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Hexany
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] |
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] |
Musical Tuning
In music, there are two common meanings for tuning: * Tuning practice, the act of tuning an instrument or voice. * Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases. Tuning practice Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as A = 440 Hz. The term "''out of tune''" refers to a pitch/tone that is either too high (sharp) or too low (flat) in relation to a given reference pitch. While an instrument might be in tune relative to its own range of notes, it may not be considered 'in tune' if it does not match the chosen reference pitch. Some instruments become 'out of tune' with temperature, humidity, damage, or simply time, and must be readjusted or repaired. Different methods of sound production require different methods of adjustment: * Tuning to a pitch with one's voic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Fokker Genus
In music theory and tuning, an Euler–Fokker genus (plural: genera), named after Leonhard Euler and Adriaan Fokker,Rasch, Rudolph (2000). ''Harry Partch'', p.31-2. Dunn, David, ed. . is a musical scale in just intonation whose pitches can be expressed as products of some of the members of some multiset of generating prime factors. Powers of two are usually ignored, because of the way the human ear perceives octaves as equivalent. An x-dimensional tone-dimension contains x factors. "An Euler-Fokker genus with two dimensions may be represented in a two-dimensional (rectangular) tone-grid, one with three dimensions in a three-dimensional (block-shaped) tone-lattice. Euler-Fokker genera are characterized by a listing of the number of steps in each dimension. The number of steps is represented by a repeated mention of the dimension, so that there arise descriptions such as 3 5 5 5 7 3 5 5 7 7 11 11 etc." For example, the multiset yields the Euler–Fokker genus , 3,&n ... [...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] |
Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, * a 0-dimensional simplex is a point, * a 1-dimensional simplex is a line segment, * a 2-dimensional simplex is a triangle, * a 3-dimensional simplex is a tetrahedron, and * a 4-dimensional simplex is a 5-cell. Specifically, a ''k''-simplex is a ''k''-dimensional polytope which is the convex hull of its ''k'' + 1 vertices. More formally, suppose the ''k'' + 1 points u_0, \dots, u_k \in \mathbb^ are affinely independent, which means u_1 - u_0,\dots, u_k-u_0 are linearly independent. Then, the simplex determined by them is the set of points : C = \left\ This representation in terms of weighted vertices is known as the barycentric coordinate system. A regular simplex is a simplex that is also a regular polytope. A ... [...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] |
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] |
