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Combination-product Sets
In musical tuning systems, the hexany, invented by Erv Wilson, represents one of the simplest structures found in his combination product sets. It is referred to as an uncentered structure, meaning that it implies no tonic. It achieves this by using consonant relations as opposed to the dissonance methods normally employed by atonality. While it is often and confusingly overlapped with the Euler–Fokker genus, the subsequent stellation of Wilson's combination product sets (CPS) are outside of that Genus. The Euler Fokker Genus fails to see 1 as a possible member of a set except as a starting point. The numbers of vertices of his combination sets follow the numbers in Pascal's triangle. In this construction, the hexany is the third cross-section of the four-factor set and the first uncentered one. hexany is the name that Erv Wilson gave to the six notes in the 2-out-of-4 combination product set, abbreviated as 2*4 CPS. Simply, the hexany is the 2 out of 4 set. It is construc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. A regular octahedron is the dual polyhedron of a cube. It is a rectified tetrahedron. It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations. An octahedron is the three-dimensional case of the more general concept of a cross polytope. A regular octahedron is a 3-ball in the Manhattan () metric. Regular octahedron Dimensions If the edge length of a regular octahedron is ''a'', the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is :r_u = \frac a \approx 0.707 \cdot a and the radius of an inscribed sphere (tangent to each of the octahedron's faces) is :r_i = \frac a \approx 0.408\cdot a while the midradius, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets. For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Just Tuning And Intervals
Just or JUST may refer to: __NOTOC__ People * Just (surname) * Just (given name) Arts and entertainment * ''Just'', a 1998 album by Dave Lindholm * "Just" (song), a song by Radiohead * "Just", a song from the album ''Lost and Found'' by Mudvayne * ''Just!'' (series), a series of short-story collections for children by Andy Griffiths JUST * Jordan University of Science and Technology, Jordan * Jessore University of Science & Technology, Bangladesh * Jinwen University of Science and Technology, New Taipei, Taiwan Businesses * Just Group plc, a British company specialising in retirement products and services * Just Group, an Australian owner and operator of seven retail brands * JUST, Inc., an American food manufacturing company See also * * List of people known as the Just * Saint-Just (other) * Justice Justice, in its broadest sense, is the principle that people receive that which they deserve, with the interpretation of what then constitutes "deserving" bein ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Pehrson
Joseph Pehrson (August 14, 1950 – April 4, 2020) was an American composer and pianist. Life Pehrson comes from Detroit, Michigan. He studied at the University of Michigan and Eastman School of Music. (D.M.A. 1981). His teachers include Leslie Bassett, Joseph Schwantner, Otto Luening and Elie Siegmeister. From 1992 to 1993 he was composer-in-residence at the University of Akron. Since 1983 he served as co-director of the Composers Concordance in New York City.Europa Publications (2003). ''International Who's Who in Classical Music 2003''. London: Routledge. . pp. 602. He mostly wrote pieces for orchestral and chamber music. His compositions have been performed at Merkin Concert Hall, Carnegie Hall and Symphony Space. Concerts were held in Eastern Europe and Russia. Recently, he was working with the German Ensemble Sortisatio Ensemble Sortisatio is a quartet (viola, oboe/cor anglais, bassoon and guitar) founded by violist Matthias Sannemüller in 1992 in Leipzig, German ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel James Wolf
Daniel James Wolf (born September 13, 1961 in Upland, California) is an American composer. Studies Wolf studied composition with Gordon Mumma, Alvin Lucier, and La Monte Young, as well as musical tunings with Erv Wilson and Douglas Leedy and ethnomusicology (M.A., Ph.D. 1990 Wesleyan University). Important contacts with Lou Harrison, John Cage, Walter Zimmermann. Managing Editor of the journal '' Xenharmonikon'', 1985-89. Based in Europe from 1989, he is known as a member of the "Material" group of composers, along with Hauke Harder, Markus Trunk and others. Compositions Wolf's compositions apply an experimental approach to musical materials, with a special interest in intonation, yet often display a surface that playfully - if accidentally - recalls historical music. Major works include ''The White Canoe'', an opera seria for hand puppets to the libretto by Edward Gorey, six string quartets, ''Figure & Ground'' for string trio, ''Field Study'' for vn, tb, ban, gui, ''Dec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kraig Grady
Kraig Grady (born 1952) is a US-Australian composer/sound artist. He has composed and performed with an ensemble of microtonal instruments of his own design and also worked as a shadow puppeteer, tuning theorist, filmmaker, world music radio DJ and concert promoter. His works feature his own ensembles of acoustic instruments, including metallophones, marimbas, hammered dulcimers and reed organs tuned to microtonal just intonation scales. His compositions include accompaniments for silent films and shadow plays. An important influence in the development of Grady's music was Harry Partch, like Grady, a musician from the Southwest, and a composer of theatrical works in Just Intonation for self-built instruments. Many of his compositions use unusual meters of very extended lengths. Biography Born in Montebello, California in 1952, Grady began composing while still in his teens. After studies with Nicolas Slonimsky, Dean Drummond, Dorrance Stalvey and Byong-Kon Kim, he produced h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birectified 5-simplex
In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a Rectification (geometry), rectification of the regular 5-simplex. There are three unique degrees of rectifications, including the zeroth, the 5-simplex itself. Vertices of the ''rectified 5-simplex'' are located at the edge-centers of the ''5-simplex''. Vertices of the ''birectified 5-simplex'' are located in the triangular face centers of the ''5-simplex''. Rectified 5-simplex In Five-dimensional space, five-dimensional geometry, a rectified 5-simplex is a uniform 5-polytope with 15 vertex (geometry), vertices, 60 Edge (geometry), edges, 80 Triangle, triangular Face (geometry), faces, 45 Cell (geometry), cells (30 Tetrahedron, tetrahedral, and 15 Octahedron, octahedral), and 12 4-faces (6 5-cell and 6 rectified 5-cells). It is also called 03,1 for its branching Coxeter-Dynkin diagram, shown as . Emanuel Lodewijk Elte, E. L. Elte identified it in 1912 as a semiregular polytope, labeling i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge Vector
This is a glossary of terms relating to computer graphics. For more general computer hardware terms, see glossary of computer hardware terms. 0–9 A B C D E F G H I K L M N O P Q R S T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexateron
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets. It has a dihedral angle of cos−1(), or approximately 78.46°. The 5-simplex is a solution to the problem: ''Make 20 equilateral triangles using 15 matchsticks, where each side of every triangle is exactly one matchstick.'' Alternate names It can also be called a hexateron, or hexa-5-tope, as a 6- facetted polytope in 5-dimensions. The name ''hexateron'' is derived from ''hexa-'' for having six facets and '' teron'' (with ''ter-'' being a corruption of ''tetra-'') for having four-dimensional facets. By Jonathan Bowers, a hexateron is given the acronym hix. As a configuration This configuration matrix represents the 5-simplex. The rows and columns correspond to vertices, edges, faces, cells and 4-faces. The diagonal numbers say how many of each element occur in the whole 5-simplex. The nondiagonal numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dispentachoron
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge has one tetrahedron and two octahedra. Each vertex has two tetrahedra and three octahedra. In total it has 30 triangle faces, 30 edges, and 10 vertices. Each vertex is surrounded by 3 octahedra and 2 tetrahedra; the vertex figure is a triangular prism. Topologically, under its highest symmetry, ,3,3 there is only one geometrical form, containing 5 regular tetrahedra and 5 rectified tetrahedra (which is geometrically the same as a regular octahedron). It is also topologically identical to a tetrahedron-octahedron segmentochoron. The vertex figure of the ''rectified 5-cell'' is a uniform triangular prism, formed by three octahedra around the sides, and two tetrahedra on the opposite ends. Despite having the same number of vertices as cells (10) and the same number of edges as faces (30), the rectified 5-cell is not self-dual becaus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentachoron
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol . It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is the 4-simplex (Coxeter's \alpha_4 polytope), the simplest possible convex 4-polytope, and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions. The 5-cell is a 4-dimensional pyramid with a tetrahedral base and four tetrahedral sides. The regular 5-cell is bounded by five regular tetrahedra, and is one of the six regular convex 4-polytopes (the four-dimensional analogues of the Platonic solids). A regular 5-cell can be constructed from a regular tetrahedron by adding a fifth vertex one edge length distant from all the vertices of the tetrahedron. This cannot be done in 3-dimensional space. The regular 5-cell is a solution to the problem: ''Make 10 equilateral triangles, all of the same size, using 10 matc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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