Off-Broadway plays at his studio. Upon returning to New York, he directed the Off-Broadway hit "Six Goumbas and a Wannabe", starring Annie McGovern and Kathrine Narducci. He also directed "Golden Ladder" (with Amy Redford) and numerous other Off and Off-Off-Broadway productions.


title: Thomas G. Waites

text: Since returning to New York City he has landed guest roles in "Law & Order" (four times), "" (two times) and starred in the soap opera "One Life to Live" as Decker Denton. Waites played Henry Stanton in "Oz" for four seasons.


title: Thomas G. Waites

text: Tom directed Joe Mantegna and Frances Fisher in a short film, "Pandora's Box", for which he won Best Director in the Atlantic City Film Festival.


title: Sarod

text: The sarod is a stringed instrument, used in Hindustani music on the Indian subcontinent. Along with the sitar, it is among the most popular and prominent instruments. It is known for a deep, weighty, introspective sound, in contrast with the sweet, overtone-rich texture of the sitar, with sympathetic strings that give it a resonant, reverberant quality. A fretless instrument, it can produce the continuous slides between notes known as meend (glissandi), which are important in Indian music.


title: Sarod

text: The word sarod, which comes from the Persian, is much older than the Indian musical instrument. It can be traced back to "sorūd" meaning "song", "melody", "hymn" and further to the Persian verb "sorūdan", which correspondingly means "to sing", "to play a musical instrument", but also means "to compose".


title: Sarod

text: Alternatively, the shahrud may have given its name to the sarod. The Persian word šāh-rūd is made up of "šāh" (shah or king) and "rūd" (string).


title: Sarod

text: Many scholars of Indian classical music believe that the sarod is a combination of the ancient chitravina, the medieval Indian rabab (aka the seniya rabab) and modern sursingar. Some scholars contend that a similar instrument may have existed about two thousand years ago in ancient India during the ages of the Gupta kings. In fact, a Gupta period coin depicts the great king Samudragupta playing a veena, which many believe to be the precursor of the sarod. The present Indian Traces of similar Rabab style instruments can also be found in southern India, especially in the states of Tamil Nadu, Kerala and Karnataka, where it is known as the swarbat. The folk rabab, an instrument popular in north India, had a wooden fingerboard, its strings were made of silk, cotton or gut, and it was played with a wooden pick. In history, reference is also made to a Sharadiya Veena from which the name Sarod have been derived. The sarod is also believed to have descended from the Afghan rubab, a similar instrument originating in Central Asia and Afghanistan.


title: Sarod

text: Although the sarod has been referred to as a "bass rubab" its tonal bandwidth is actually considerably greater than that of the rubab, especially in the middle and high registers. Lalmani Misra opines in his "Bharatiya Sangeet Vadya" that the sarod is a combination of the ancient chitravina, the medieval rubab and modern sursingar. Another instrument, the sur-rabab, is known to exist, which has the characteristics of both the dhrupad rabab/seniya rabab and the sarod. The sur-rabab has the structure of the dhrupad rabab but has a metal fretboard and uses metal strings.


title: Sarod

text: Among the many conflicting and contested histories of the sarod, there is one that attributes its invention to the ancestors of the present-day sarod maestro, Amjad Ali Khan. Amjad Ali Khan’s ancestor Mohammad Hashmi Khan Bangash, a musician and horse trader, came to India with the Afghan rubab in the mid-18th century, and became a court musician to the Maharajah of Rewa (now in Madhya Pradesh). It was his descendants, notably his grandson Ghulam Ali Khan Bangash, a court musician in Gwalior, who changed the rubab into the sarod we know today. A parallel theory credits descendants of Madar Khan, Niyamatullah Khan in particular, with the same innovation around 1820. The sarod in its present form dates back to approximately 1820, when it started gaining recognition as a serious instrument in Rewa, Shahjahanpur, Gwalior and Lucknow. In the 20th century, the sarod was improved significantly by Allauddin Khan and his brother Ayet Ali Khan. They increased the number of chikari (drone) strings and increased the number of tarafdar (sympathetic) strings. However, as is the case with most young, evolving instruments, much work remains to be done in the area of sarod luthiery in order to achieve reliable customization, and precise replication of successful instruments. This reflects the general state of Indian instrument-making in the present day.


title: Sarod

text: The design of the instrument depends on the school (gharana) of playing. There are three distinguishable types:


title: Sarod

text: The conventional sarod is a 17 to 25-stringed lute-like instrument—four to five main strings used for playing the melody, one or two drone strings, two "chikari" strings and nine to eleven sympathetic strings. The design of this early model is generally credited to Niyamatullah Khan of the Lucknow Gharana as well as Ghulam Ali Khan of the Gwalior-Bangash Gharana. Among the contemporary sarod players, this basic design is kept intact by two streams of sarod playing. Amjad Ali Khan and his disciples play this model, as do the followers of Radhika Mohan Maitra. Both Amjad Ali Khan and Buddhadev Dasgupta have introduced minor changes to their respective instruments which have become the design templates for their followers. Both musicians use sarods made of teak wood, and a soundboard made of goat skin stretched across the face of the resonator. Buddhadev Dasgupta prefers a polished stainless steel fingerboard for the ease of maintenance while Amjad Ali Khan uses the conventional chrome or nickel-plated cast steel fingerboard. Visually, the two variants are similar, with six pegs in the main pegbox, two rounded chikari pegs and 11 (Amjad) to 15 (Buddhadev) sympathetic strings. The descendants of Niyamatullah Khan (namely Irfan Khan and Ghulfam Khan) also play similar instruments. Some of the followers of Radhika Mohan Maitra still carry the second resonator on their sarods. Amjad Ali Khan and his followers have rejected the resonator altogether. These instruments are typically tuned to B, which is the traditional setting.


title: Sarod

text: Another type is that designed by Allauddin Khan and his brother Ayet Ali Khan. This instrument, referred to by David Trasoff as the 1934 Maihar Prototype, is larger and longer than the conventional instrument, though the fingerboard is identical to the traditional sarod. This instrument has 25 strings in all. These include four main strings, four "jod" strings (tuned to "Ni" or "Dha", "R/r", "G/g" and "Sa" respectively), two "chikari" strings (tuned to "Sa" of the upper octave) and fifteen "tarab" strings. The main strings are tuned to "Ma" ("fa"), "Sa" ("do"), lower "Pa" ("so") and lower "Sa", giving the instrument a range of three octaves. The Maihar sarod lends itself extremely well to the presentation of alap with the four "jod" strings providing a backdrop for the ambiance of the raga. This variant is, however, not conducive to the performance of clean right-hand picking on individual strings. The instrument is typically tuned to C.


title: Sarod

text: Sarod strings are either made of steel or phosphor bronze. Most contemporary sarod players use German or American-made strings, such as Roslau (Germany), Pyramid (Germany) and Precision (USA). The strings are plucked with a triangular plectrum ("java") made of polished coconut shell, ebony, cocobolo wood, horn, cowbone, Delrin or other such materials. Early sarod players used plain wire plectrums, which yielded a soft, ringing tone.


title: Sarod

text: The lack of frets and the tension of the strings make the sarod a very demanding instrument to play, as the strings must be pressed hard against the fingerboard.


title: Sarod

text: There are two approaches to stopping the strings of the sarod. One involves using the tip of one's fingernails to stop the strings, and the other uses a combination of the nail and the fingertip to stop the strings against the fingerboard.


title: Sarod

text: Fingering techniques and how they are taught depends largely on the personal preferences of musicians rather than on the basis of school affiliation. Radhika Mohan Maitra, for example, used the index, middle and ring finger of his left hand to stop the string, just like followers of Allauddin Khan do. Maitra, however, made much more extensive use of the third fingernail for slides and hammers. Amjad Ali Khan, while a member of approximately the same stylistic school as Radhika Mohan, prefers to use just the index and middle fingers of his left hand. Amjad Ali is, however, pictured circa 1960 playing with all three fingers.


title: History of Thailand (1932–1973)

text: The history of Thailand from 1932 to 1973 was dominated by military dictatorships which were in power for much of the period. The main personalities of the period were the dictator Luang Phibunsongkhram (better known as Phibun), who allied the country with Japan during the Second World War, and the civilian politician Pridi Phanomyong, who founded Thammasat University and was briefly prime minister after the war.


title: History of Thailand (1932–1973)

text: A succession of military dictators followed Pridi's ouster—Phibun again, Sarit Thanarat, then Thanom Kittikachorn—under whom traditional, authoritarian rule was combined with increasing modernisation and Westernisation under the influence of the US. The end of the period was marked by Thanom's resignation, following a massacre of pro-democracy protesters led by Thammasat students.


title: History of Thailand (1932–1973)

text: The military came to power in the bloodless Siamese revolution of 1932, which transformed the government of Siam (as Thailand was then known) from an absolute to a constitutional monarchy. King Prajadhipok initially accepted this change but later abdicated due to his strained relations with the government. Upon his abdication, King Prajadhipok issued a brief statement criticising the regime. His statement included the following phrases—often quoted by critics of the slow pace of Siam's political development:


title: History of Thailand (1932–1973)

text: The new regime of 1932 was led by a group of colonels headed by Phraya Phahol Pholphayuhasena and Phraya Songsuradej. In December they produced a constitution—Siam's first—which included a national assembly, half appointed and half indirectly elected. The people were promised that full democratic elections would be held once half the population had completed primary education—which was expected to be sometime in the 1940s. A prime minister and cabinet were appointed and a facade of constitutional rule was maintained.


title: History of Thailand (1932–1973)

text: Once the new government had been established and the constitution put into effect, conflict began to erupt among the members of the new ruling coalition. There were four major factions competing for power: the older conservative civilian faction led by Phraya Manopakorn Nititada (Mano); the senior military faction led by Phraya Phahol; the junior army and navy faction led by Luang Phibunsongkhram; and the young civilian faction led by Pridi Phanomyong.


title: History of Thailand (1932–1973)

text: The first serious conflict arose in 1933 when Pridi was given the task of drafting a new economic plan for the nation. His radical programme called for the nationalisation of large tracts of farmland as well as rapid government-directed industrialisation. It also called for the growth of higher education so that entry into the bureaucracy would not be completely dominated by royalty and the aristocracy. However, the plan was condemned immediately by most of the government factions as being communist.


title: History of Thailand (1932–1973)

text: Because of its attack on private property, the members of the conservative clique were the ones most alarmed by Pridi's plan. They urged the Mano government to adopt policies that would reverse the course of the "revolution". However, when Phraya Mano attempted to do this, Phibun and Phraya Phahol launched a second coup that toppled the Mano government. Phraya Pahon was made the new prime minister, and his new government excluded all of the royalists.


title: History of Thailand (1932–1973)

text: A royalist reaction came in late 1933 when Prince Boworadej, a grandson of Mongkut and one-time Minister of Defence, led an armed revolt against the government. He mobilised various provincial garrisons and marched on Bangkok, capturing the Don Muang Aerodrome along the way. The prince accused the government of disrespecting the king and promoting communism, and he demanded that the government leaders resign. He had hoped that some of the garrisons in the Bangkok area would join the revolt, but they remained loyal to the government. Meanwhile, the navy declared itself neutral and left for its bases in the south. After heavy fighting in the northern outskirts of Bangkok, the royalists were finally defeated and Prince Bovoradej left for exile in French Indochina.


title: History of Thailand (1932–1973)

text: One effect of the repression of the insurrection was the diminution of the king's prestige. After the revolt started, King Prajadhipok declared in a telegram that he regretted the strife and civil disturbances. It is not clear whether he was motivated by a fear of being captured by rebels, a fear of being viewed as a supporter of the rebels, or a wish to avoid further choices between Phahol and Bovoradej. Either way, the fact remains that at the height of the conflict, the royal couple took refuge at Songkhla. The king's withdrawal from the scene of the fighting was interpreted by the victorious party as a sign that he had failed in his duty. By refusing to give his full support to the legitimate government, his credibility was undermined.


title: History of Thailand (1932–1973)

text: A few months later in 1934, King Prajadhipok, whose relations with the new government had been deteriorating for some time, went abroad to receive medical treatment. While abroad, he carried on a correspondence with the government that discussed the terms under which he would continue to serve as a constitutional monarch. He requested the continuation of some traditional royal prerogatives. The government, however, would not agree.


title: History of Thailand (1932–1973)

text: In his abdication speech, Prajadhipok accused the government of having no regard for democratic principles, employing methods of administration incompatible with individual freedom and the principles of justice, ruling in an autocratic manner and not letting the people have a real voice in Siam's affairs. In 1934, the Press Act came into effect, forbidding the publication of any material deemed to be detrimental to the public order or to undermine morals. The law has been strictly enforced to the present day.


title: History of Thailand (1932–1973)

text: Reaction to the abdication was muted. Everybody was afraid of what might happen next. The government refrained from challenging any assertions in the king's abdication statement for fear of arousing further controversy. Opponents of the government kept quiet after the failure of the royalist rebellion.


title: History of Thailand (1932–1973)

text: Having defeated the royalists, the government now was put to the test of living up to the promises on which it had come to power. It took much more aggressive steps to carry out some important reforms. The currency went off the gold standard, allowing trade to recover. Expenditures on education were increased four-fold, thereby significantly raising the literacy rate. Elected local and provincial governments were introduced, and in November 1937 democratic development was brought forward when direct elections were held for the national assembly, although political parties were still not allowed. Thammasat University was founded, at Pridi's initiative, as a more accessible alternative to the elitist Chulalongkorn University. Military expenditure was also greatly expanded, a clear indication of the increasing influence of the military. In the years between 1934 and 1940 the kingdom's army, navy, and air force were equipped as never before.


title: History of Thailand (1932–1973)

text: After King Prajadhipok left Siam and abdicated the following year, The government then chose Prince Ananda Mahidol, who was at that time in school in Switzerland, as the next king, becoming King Rama VIII. For the first time in history, Siam was without a resident monarch and was to remain so for the next fifteen years, the Khana Ratsadon believing that he would be more pliable than Prajadhipok.


title: History of Thailand (1932–1973)

text: The military, now led by Major General Phibun as defence minister, and the civilian liberals led by Pridi as foreign minister, worked together harmoniously for several years, but when Phibun became prime minister in December 1938 this co-operation broke down, and military domination became more overt. Phibun was an admirer of Benito Mussolini, and his regime soon developed some fascist characteristics. In early 1939 forty political opponents, both monarchists and democrats, were arrested, and after rigged trials eighteen were executed, the first political executions in Siam in over a century. Many others, among them Prince Damrong and Phraya Songsuradej, were exiled. Phibun launched a demagogic campaign against the Chinese business class. Chinese schools and newspapers were closed, and taxes on Chinese businesses increased.


title: History of Thailand (1932–1973)

text: Phibun and Luang Wichitwathakan, the government's ideological spokesman, copied the propaganda techniques used by Hitler and Mussolini to build up the cult of the leader. Aware of the power of mass media, they used the government's monopoly on radio broadcasting to shape popular support for the regime. Popular government slogans were constantly aired on the radio and plastered on newspapers and billboards. Phibun's picture was also to be seen everywhere in society, while portraits of the ex-monarch King Prajadhipok, an outspoken critic of the autocratic regime, were banned. At the same time Phibun passed a number of authoritarian laws which gave the government the power of almost unlimited arrest and complete press censorship. During the Second World War, newspapers were instructed to print only good news emanating from Axis sources, while sarcastic comments about the internal situation were banned.


title: History of Thailand (1932–1973)

text: On 23 June 1939, Phibun changed the country's name from Siam to Prathet Thai (), or Thailand, said to mean "land of the free". This was a nationalist gesture: it implied the unity of all the Tai-speaking peoples, including the Lao and the Shan, but excluding the Chinese. The regime's slogan became "Thailand for the Thai."


title: History of Thailand (1932–1973)

text: Modernisation was also an important theme in Phibun's new Thai nationalism. From 1939 to 1942 he issued a set of twelve Cultural Mandates. In addition to requiring that all Thais salute the flag, know the national anthem, and speak the national language, the mandates also encouraged Thais to work hard, stay informed on current events, and to dress in a Western fashion. By 1941 it became illegal, among other things, to ridicule those who attempted to promote national customs. The programme also encompassed fine arts. Fiercely nationalistic plays and films were sponsored by the government. Often these depicted a glorious past when Thai warriors fearlessly gained freedom for the country, defended their honour, or sacrificed themselves. Patriotism was taught in schools and was a recurrent theme in songs and dances.


title: History of Thailand (1932–1973)

text: At the same time, Phibun worked rigorously to rid society of its royalist influences. Traditional royal holidays were replaced with new national events and royal and aristocratic titles were abandoned. Ironically, he retained his aristocratic surname. Even the Sangha was affected when the status of the royally sponsored Thammayuth sect was downgraded.


title: History of Thailand (1932–1973)

text: Meanwhile, all cinemas were instructed to display Phibun's picture at the end of every performance as if it were the king's portrait, and the audience were expected to rise and bow. Another aspect of Phibun's growing personality cult was becoming apparent in official décor. He was born in the year of the cock, and this symbol began to replace the wheel. Similarly, Phibun's auspicious birth-colour, green, was used in official decorations.


title: History of Thailand (1932–1973)

text: In 1940, most of France was occupied by Nazi Germany, and Phibun immediately set out to avenge Siam's humiliations by France in 1893 and 1904, when the French had used force to redraw the borders of Siam with Laos and Cambodia, requiring the Thais to sign a series of unequal treaties. To accomplish that, the Thai government needed Japanese assistance against France, which was secured through the Treaty between Thailand and Japan Concerning the Continuance of Friendly Relations and the Mutual Respect of Each Other's Territorial Integrity, concluded in June 1940. Also concluded in 1940 was the British-Thai Non-Aggression Pact between the governments of Great Britain and the Kingdom of Thailand. On 18 July 1940, the British government accepted Japanese demands to close the Burma Road for three months to prevent war supplies from reaching China. As the government of Thailand was now becoming aligned with the Japanese, the British government concluded the pact with Bangkok so as not to antagonize Tokyo.


title: History of Thailand (1932–1973)

text: Luang Wichit wrote a number of popular dramas that glorified the idea of many ethnic groups belonging to a greater "Thai" empire and condemned the evils of European colonial rule. Irredentist and anti-French demonstrations were incessantly held around Bangkok, and in late 1940 border skirmishes erupted along the Mekong frontier. In 1941 the skirmishes turned into the small–scale Franco-Thai War between Vichy France and Thailand. Thai forces dominated the war on the ground and in the air, but the Thai Navy suffered a crushing naval defeat at the battle of Ko Chang. The Japanese then stepped in to mediate the conflict. The final settlement thus returned most of the disputed areas in Laos and Cambodia to Thailand.


title: History of Thailand (1932–1973)

text: Phibun's prestige was so increased that he was able to bask in a feeling of being truly the nation's leader. To celebrate the occasion, he promoted himself to field marshal, skipping the ranks of lieutenant general and general.


title: History of Thailand (1932–1973)

text: This caused a rapid deterioration of relations with Britain and the United States. In April 1941 the United States cut off petroleum supplies to Thailand. Thailand's brief period of glory came to an end on 8 December 1941 when Japan invaded the country along its southeastern coastline and from Cambodia. After initially resisting, the Phibun regime gave in and allowed the Japanese to pass through the country to attack Burma and invade Malaya. Convinced by the Allied defeats of early 1942 that Japan was winning the war, Phibun decided to form a military alliance with Imperial Japan.


title: History of Thailand (1932–1973)

text: In return, Japan allowed Thailand to invade and annex the Shan States and Kayah State in northern Burma, and resume sovereignty over the sultanates of northern Malaya which had been surrendered in the Anglo-Siamese Treaty of 1909 with Britain. In January 1942 Phibun declared war on Britain and the United States, though the Thai Ambassador to the United States, Seni Pramoj, refused to deliver it to the state department. Seni denounced the Phibun regime as illegal and formed a Seri Thai Movement in Washington. Pridi, now serving in the role of an almost powerless regent, led the resistance movement inside Thailand, while former Queen Ramphaiphanni was the nominal head in Great Britain.


title: History of Thailand (1932–1973)

text: Secret training camps were set up in remote areas, the majority by the populist politician Tiang Sirikhanth in the northeast region of the country. There were a dozen camps alone in Sakhon Nakhon Province. Clandestine airfields also appeared in the northeast, where Royal Air Force and United States Army Air Forces planes brought in supplies, as well as Special Operations Executive, Office of Strategic Services, and Seri Thai agents, at the same time evacuating escaped prisoners of war. By early 1945, Thai air force officers were performing liaison duties with South East Asia Command in Kandy and Calcutta.


title: History of Thailand (1932–1973)

text: By 1944, it was evident that the Japanese were going to lose the war, and their behaviour in Thailand had become increasingly arrogant. Bangkok also suffered heavily from Allied strategic bombing. Coupled with economic hardships caused by the loss of Thailand's rice export markets, this made both the war and Phibun's regime very unpopular. In July 1944 Phibun was ousted by the Seri Thai-infiltrated government. The national assembly reconvened and appointed the liberal lawyer Khuang Aphaiwong as prime minister. The new government hastily evacuated the British territories that Phibun had occupied and surreptitiously aided the Seri Thai movement, while at the same time maintaining ostensibly friendly relations with the Japanese.


title: History of Thailand (1932–1973)

text: The Japanese surrendered on 15 August 1945. Immediately, Allied military responsibility for Thailand fell to the British. As soon as practicable, British and Indian troops were flown in and rapidly secured the release of surviving POWs. The British were surprised to find that the Japanese soldiers had already been largely disarmed by the Thais.


title: History of Thailand (1932–1973)

text: Britain regarded Thailand as having been partly responsible for the damage dealt to the Allied cause and favoured treating the kingdom as a defeated enemy. However, the US had no sympathy for what they considered British and French colonialism and supported the new government. Thailand thus received little punishment for its wartime role under Phibun.


title: History of Thailand (1932–1973)

text: Seni Pramoj became prime minister in 1945 and promptly restored the name Siam as a symbol of the end of Phibun's nationalist regime. However, he found his position at the head of a cabinet packed with Pridi's loyalists quite uncomfortable. Northeastern populist politicians like Tiang Sirikhanth and Bangkok upstarts like Sanguan Tularaksa were not the sort that the aristocratic Seni preferred to associate with. They, in turn, viewed Seni as an elitist who was entirely out of touch with Thailand's political realities. Pridi continued to wield power behind the scenes as he had done during the Khuang government. The regent's looming presence and overarching authority rankled the proud, thin-skinned Seni, fuelling a personal animosity that would poison Thailand's postwar politics.


title: History of Thailand (1932–1973)

text: Following the signature by Thailand of the Washington Accord of 1946, the territories that had been annexed after the Franco-Thai War, which included Phibunsongkhram Province, Nakhon Champassak Province, Phra Tabong Province, Koh Kong Province, and Lan Chang Province, were returned to Cambodia and Laos.


title: History of Thailand (1932–1973)

text: Democratic elections were subsequently held in January 1946. These were the first elections in which political parties were legal, and Pridi's People's Party and its allies won a majority. In March 1946 Pridi became Siam's first democratically elected prime minister. In 1946, after he agreed to hand back the Indochinese territories occupied in 1941 as the price for admission to the United Nations, all wartime claims against Siam were dropped and a substantial package of US aid was received.


title: History of Thailand (1932–1973)

text: In December 1945, the young King Ananda had returned to Siam from Europe, but in June 1946, he was found shot dead in his bed, under mysterious circumstances. Three palace servants were tried and executed for his murder, although there are significant doubts as to their guilt and the case remains both murky and a highly sensitive topic in Thailand today. The king was succeeded by his younger brother, Bhumibol Adulyadej, who became King Rama IX. In August, Pridi was forced to resign amid suspicion that he had been involved in the regicide. Without his leadership, the civilian government floundered, and in November 1947 the army, its confidence restored after the debacle of 1945, seized power. After an interim Khuang-headed government, in April 1948 the army brought Phibun back from exile and made him prime minister. Pridi, in turn, was driven into exile, eventually settling in Beijing as a guest of the People's Republic of China.


title: History of Thailand (1932–1973)

text: Phibun's return to power coincided with the onset of the Cold War and the establishment of a communist regime in North Vietnam. He soon won the support of the US, beginning a long tradition of US-backed military regimes in Thailand (as the country was again renamed in July 1949, this time permanently).


title: History of Thailand (1932–1973)

text: Once again political opponents were arrested and tried, and some were executed. During this time, several of the key figures in the wartime Free Thai underground, including Thawin Udom, Thawi Thawethikul, Chan Bunnak, and Tiang Sirikhanth, were eliminated in extra-legal fashion by the Thai police, run by Phibun's ruthless associate Phao Sriyanond. There were attempted counter-coups by Pridi supporters in 1948, 1949, and 1951, the second leading to heavy fighting between the army and navy before Phibun emerged victorious. In the navy's 1951 attempt, popularly known as the Manhattan Coup, Phibun was nearly killed when the ship where he was held hostage was bombed by the pro-government air force.


title: History of Thailand (1932–1973)

text: In 1949 a new constitution was promulgated, creating a senate appointed by the king (in practice, by the government). But in 1951 the regime abolished its own constitution and reverted to the 1932 arrangements, effectively abolishing the national assembly as an elected body. This provoked strong opposition from the universities and the press and led to a further round of trials and repression. The regime was greatly helped, however, by a postwar boom which gathered pace through the 1950s, fuelled by rice exports and US aid. Thailand's economy began to diversify, while the population and urbanisation increased.


title: History of Thailand (1932–1973)

text: In 1956, it became clearer that Plaek, allied to Phao, was losing to another influential groups led by Sarit, and consisted of "Sakdina" (royalties and royalists). Both Plaek and Phao intended to bring home Pridi Banomyong to clear his name from the mystery around the death of King Rama VIII. However, the US government disapproved, cancelling the plan. In June 1957, he told one of Pridi's son to "tell your father that I want [him] to come back [and] help me work for the nation. I alone can no longer contest Sakdina."


title: History of Thailand (1932–1973)

text: By 1955, Phibun was losing his leading position in the army to younger rivals, led by Field Marshal Sarit Thanarat and General Thanom Kittikachorn. To shore up his position he restored the 1949 constitution and called elections, which his supporters won. But the army was not prepared to give up power, and in September 1957 it demanded Phibun's resignation. When Phibun tried to have Sarit arrested, the army staged a bloodless coup on 17 September 1957, ending Phibun's career for good.


title: History of Thailand (1932–1973)

text: Sarit began the restoration of the monarchy so much that by Thanom's time their rule was a close partnership between the military and the king. In this period the Monarchy was again restored its power since the Siamese revolution in 1932.


title: History of Thailand (1932–1973)

text: Thanom became prime minister until 1958, then yielded his place to Sarit, the real head of the regime. Sarit held power until his death in 1963, when Thanom again took the lead.


title: History of Thailand (1932–1973)

text: Sarit and Thanom were the first Thai leaders to have been educated entirely in Thailand, and were less influenced by European political ideas, whether fascist or democratic, than the generation of Pridi and Phibun had been. Rather, they were Thai traditionalists, who sought to restore the prestige of the monarchy and to maintain a society based on order, hierarchy, and religion. They saw rule by the army as the best means of ensuring this, and also of defeating communism, which they now associated with Thailand's traditional enemies, the Vietnamese. The young King Bhumibol, who returned to Thailand in 1951, co-operated with this project. The Thai monarchy's present elevated status thus has its origins in this era.


title: History of Thailand (1932–1973)

text: The regimes of Sarit and Thanom were strongly supported by the US. Thailand had formally become a US ally in 1954 with the formation of the Southeast Asia Treaty Organization (SEATO). While the war in Indochina was being fought between the Vietnamese and the French, Thailand (disliking both equally) stayed aloof, but once it became a war between the US and the Vietnamese communists, Thailand committed itself strongly to the US side, concluding a secret agreement with the US in 1961, sending troops to Vietnam and Laos, and allowing the US to use airbases in the east of the country to conduct its bombing war against North Vietnam. The Vietnamese retaliated by supporting the Communist Party of Thailand's insurgency in the north, northeast, and sometimes in the south, where guerrillas co-operated with local discontented Muslims. In the postwar period, Thailand had close relations with the US, which it saw as a protector from communist revolutions in neighboring countries. The Seventh and Thirteenth US Air Forces were headquartered at Udon Royal Thai Air Force Base.


title: History of Thailand (1932–1973)

text: Agent Orange is a herbicide and defoliant chemical used by the U.S. military as part of its herbicidal warfare program, Operation Ranch Hand. Agent Orange was tested by the United States in Thailand during the war in Southeast Asia. Buried drums were uncovered and confirmed to be Agent Orange in 1999. Workers who uncovered the drums fell ill while upgrading the airport near Hua Hin District, 100 km south of Bangkok.


title: History of Thailand (1932–1973)

text: A declassified Department of Defense report written in 1973, suggests that there was a significant use of herbicides on the fenced-in perimeters of military bases in Thailand to remove foliage that provided cover for enemy forces.


title: History of Thailand (1932–1973)

text: The Vietnam War hastened the modernisation and Westernisation of Thai society. The American presence and the exposure to Western culture that came with it had an effect on almost every aspect of Thai life. Before the late 1960s, full access to Western culture was limited to a highly educated elite in society, but the Vietnam War brought the outside world face to face with large segments of the Thai society as never before. With US dollars pumping up the economy, the service, transportation, and construction industries grew phenomenally as did drug abuse and prostitution. The traditional rural family unit was broken down as more and more rural Thais moved to the city to find new jobs. This led to a clash of cultures as Thais were exposed to Western ideas about fashion, music, values, and moral standards.


title: History of Thailand (1932–1973)

text: The population began to grow explosively as the standard of living rose, and a flood of people began to move from the villages to the cities, and above all to Bangkok. Thailand had 30 million people in 1965, while by the end of the 20th century the population had doubled. Bangkok's population had grown tenfold since 1945 and had tripled since 1970.


title: History of Thailand (1932–1973)

text: Educational opportunities and exposure to mass media increased during the Vietnam War years. Bright university students learned more about ideas related to Thailand's economic and political systems, resulting in a revival of student activism. The Vietnam War period also saw the growth of the Thai middle class which gradually developed its own identity and consciousness.


title: History of Thailand (1932–1973)

text: Economic development did not bring prosperity to all. During the 1960s many of the rural poor felt increasingly dissatisfied with their condition in society and disillusioned by their treatment by the central government in Bangkok. Efforts by the Thai government to develop poor rural regions often did not have the desired effect in that they contributed to the farmers' awareness of how bad off they really were. It was not always the poorest of the poor who joined the anti-government insurgency. Increased government presence in the rural villages did little to improve the situation. Villagers became subject to increased military and police harassment and bureaucratic corruption. Villagers often felt betrayed when government promises of development were frequently not fulfilled. By the early 1970s rural discontent had manifested itself into a peasant's activist movement.


title: History of Thailand (1932–1973)

text: The peasant's movement got started in the regions just north of the central plains and the Chiang Mai area (not the areas where the insurgency was most active). When these regions had been organised into the centralised Siamese state in King Chulalongkorn's reign, the old local nobility had been allowed to grab large tracts of land. The end result was that by the 1960s close to 30% of the households were landless.


title: History of Thailand (1932–1973)

text: In the early 1970s university students helped to bring some of the local protests on to the national stage. The protests focused on land loss, high rents, the heavy-handed role of the police, corruption among the bureaucracy and the local elites, poor infrastructure, and overwhelming poverty. The government agreed to establish a committee to hear peasant grief. Within a short time the committee was flooded with more than 50,000 petitions, more than it could possibly handle. Officials called many of the peasants' demands unrealistic and too far-reaching.


title: History of Thailand (1932–1973)

text: The political environment of Thailand changed little during the mid-1960s. Thanom and his chief deputy Praphas maintained a tight grip on power. The alliance between these two was further cemented by the marriage of Praphas's daughter to Thanom's son Narong. By the late 1960s, however, more elements in Thai society had become openly critical of the military government which was seen as being increasingly incapable of dealing with the country's problems. It was not only the student activists, but also the business community that had begun to question the leadership of the government as well as its relationship with the United States.


title: History of Thailand (1932–1973)

text: Thanom came under increasing pressure to loosen his grip on power when the king commented that it was time for parliament to be restored and a new constitution put into effect. After Sarit had suspended the constitution in 1958, a committee was established to write a new one, but almost ten years later, it had still not been completed. Finally, in 1968 the government issued a new constitution and scheduled elections for the following year. The government party founded by the military junta won the election and Thanom remained prime minister.


title: History of Thailand (1932–1973)

text: Surprisingly, the assembly was not totally tame. A number of MPs (mostly professionals such as doctors, lawyers, and journalists) began to openly challenge some of the government's policies, producing evidence of widespread government corruption on a number of large projects. As a new budget was being debated in 1971, it actually appeared that the military's demand for more funds might be voted down. Rather than suffer such a loss of face, Thanom carried out a putsch against his own government, suspended the constitution, and dissolved parliament. Once again Thailand had been returned to absolute military rule.


title: History of Thailand (1932–1973)

text: This strongman approach which had worked for Phibun in 1938 and 1947, and for Sarit in 1957–58, would prove to be unsuccessful. By the early 1970s Thai society as a whole had developed a level of political awareness which would no longer accept unjustified authoritarian rule. The king, using various holidays to give speeches on public issues, became openly critical of the Thanom-Praphas regime. He expressed doubt on the use of extreme violence in the efforts to combat insurgency. He mentioned the widespread existence of corruption in the government and expressed the view that coups should become a thing of the past in the Thai political system.


title: History of Thailand (1932–1973)

text: The junta began to face increasing opposition from within the military itself. Being preoccupied with their political roles, Thanom and Praphas had become more removed from direct control of the army. Many officers felt outraged by the rapid promotion of Narong and the fact that he seemed destined to be Thanom's successor. To these officers, it appeared that a political dynasty was being created.


title: History of Thailand (1932–1973)

text: Student demonstrations had started in 1968 and grew in size and numbers in the early 1970s despite the continued ban on political meetings. In June 1973, nine Ramkhamhaeng University students were expelled for publishing an article in a student newspaper that was critical of the government. Shortly after, thousands of students held a protest at the Democracy Monument demanding the re-enrolment of the nine students. The government ordered the universities to shut, but shortly afterwards allowed the students to be re-enrolled.


title: History of Thailand (1932–1973)

text: In October another 13 students were arrested on charges of conspiracy to overthrow the government. This time the student protesters were joined by workers, businessmen, and other ordinary citizens. The demonstrations swelled to several hundred thousand and the issue broadened from the release of the arrested students to demands for a new constitution and the replacement of the current government.


title: History of Thailand (1932–1973)

text: On 13 October, the government released the detainees. Leaders of the demonstrations, among them Seksan Prasertkul, called off the march in accordance with the wishes of the king who was publicly against the democracy movement. In a speech to graduating students, he criticized the pro-democracy movement by telling students to concentrate on their studies and leave politics to their elders [military government].


title: History of Thailand (1932–1973)

text: As the crowds were breaking up the next day, on 14 October, many students found themselves unable to leave because the police had attempted to control the flow of the crowd by blocking the southern route to Rajavithi Road. Cornered and overwhelmed by the hostile crowd, the police responded with tear gas and gunfire.


title: History of Thailand (1932–1973)

text: The military was called in, and tanks rolled down Rajdamnoen Avenue and helicopters fired down at Thammasat University. A number of students commandeered buses and fire engines in an attempt to halt the progress of the tanks by ramming into them. With chaos on the streets, King Bhumibol opened the gates of Chitralada Palace to the students who were being gunned down by the army. Despite orders from Thanom that the military action be intensified, army commander Kris Sivara had the army withdrawn from the streets.


title: History of Thailand (1932–1973)

text: The king condemned the government's inability to handle the demonstrations and ordered Thanom, Praphas, and Narong to leave the country, and notably condemned the students' supposed role as well. At 18:10 Field Marshal Thanom Kittikachorn resigned from his post as prime minister. An hour later, the king appeared on national television, asking for calm, and announcing that Field Marshal Thanom Kittikachorn had been replaced with Dr. Sanya Dharmasakti, a respected law professor, as prime minister.


title: History of Thailand (1932–1973)

text: Political freedom was in full bloom. The most active movements were those of students and now the worker's union and even farmers.


title: Docking (molecular)

text: In the field of molecular modeling, docking is a method which predicts the preferred orientation of one molecule to a second when a ligand and a target are bound to each other to form a stable complex. Knowledge of the preferred orientation in turn may be used to predict the strength of association or binding affinity between two molecules using, for example, scoring functions.


title: Docking (molecular)

text: The associations between biologically relevant molecules such as proteins, peptides, nucleic acids, carbohydrates, and lipids play a central role in signal transduction. Furthermore, the relative orientation of the two interacting partners may affect the type of signal produced (e.g., agonism vs antagonism). Therefore, docking is useful for predicting both the strength and type of signal produced.


title: Docking (molecular)

text: Molecular docking is one of the most frequently used methods in structure-based drug design, due to its ability to predict the binding-conformation of small molecule ligands to the appropriate target binding site. Characterisation of the binding behaviour plays an important role in rational design of drugs as well as to elucidate fundamental biochemical processes.


title: Docking (molecular)

text: One can think of molecular docking as a problem of "“lock-and-key”", in which one wants to find the correct relative orientation of the "“key”" which will open up the "“lock”" (where on the surface of the lock is the key hole, which direction to turn the key after it is inserted, etc.). Here, the protein can be thought of as the “lock” and the ligand can be thought of as a “key”. Molecular docking may be defined as an optimization problem, which would describe the “best-fit” orientation of a ligand that binds to a particular protein of interest. However, since both the ligand and the protein are flexible, a "“hand-in-glove”" analogy is more appropriate than "“lock-and-key”". During the course of the docking process, the ligand and the protein adjust their conformation to achieve an overall "best-fit" and this kind of conformational adjustment resulting in the overall binding is referred to as "induced-fit".


title: Docking (molecular)

text: Molecular docking research focuses on computationally simulating the molecular recognition process. It aims to achieve an optimized conformation for both the protein and ligand and relative orientation between protein and ligand such that the free energy of the overall system is minimized.


title: Docking (molecular)

text: Two approaches are particularly popular within the molecular docking community. One approach uses a matching technique that describes the protein and the ligand as complementary surfaces. The second approach simulates the actual docking process in which the ligand-protein pairwise interaction energies are calculated. Both approaches have significant advantages as well as some limitations. These are outlined below.


title: Docking (molecular)

text: Geometric matching/ shape complementarity methods describe the protein and ligand as a set of features that make them dockable. These features may include molecular surface / complementary surface descriptors. In this case, the receptor's molecular surface is described in terms of its solvent-accessible surface area and the ligand's molecular surface is described in terms of its matching surface description. The complementarity between the two surfaces amounts to the shape matching description that may help finding the complementary pose of docking the target and the ligand molecules. Another approach is to describe the hydrophobic features of the protein using turns in the main-chain atoms. Yet another approach is to use a Fourier shape descriptor technique. Whereas the shape complementarity based approaches are typically fast and robust, they cannot usually model the movements or dynamic changes in the ligand/ protein conformations accurately, although recent developments allow these methods to investigate ligand flexibility. Shape complementarity methods can quickly scan through several thousand ligands in a matter of seconds and actually figure out whether they can bind at the protein's active site, and are usually scalable to even protein-protein interactions. They are also much more amenable to pharmacophore based approaches, since they use geometric descriptions of the ligands to find optimal binding.


title: Docking (molecular)

text: Simulating the docking process is much more complicated. In this approach, the protein and the ligand are separated by some physical distance, and the ligand finds its position into the protein's active site after a certain number of “moves” in its conformational space. The moves incorporate rigid body transformations such as translations and rotations, as well as internal changes to the ligand's structure including torsion angle rotations. Each of these moves in the conformation space of the ligand induces a total energetic cost of the system. Hence, the system's total energy is calculated after every move.


title: Docking (molecular)

text: The obvious advantage of docking simulation is that ligand flexibility is easily incorporated, whereas shape complementarity techniques must use ingenious methods to incorporate flexibility in ligands. Also, it more accurately models reality, whereas shape complementary techniques are more of an abstraction.


title: Docking (molecular)

text: Clearly, simulation is computationally expensive, having to explore a large energy landscape. Grid-based techniques, optimization methods, and increased computer speed have made docking simulation more realistic.


title: Docking (molecular)

text: To perform a docking screen, the first requirement is a structure of the protein of interest. Usually the structure has been determined using a biophysical technique such as x-ray crystallography, NMR spectroscopy or cryo electron microscopy (cryo-EM), but can also derive from homology modeling construction. This protein structure and a database of potential ligands serve as inputs to a docking program. The success of a docking program depends on two components: the search algorithm and the scoring function.


title: Docking (molecular)

text: The search space in theory consists of all possible orientations and conformations of the protein paired with the ligand. However, in practice with current computational resources, it is impossible to exhaustively explore the search space—this would involve enumerating all possible distortions of each molecule (molecules are dynamic and exist in an ensemble of conformational states) and all possible rotational and translational orientations of the ligand relative to the protein at a given level of granularity. Most docking programs in use account for the whole conformational space of the ligand (flexible ligand), and several attempt to model a flexible protein receptor. Each "snapshot" of the pair is referred to as a pose.


title: Docking (molecular)

text: A variety of conformational search strategies have been applied to the ligand and to the receptor. These include:


title: Docking (molecular)

text: Conformations of the ligand may be generated in the absence of the receptor and subsequently docked or conformations may be generated on-the-fly in the presence of the receptor binding cavity, or with full rotational flexibility of every dihedral angle using fragment based docking. Force field energy evaluation are most often used to select energetically reasonable conformations, but knowledge-based methods have also been used.


title: Docking (molecular)

text: Peptides are both highly flexible and relatively large-sized molecules, which makes modeling their flexibility a challenging task. A number of methods were developed to allow for efficient modeling of flexibility of peptides during protein-peptide docking.


title: Docking (molecular)

text: Computational capacity has increased dramatically over the last decade making possible the use of more sophisticated and computationally intensive methods in computer-assisted drug design. However, dealing with receptor flexibility in docking methodologies is still a thorny issue. The main reason behind this difficulty is the large number of degrees of freedom that have to be considered in this kind of calculations. Neglecting it, however, in some of the cases may lead to poor docking results in terms of binding pose prediction.


title: Docking (molecular)

text: Multiple static structures experimentally determined for the same protein in different conformations are often used to emulate receptor flexibility. Alternatively rotamer libraries of amino acid side chains that surround the binding cavity may be searched to generate alternate but energetically reasonable protein conformations.


title: Docking (molecular)

text: Docking programs generate a large number of potential ligand poses, of which some can be immediately rejected due to clashes with the protein. The remainder are evaluated using some scoring function, which takes a pose as input and returns a number


title: Docking (molecular)

text: indicating the likelihood that the pose represents a favorable binding interaction and ranks one ligand relative to another.


title: Docking (molecular)

text: Most scoring functions are physics-based molecular mechanics force fields that estimate the energy of the pose within the binding site. The various contributions to binding can be written as an additive equation:


title: Docking (molecular)

text: The components consist of solvent effects, conformational changes in the protein and ligand, free energy due to protein-ligand interactions, internal rotations, association energy of ligand and receptor to form a single complex and free energy due to changes in vibrational modes. A low (negative) energy indicates a stable system and thus a likely binding interaction.


title: Docking (molecular)

text: Alternative approaches use modified scoring functions to include constraints based on known key protein-ligand interactions, or knowledge-based potentials derived from interactions observed in large databases of protein-ligand structures (e.g. the Protein Data Bank).


title: Docking (molecular)

text: There are a large number of structures from X-ray crystallography for complexes between proteins and high affinity ligands, but comparatively fewer for low affinity ligands as the latter complexes tend to be less stable and therefore more difficult to crystallize. Scoring functions trained with this data can dock high affinity ligands correctly, but they will also give plausible docked conformations for ligands that do not bind. This gives a large number of false positive hits, i.e., ligands predicted to bind to the protein that actually don't when placed together in a test tube.


title: Docking (molecular)

text: One way to reduce the number of false positives is to recalculate the energy of the top scoring poses using (potentially) more accurate but computationally more intensive techniques such as Generalized Born or Poisson-Boltzmann methods.


title: Docking (molecular)

text: The interdependence between sampling and scoring function affects the docking capability in predicting plausible poses or binding affinities for novel compounds. Thus, an assessment of a docking protocol is generally required (when experimental data is available) to determine its predictive capability. Docking assessment can be performed using different strategies, such as:


title: Docking (molecular)

text: Docking accuracy represents one measure to quantify the fitness of a docking program by rationalizing the ability to predict the right pose of a ligand with respect to that experimentally observed.


title: Docking (molecular)

text: Docking screens can also be evaluated by the enrichment of annotated ligands of known binders from among a large database of presumed non-binding, “decoy” molecules. In this way, the success of a docking screen is evaluated by its capacity to enrich the small number of known active compounds in the top ranks of a screen from among a much greater number of decoy molecules in the database. The area under the receiver operating characteristic (ROC) curve is widely used to evaluate its performance.


title: Docking (molecular)

text: Resulting hits from docking screens are subjected to pharmacological validation (e.g. IC affinity or potency measurements). Only prospective studies constitute conclusive proof of the suitability of a technique for a particular target. In the case of G protein-coupled receptors (GPCRs), which are targets of more than 30% of marketed drugs, molecular docking led to the discovery of more than 500 GPCR ligands.


title: Docking (molecular)

text: The potential of docking programs to reproduce binding modes as determined by X-ray crystallography can be assessed by a range of docking benchmark sets.


title: Docking (molecular)

text: For small molecules, several benchmark data sets for docking and virtual screening exist e.g. "Astex Diverse Set" consisting of high quality protein−ligand X-ray crystal structures or the "Directory of Useful Decoys" (DUD) for evaluation of virtual screening performance.


title: Docking (molecular)

text: An evaluation of docking programs for their potential to reproduce peptide binding modes can be assessed by "Lessons for Efficiency Assessment of Docking and Scoring" (LEADS-PEP).


title: Docking (molecular)

text: A binding interaction between a small molecule ligand and an enzyme protein may result in activation or inhibition of the enzyme. If the protein is a receptor, ligand binding may result in agonism or antagonism. Docking is most commonly used in the field of drug design — most drugs are small organic molecules, and docking may be applied to:


title: Small Arms Protective Insert

text: The Small Arms Protective Insert (SAPI) is a ceramic ballistic plate used by the United States Armed Forces. It was first used in the Interceptor Body Armor, a ballistic vest. It is now also used in the Improved Outer Tactical Vest as well as the Modular Tactical Vest, in addition to commercially available "plate carriers". The Kevlar Interceptor vest itself is designed to stop projectiles up to and including 9×19mm Parabellum submachine gun rounds, in addition to fragmentation. To protect against higher-velocity rifle rounds, SAPI plates are needed.


title: Small Arms Protective Insert

text: In May 2005, the U.S. Armed Forces began replacing the standard Small Arms Protective Insert plates with the Enhanced Small Arms Protective Insert (ESAPI).


title: Small Arms Protective Insert

text: An ESAPI provides protection from .30-06 Springfield M2 armor-piercing (AP) with a steel penetrator in accordance with the NIJ Level IV standard, but costs about $600 per plate, 50% more than SAPI plates. They are produced by Ceradyne, BAE Systems, and ArmorWorks Enterprises.


title: Small Arms Protective Insert

text: A call for a next generation plate, to stop even greater velocity threats than the ESAPI plate was issued by the U.S. Army in 2008. The X Threat Small Arms Protective Insert plates are specifically allowed scalar or flexible systems, and asked for better coverage, with less than a pound of additional weight. XSAPI did in fact offer slightly better protection, at the cost of more weight and thicker armor profile.


title: Small Arms Protective Insert

text: The XSAPI is intended to protect against an "X-Threat", which is able to be inferred from another source to be the M993 7.62 NATO armor piercing projectile. In addition, there is record of the FBI utilizing the plate for their purposes in May 2011.


title: Small Arms Protective Insert

text: The plates were developed in response to a perceived threat of AP projectiles in Iraq and Afghanistan. Over 120,000 inserts were procured; however, the AP threats they were meant to stop never materialized, and the plates were put into storage.


title: Small Arms Protective Insert

text: The standard plate for the Interceptor body armor is made of boron carbide or silicon carbide ceramic. The standard plates are not given an NIJ rating, as they are tested in accordance with specific protocols for the military and not the NIJ's testing. Military testing calls for survivability of three hits from the round marked on the plate - for standard SAPI, of a caliber up to 7.62×51mm NATO M80 ball and of a muzzle velocity up to 2,750 ft/s (840 m/s). For ESAPI, a .30-06 Springfield M2 armor-piercing (AP) (.30-06 black-tip armor-piercing) cartridge. This performance is only assured when backed by the soft armor of the OTV (or any soft armor which meets military requirements for protection). The ceramic plate is backed with a shield made of Spectra, a material up to 40% stronger than Kevlar, to trap any fragments of either plate or projectile and prevent them from injuring the wearer.


title: Small Arms Protective Insert

text: SAPI plates meant for body armor come in front and back plates which are identical, and smaller side plates. The front and back plates come in five sizes. Their dimensions are the following:


title: Small Arms Protective Insert

text: Side SAPI (SSAPI) torso side plates, and their replacement, the Enhanced Side Ballistic Inserts (ESBI), have identical weights and dimensions. ESBI plates can be replaced with size X-Small ESAPI plates (by unfolding an extension built into the bottom of the ESBI Carrier assembly), if permitted by the unit commander.


title: Small Arms Protective Insert

text: The mechanism of effect lies in absorbing and dissipating the projectile's kinetic energy in local shattering of the ceramic plate and blunting the bullet material on the hard ceramic. The Spectra backing then spreads the energy of the impact to a larger area and stops the fragments, reducing the likelihood of fatal injury to the wearer. The same principle is used for the ceramic tiles used for the armored cockpits of some military airplanes, and the anti-spallation liners used in modern armored personnel carriers.


title: Small Arms Protective Insert

text: It is a false assumption that eliminating the penetration of a projectile into the body by using a personal armor system ensures that the wearer will not experience serious injury or death. Blunt force trauma can cause fatal damage to internal organs.


title: Map of the Soul Tour

text: BTS Map of the Soul Tour was a planned worldwide concert tour headlined by South Korean band BTS to promote their "Map of the Soul" series, including their "" EP, and "" studio album. The all-stadium tour was announced on January 22, 2020 and was set to begin on April 11, 2020 at the Seoul Olympic Stadium in Seoul, South Korea until it was postponed due to the COVID-19 pandemic. A two-day online concert, titled BTS Map of the Soul ON:E, was held on October 10–11, 2020 in replacement of the postponed world tour. In total, the concert had an attendance of 993,000 viewers from 191 countries and territories. The postponed world tour was cancelled on August 19, 2021 due to uncertain circumstances and concerns over COVID-19.


title: Map of the Soul Tour

text: On January 21, 2020, the group first announced 38 tour dates spanning across Asia, North America, and Europe. The tour features extended North American and European visits as compared to previous tours due to popular demand. On February 27, 2020, the group cancelled all four shows in South Korea amid the ongoing COVID-19 pandemic. On March 26, 2020, the group postponed all 18 shows in North America as the COVID-19 pandemic continued to raise health concerns. On April 28, 2020, BTS announced that the entire tour would be postponed due to the COVID-19 pandemic. On August 19, 2021, the group's label Big Hit Music announced through Weverse that the entire world tour was cancelled due to uncertain circumstances.


title: Map of the Soul Tour

text: BTS Map of the Soul ON:E was a 2-day virtual pay-per-view concert headlined by South Korean band BTS to promote their "Map of the Soul" series, including their "" EP, and "" studio album in replacement of the postponed world tour. The concert was broadcast live from the KSPO Dome in Seoul on October 10–11, 2020. It was initially intended to have both a limited number of in-person tickets with a simultaneous online livestream but Big Hit Entertainment later cancelled the offline portion of the concert due to tightened COVID-19 pandemic government restrictions. The concert had different set lists each day and the production costs were an estimated 8 times higher than for their previous online show, BangBangCon: The Live. In total, the concert was attended by 993,000 viewers from 191 countries and territories.


title: Map of the Soul Tour

text: The two-and-a-half-hour show began with "On" and focused on songs from the group's most recent album, "Map of the Soul: 7," such as "N.O" and "Black Swan." For the hip-hop hit "UGH!", rappers Suga, RM, and J-Hope formed a group, while Jin, Jungkook, V, and Jimin sang the soft-pop ballad "Zero O' Clock." Jimin's debut of his dance performance for "Filter" was the show's high point. For their solo performances, RM, Suga, Jungkook, Jin, V, and J-Hope all chose different songs from the same song list: "," "Shadow," “Inner Child,” "My Time," "Moon," and "Ego." The visual effects of AR and XR extend beyond simply enhancing the scenery. Dark screens resembling underwater scenery filled up the sides of the stage as the septet sang "Black Swan," while with "Dope," the large screen behind the stage made it appear as though the members were dancing on an elevator as it shot upward as RM was smashing his "Persona" stage and a huge figure exactly like him suddenly appeared in front of the stage as planets and asteroids hovered above Jin as he sang to "Moon." The band's biggest hits, "Dionysus," "DNA," "Boy With Luv," and "No More Dream," were all included in the 23-song set list for the evening, as were the three songs from Saturday's encore stage: "Butterfly," "Run," and "Dynamite." "Spring Day" and "Idol," as well as the group's most recent hit, were performed on the second day.


title: Financial engineering

text: Financial engineering is a multidisciplinary field involving financial theory, methods of engineering, tools of mathematics and the practice of programming. It has also been defined as the application of technical methods, especially from mathematical finance and computational finance, in the practice of finance.


title: Financial engineering

text: which encompasses quantitative modelling, quantitative programming and risk managing financial products in compliance with the regulations and Basel capital/liquidity requirements.


title: Financial engineering

text: An older use of the term "financial engineering" that is less common today is aggressive restructuring of corporate balance sheets.


title: Financial engineering

text: Mathematical finance is the application of mathematics to finance. Computational finance and mathematical finance are both subfields of financial engineering. Computational finance is a field in computer science and deals with the data and algorithms that arise in financial modeling.


title: Financial engineering

text: Financial engineering draws on tools from applied mathematics, computer science, statistics and economic theory.


title: Financial engineering

text: In the broadest sense, anyone who uses technical tools in finance could be called a financial engineer, for example any computer programmer in a bank or any statistician in a government economic bureau. However, most practitioners restrict the term to someone educated in the full range of tools of modern finance and whose work is informed by financial theory. It is sometimes restricted even further, to cover only those originating new financial products and strategies.


title: Financial engineering

text: Despite its name, financial engineering does not belong to any of the fields in traditional professional engineering even though many financial engineers have studied engineering beforehand and many universities offering a postgraduate degree in this field require applicants to have a background in engineering as well. In the United States, the Accreditation Board for Engineering and Technology (ABET) does not accredit financial engineering degrees. In the United States, financial engineering programs are accredited by the "International Association of Quantitative Finance".


title: Financial engineering

text: Quantitative analyst ("Quant") is a broad term that covers any person who uses math for practical purposes, including financial engineers. Quant is often taken to mean "financial quant", in which case it is similar to financial engineer. The difference is that it is possible to be a theoretical quant, or a quant in only one specialized niche in finance, while "financial engineer" usually implies a practitioner with broad expertise.


title: Financial engineering

text: "Rocket scientist" (aerospace engineer) is an older term, first coined in the development of rockets in WWII (Wernher von Braun), and later, the NASA space program; it was adapted by the first generation of financial quants who arrived on Wall Street in the late 1970s and early 1980s. While basically synonymous with financial engineer, it implies adventurousness and fondness for disruptive innovation. Financial "rocket scientists" were usually trained in applied mathematics, statistics or finance and spent their entire careers in risk-taking. They were not hired for their mathematical talents, they either worked for themselves or applied mathematical techniques to traditional financial jobs. The later generation of financial engineers were more likely to have PhDs in mathematics, physics, electrical and computer engineering, and often started their careers in academics or non-financial fields.


title: Financial engineering

text: One of the prominent critics of financial engineering is Nassim Taleb, a professor of financial engineering at Polytechnic Institute of New York University who argues that it replaces common sense and leads to disaster. A series of economic collapses has led many governments to argue a return to "real" engineering from financial engineering.


title: Financial engineering

text: A gentler criticism came from Emanuel Derman who heads a financial engineering degree program at Columbia University. He blames over-reliance on models for financial problems; see Financial Modelers' Manifesto.


title: Financial engineering

text: Many other authors have identified specific problems in financial engineering that caused catastrophes:


title: Financial engineering

text: The financial innovation often associated with financial engineers was mocked by former chairman of the Federal Reserve Paul Volcker in 2009 when he said it was a code word for risky securities, that brought no benefits to society. For most people, he said, the advent of the ATM was more crucial than any asset-backed bond.