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Euclidean Rhythm
The Euclidean rhythm in music was discovered by Godfried Toussaint in 2004 and is described in a 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms".The Euclidean algorithm generates traditional musical rhythms by G. T. Toussaint, ''Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science'', Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47–56. The of two numbers is used rhythmically giving the number of beats ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Godfried Toussaint
Godfried Theodore Patrick Toussaint (1944 – July 2019) was a Canadian computer scientist, a professor of computer science, and the head of the Computer Science Program at New York University Abu Dhabi (NYUAD) in Abu Dhabi, United Arab Emirates. He is considered to be the father of computational geometry in Canada. He did research on various aspects of computational geometry, discrete geometry, and their applications: pattern recognition (k-nearest neighbor algorithm, cluster analysis), motion planning, visualization (computer graphics), knot theory (stuck unknot problem), linkage (mechanical) reconfiguration, the art gallery problem, polygon triangulation, the largest empty circle problem, unimodality (unimodal function), and others. Other interests included meander (art), compass and straightedge constructions, instance-based learning, music information retrieval, and computational music theory. He was a co-founder of the Annual ACM Symposium on Computational Geometry, and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Algorithm
In mathematics, the Euclidean algorithm,Some widely used textbooks, such as I. N. Herstein's ''Topics in Algebra'' and Serge Lang's ''Algebra'', use the term "Euclidean algorithm" to refer to Euclidean division or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in Euclid's Elements, his ''Elements'' (c. 300 BC). It is an example of an ''algorithm'', a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use. It can be used to reduce Fraction (mathematics), fractions to their Irreducible fraction, simplest form, and is a part of many other number-theoretic and cryptographic calculations. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greatest Common Divisor
In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers ''x'', ''y'', the greatest common divisor of ''x'' and ''y'' is denoted \gcd (x,y). For example, the GCD of 8 and 12 is 4, that is, \gcd (8, 12) = 4. In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), etc. Historically, other names for the same concept have included greatest common measure. This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see below). Overview Definition The ''greatest common divisor'' (GCD) of two nonzero integers and is the greatest positive integer such that is a divisor of both and ; that is, there are integers and such that and , and is the largest s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhythm
Rhythm (from Greek , ''rhythmos'', "any regular recurring motion, symmetry") generally means a " movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions". This general meaning of regular recurrence or pattern in time can apply to a wide variety of cyclical natural phenomena having a periodicity or frequency of anything from microseconds to several seconds (as with the riff in a rock music song); to several minutes or hours, or, at the most extreme, even over many years. Rhythm is related to and distinguished from pulse, meter, and beats: In the performance arts, rhythm is the timing of events on a human scale; of musical sounds and silences that occur over time, of the steps of a dance, or the meter of spoken language and poetry. In some performing arts, such as hip hop music, the rhythmic delivery of the lyrics is one of the most important elements of the style. Rhythm may also refer to visual presentation, as "timed mov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beat (music)
In music and music theory, the beat is the basic unit of time, the pulse (regularly repeating event), of the ''mensural level'' (or ''beat level''). The beat is often defined as the rhythm listeners would tap their toes to when listening to a piece of music, or the numbers a musician counts while performing, though in practice this may be technically incorrect (often the first multiple level). In popular use, ''beat'' can refer to a variety of related concepts, including pulse, tempo, meter, specific rhythms, and groove. Rhythm in music is characterized by a repeating sequence of stressed and unstressed beats (often called "strong" and "weak") and divided into bars organized by time signature and tempo indications. Beats are related to and distinguished from pulse, rhythm (grouping), and meter: Metric levels faster than the beat level are division levels, and slower levels are multiple levels. Beat has always been an important part of music. Some music genres such as fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Music Of India
Owing to India's vastness and diversity, Indian music encompasses numerous genres in multiple varieties and forms which include classical music, folk (Bollywood), rock, and pop. It has a history spanning several millennia and developed over several geo-locations spanning the sub-continent. Music in India began as an integral part of socio-religious life. History Pre-history Paleolithic The 30,000-year-old paleolithic and neolithic cave paintings at the UNESCO world heritage site at Bhimbetka rock shelters in Madhya Pradesh show a type of dance. Mesolithic and chalcolithic cave art of Bhimbetka illustrates musical instruments such as Gongs, Bowed Lyre, daf etc. Neolithic Chalcolithic era (4000 BCE onward) narrow bar shaped polished stone celts like music instruments, one of the earlier musical instrument in India, were excavated at Sankarjang in the Angul district of Odisha. There is historical evidence in the form of sculptural evidence, i.e. musical instruments, si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bresenham's Line Algorithm
Bresenham's line algorithm is a line drawing algorithm that determines the points of an ''n''-dimensional raster that should be selected in order to form a close approximation to a straight line between two points. It is commonly used to draw line primitives in a bitmap image (e.g. on a computer screen), as it uses only integer addition, subtraction and bit shifting, all of which are very cheap operations in commonly used computer instruction sets such as x86_64. It is an incremental error algorithm, and one of the earliest algorithms developed in the field of computer graphics. An extension to the original algorithm may be used for drawing circles. While algorithms such as Wu's algorithm are also frequently used in modern computer graphics because they can support antialiasing, Bresenham's line algorithm is still important because of its speed and simplicity. The algorithm is used in hardware such as plotters and in the graphics chips of modern graphics cards. It can also be fou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisible
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder. Definition An integer is divisible by a nonzero integer if there exists an integer such that n=km. This is written as :m\mid n. Other ways of saying the same thing are that divides , is a divisor of , is a factor of , and is a multiple of . If does not divide , then the notation is m\not\mid n. Usually, is required to be nonzero, but is allowed to be zero. With this convention, m \mid 0 for every nonzero integer . Some definitions omit the requirement that m be nonzero. General Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conrad Henfling
Conrad Henfling (1648–1716 Ansbach, Germany),Leibniz und Der Briefwechsel zwischen Henfling Conrad by Rudolf von Herausgegeben Haase, Vittorio Klostermann, Frankfurt am Main, 1982, musicologist, musician, mathematician and lawyerBaierisches Musik-Lexikon by Lipowsky, Felix Joseph, Munich, 1811, page 122. was an official and privy councilor (Hofrat) at the court of the Margrave of Ansbach, Germany. He also invented a new type of keyboard for organ and harpsichord,La musique, une pratique cachée de l'arithmétique? by Patrice Bailhace, ''Studia Leibniztiana'', Actes du colloque L'actualité de Leibniz: les deux labyrinthes, Cerisy, 1995 the design of which was extended by Paul von Janko in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science: while serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Instruments
A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who plays a musical instrument is known as an instrumentalist. The history of musical instruments dates to the beginnings of human culture. Early musical instruments may have been used for rituals, such as a horn to signal success on the hunt, or a drum in a religious ceremony. Cultures eventually developed composition and performance of melodies for entertainment. Musical instruments evolved in step with changing applications and technologies. The date and origin of the first device considered a musical instrument is disputed. The oldest object that some scholars refer to as a musical instrument, a simple flute, dates back as far as 50,000 - 60,000 years. Some consensus dates early flutes to about 40,000 years ago. However, most historians be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
