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Nomos Alpha
''Nomos Alpha'' ( el, Νόμος α΄) is a piece for solo cello composed by Iannis Xenakis in 1965, commissioned by Radio Bremen for cellist Siegfried Palm, and dedicated to mathematicians Aristoxenus of Tarentum, Évariste Galois, and Felix Klein. This piece is an example of a style of music called, by Xenakis, symbolic music – a style of music which makes use of set theory, abstract algebra, and mathematical logic in order to create and analyze musical compositions. Along with symbolic music, Xenakis is known for his development of stochastic music. During his lifetime, Xenakis was a vocal critic of modern Western music since the development of polyphony for its diminished set of outside-time structures, especially when compared to folk and the Byzantine musical traditions. This perceived incompleteness of Western music was the main impetus for the development of symbolic music and for composing Nomos Alpha, his most well-known example of the genre. ''Nomos Alpha'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cello
The cello ( ; plural ''celli'' or ''cellos'') or violoncello ( ; ) is a Bow (music), bowed (sometimes pizzicato, plucked and occasionally col legno, hit) string instrument of the violin family. Its four strings are usually intonation (music), tuned in perfect fifths: from low to high, scientific pitch notation, C2, G2, D3 and A3. The viola's four strings are each an octave higher. Music for the cello is generally written in the bass clef, with tenor clef, and treble clef used for higher-range passages. Played by a ''List of cellists, cellist'' or ''violoncellist'', it enjoys a large solo repertoire Cello sonata, with and List of solo cello pieces, without accompaniment, as well as numerous cello concerto, concerti. As a solo instrument, the cello uses its whole range, from bassline, bass to soprano, and in chamber music such as string quartets and the orchestra's string section, it often plays the bass part, where it may be reinforced an octave lower by the double basses. Figure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Folk Music
Folk music is a music genre that includes traditional folk music and the contemporary genre that evolved from the former during the 20th-century folk revival. Some types of folk music may be called world music. Traditional folk music has been defined in several ways: as music transmitted orally, music with unknown composers, music that is played on traditional instruments, music about cultural or national identity, music that changes between generations (folk process), music associated with a people's folklore, or music performed by custom over a long period of time. It has been contrasted with commercial and classical styles. The term originated in the 19th century, but folk music extends beyond that. Starting in the mid-20th century, a new form of popular folk music evolved from traditional folk music. This process and period is called the (second) folk revival and reached a zenith in the 1960s. This form of music is sometimes called contemporary folk music or folk rev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compositions By Iannis Xenakis
Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include visuals and digital space *Composition (music), an original piece of music and its creation *Composition (visual arts), the plan, placement or arrangement of the elements of art in a work * ''Composition'' (Peeters), a 1921 painting by Jozef Peeters *Composition studies, the professional field of writing instruction * ''Compositions'' (album), an album by Anita Baker *Digital compositing, the practice of digitally piecing together a video Computer science *Function composition (computer science), an act or mechanism to combine simple functions to build more complicated ones *Object composition, combining simpler data types into more complex data types, or function calls into calling functions History *Composition of 1867, Austro-Hungarian/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solo Cello Pieces
Solo or SOLO may refer to: Arts and entertainment Comics * ''Solo'' (DC Comics), a DC comics series * Solo, a 1996 mini-series from Dark Horse Comics Characters * Han Solo, a ''Star Wars'' character * Jacen Solo, a Jedi in the non-canonical ''Star Wars Legends'' continuity * Kylo Ren, real name Ben Solo, a ''Star Wars'' character * Napoleon Solo, from the TV spy series ''Man from U.N.C.L.E.'' * Sky Solo, from the comic book series ''1963'' * Solo (Marvel Comics), a fictional counter-terrorism operative Films * ''Solo'' (1969 film), directed by Jean-Pierre Mocky * ''Solo'' (1972 film), directed by Mike Hoover * ''Solo'' (1977 film), a New Zealand film * ''Solo'' (1984 film), starring Sandra Kerns * ''Solo'' (1996 film), a science fiction action film * ''Solo'' (2006 film), an Australian film written and directed by Morgan O'Neill * ''Solo'' (2008 film), an Australian documentary film directed by David Michod and Jennifer Peedom * ''Solo'' (2011 film), a Telugu-language fil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moritz Müllenbach
Moritz is the German equivalent of the name Maurice. It may refer to: People Given name * Saint Maurice, also called Saint Moritz, the leader of the legendary Roman Theban Legion in the 3rd century * Prince Moritz of Hesse (2007), the son of Donatus, Prince and Landgrave of Hesse * Prince Moritz of Anhalt-Dessau (1712–1760), a German prince of the House of Ascania from the Anhalt-Dessau branch * Moritz, Landgrave of Hesse (1926), the head of the House of Hesse, pretendant to the throne of Finland, son of Prince Philip, Landgrave of Hesse * Moritz, Prince of Dietrichstein (1775–1864) * Moritz Becker, American politician * Moritz Benedikt (1849–1920), Jewish-Austrian newspaper editor * Moritz Borman, film producer * Moritz Michael Daffinger (1790–1849), Austrian miniature painter and sculptor * Moritz Duschak (1815–1890), Moravian rabbi and writer * Moritz Schlick, German philosopher and physicist * Moritz von Schwind, Austrian painter * Moritz Steinla (1791–1858), Ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Composition
In mathematics, function composition is an operation that takes two functions and , and produces a function such that . In this operation, the function is applied to the result of applying the function to . That is, the functions and are composed to yield a function that maps in domain to in codomain . Intuitively, if is a function of , and is a function of , then is a function of . The resulting ''composite'' function is denoted , defined by for all in . The notation is read as " of ", " after ", " circle ", " round ", " about ", " composed with ", " following ", " then ", or " on ", or "the composition of and ". Intuitively, composing functions is a chaining process in which the output of function feeds the input of function . The composition of functions is a special case of the composition of relations, sometimes also denoted by \circ. As a result, all properties of composition of relations are true of composition of functions, such as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Operator
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation ''on a set'' is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. An operation of arity two that involves several sets is sometimes also called a ''binary operation''. For example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Such binary operations may be called simply binary functions. Binary operations are the keystone of most algebraic structures that are studied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutations
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices. The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron a 3-zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the octahedron. It has cubical or octahedral symmetry. The cube is the only convex polyhedron whose faces are all squares. Orthogonal projections The ''cube'' has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure. The first and third correspond to the A2 and B2 Coxeter planes. Spherical tiling The cube can also be represented as a spherical tiling, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: ἴσος ''isos'' "equal", and μορφή ''morphe'' "form" or "shape". The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects). Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may be identified. In mathematical jargon, one says that two objects are . An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism between the two structures (as it is the case for solutions of a univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octahedral Group
A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation. A cube has the same set of symmetries, since it is the polyhedron that is dual to an octahedron. The group of orientation-preserving symmetries is ''S''4, the symmetric group or the group of permutations of four objects, since there is exactly one such symmetry for each permutation of the four diagonals of the cube. Details Chiral and full (or achiral) octahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups compatible with translational symmetry. They are among the crystallographic point groups of the cubic crystal system. As the hyperoctahedral group of dimension 3 the full octahedral group is the wreath product S_2 \wr S_3 \simeq S_2^3 \rtimes S_3,and a natural way to identify its elements is as pairs (m, n) with m \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
