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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 constru ... [...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 produce ... [...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,&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Tuning
In music, there are two common meanings for tuning: * #Tuning practice, Tuning practice, the act of tuning an instrument or voice. * #Tuning systems, Tuning systems, the various systems of Pitch (music), 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 A440 (pitch standard), A = 440 Hz. The term "''out of tune''" refers to a pitch/tone that is either too high (Sharp (music), sharp) or too low (Flat (music), 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 method ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octahedron
In geometry, an octahedron (: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Many types of irregular octahedra also exist, including both convex set, convex and non-convex shapes. Combinatorially equivalent to the regular octahedron The following polyhedra are combinatorially equivalent to the regular octahedron. They all have six vertices, eight triangular faces, and twelve edges that correspond one-for-one with the features of it: * Triangular antiprisms: Two faces are equilateral, lie on parallel planes, and have a common axis of symmetry. The other six triangles are isosceles. The regular octahedron is a special case in which the six lateral triangles are also equilateral. * Tetragonal bipyramids, in which at least one of the equatorial quadrilaterals lies on a plane. The regular octahedron is a special case in which all thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st harmonic''; the other harmonics are known as ''higher harmonics''. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a '' harmonic series''. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz. In music, harmonics are used on string instruments and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Just Tuning And Intervals
Just or JUST may refer to: Arts and entertainment * "Just" (song), 1995, by Radiohead * ''Just!'', Australian author Andy Griffiths' children's story collections * ''Just'', a 1998 album by Dave Lindholm * "Just", a 2005 song on ''Lost and Found'' by Mudvayne * "Just", a 2016 song on ''Melting'' by Mamamoo Businesses * JUST, Inc., an American food manufacturing company * Just Group, an Australian owner and operator of seven retail brands * Just Group plc, a British company specialising in retirement products and services Education * Jashore University of Science and Technology, Bangladesh * Jinwen University of Science and Technology, Taiwan * Jordan University of Science and Technology, Jordan People * Just (surname) * Just (given name) * List of people known as the Just See also * * Jus (other) * Justice (other) Justice is the philosophical concept of the morally correct assignment of goods and evils. Justice or Justices may also refer to: Common uses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-dimensional Geometry
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or Mathematical object, object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), line has a One-dimensional space, dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A Surface (mathematics), surface, such as the Boundary (mathematics), boundary of a Cylinder (geometry), cylinder or sphere, has a Two-dimensional space, dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the Euclidean plane, plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these ... [...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. He mostly wrote pieces for orchestral and chamber music. His compositions have been performed at Merkin Concert Hall, Carnegie Hall and Symphony Space Symphony Space, founded by Isaiah Sheffer and Allan Miller, is a multi-disciplinary performing arts organization at 2537 Broadway on the Upper West Side of Manhattan in New York City. Performances take place in the 760-seat Peter Jay Sharp Theat .... Concerts were held in Eastern Europe and Russia. Recently, he was working with the German Ensemble Sortisatio. Fu ... [...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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subharmonic
In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways. While the overtone series is based upon arithmetic multiplication of frequencies, resulting in a harmonic series, the undertone series is based on arithmetic division. Nattiez shows the undertone series on E, as Riemann (''Handbuch der Harmonielehre'', 10th ed., 1929, p. 4) and D'Indy (''Cours de composition musicale'', vol. I, 1912, p. 100) had done. Terminology The hybrid term ''subharmonic'' is used in music in a few different ways. In its pure sense, the term ''subharmonic'' refers strictly to any member of the subharmonic series (, , , , etc.). When the subharmonic series is used to refer to frequency relationships, it is written with f representing some highest known reference frequency (, , , , e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utonal
''Otonality'' and ''utonality'' are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: , , ,... or , , ,.... Definition An otonality is a collection of pitches which can be expressed in ratios, expressing their relationship to the fixed tone, that have equal denominators and consecutive numerators. For example, , , and ( just major chord) form an otonality because they can be written as , , . This in turn can be written as an extended ratio 4:5:6. Every otonality is therefore composed of members of a harmonic series. Similarly, the ratios of a utonality share the same numerator and have consecutive denominators. , , , and () form a utonality, sometimes written as , or as . Every utonality is therefore composed of members of a subharmonic series. This term is used extensively by Harry Partch in ''Genesis of a Music''. An otonality corresponds to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
