All-interval Tetrachord

picture info	All-interval Tetrachord An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form. In set theory (music), set theory notation, these are [0,1,4,6] (4-Z15) and [0,1,3,7] (4-Z29). Their inversions are [0,2,5,6] (4-Z15b) and [0,4,6,7] (4-Z29b). The interval vector for all all-interval tetrachords is [1,1,1,1,1,1]. Table of interval classes as relating to all-interval tetrachords In the examples below, the tetrachords [0,1,4,6] and [0,1,3,7] are built on E (musical note), E. Use in modern music The unique qualities of the all-interval tetrachord have made it very popular in 20th-century music. Composers including Elliott Carter (String Quartet No. 1 (Carter), First String Quartet) and George Perle used it extensively. See also All-interval twelve-tone row All-trichord hexachord Perfect ruler Serialism Trichord References Externa ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
	String Quartet No String or strings may refer to: String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films Strings (1991 film), ''Strings'' (1991 film), a Canadian animated short * Strings (2004 film), ''Strings'' (2004 film), a film directed by Anders Rønnow Klarlund * Strings (2011 film), ''Strings'' (2011 film), an American dramatic thriller film * Strings (2012 film), ''Strings'' (2012 film), a British film by Rob Savage * ''Bravetown'' (2015 film), an American drama film originally titled ''Strings'' * ''The String'' (2009), a French film Music Instruments * String (music), the flexible element that produces vibrations and sound in string instruments * String instrument, a musical instrument that produces sound through vibrating strings ** List of string instruments * String piano, a pianistic extended technique in which sound is produced by direct manipulation of the strings, r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Post-tonal Music Theory Post-tonal music theory is the set of theories put forward to describe music written outside of, or 'after', the tonal system of the common practice period. It revolves around the idea of 'emancipating dissonance', that is, freeing the structure of music from the familiar harmonic patterns that are derived from natural overtones. As music becomes more complex, dissonance becomes indistinguishable from consonance. Overview In the latter part of the 19th century, composers began to move away from the tonal system. This is typified in Richard Wagner's music, especially ''Tristan und Isolde'' (the Tristan chord, for example). Arnold Schoenberg and his pupil Anton Webern proposed a theory on the emancipation of the dissonance to help analyse the general trend and, in particular, their own atonal music. Composers such as Charles Ives, Dane Rudhyar, and even Duke Ellington and Lou Harrison, connected the emancipation of the dissonance with the emancipation of society and humanity. The ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Chords Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a particular tuning * Chord (geometry), a line segment joining two points on a curve * Chord (astronomy), a line crossing a foreground astronomical object during an occultation which gives an indication of the object's size and/or shape * Chord (graph theory), an edge joining two nonadjacent nodes in a cycle * Chord in truss construction – an outside member of a truss, as opposed to the inner "webbed members" * Chord (aeronautics), the distance between the front and back of a wing, measured in the direction of the normal airflow. The term chord was selected due to the curved nature of the wing's surface * Chord (peer-to-peer), a peer-to-peer protocol and algorithm for distributed hash tables (DHT) * Chord (concurrency), a concurrency construct in some object-oriented programming languages * In British railway terminology, a chord c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Trichord In music theory, a trichord () is a group of three different pitch classes found within a larger group. A trichord is a contiguous three-note set from a musical scale or a twelve-tone row. In musical set theory there are twelve trichords given inversional equivalency, and, without inversional equivalency, nineteen trichords. These are numbered 1–12, with symmetrical trichords being unlettered and with uninverted and inverted nonsymmetrical trichords lettered A or B, respectively. They are often listed in prime form, but may exist in different voicings; different inversions at different transpositions. For example, the major chord, 3-11B (prime form: ,4,7, is an inversion of the minor chord, 3-11A (prime form: ,3,7. 3-5A and B are the Viennese trichord (prime forms: ,1,6and ,5,6. Historical Russian definition In late-19th to early 20th-century Russian musicology, the term trichord (трихорд ()) meant something more specific: a set of three pitches, each at least ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Serialism In music, serialism is a method of Musical composition, composition using series of pitches, rhythms, dynamics, timbres or other elements of music, musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were also working to establish serialism as a form of atonality, post-tonal thinking. Twelve-tone technique orders the twelve notes of the chromatic scale, forming a tone row, row or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and variation (music), variations. Other types of serialism also work with set (music), sets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "parameter (music), parameters"), such as duration (music), duration, Dynamics (music), dynamics, and timbre. The idea of serialism is also applied in various ways in the visual arts, design, and architectu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Perfect Ruler A perfect ruler of length \ell is a ruler with integer markings a_1=0 < a_2 < \dots < a_n=\ell, for which there exists an integer $m$ such that any positive integer $k\leq m$ is uniquely expressed as the difference $k=a_i-a_j$ for some $i,j$ . This is referred to as an $m$ -perfect ruler. An optimal perfect ruler is one of the smallest length for fixed values of $m$ and $n$ . Example A 4-perfect ruler of length $7$ is given by $(a_1,a_2,a_3,a_4)=(0,1,3,7)$ . To verify this, we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	All-trichord Hexachord In music, the all-trichord hexachord is a unique hexachord that contains all twelve trichords, or from which all twelve possible trichords may be derived. The prime form of this set class is and its Forte number is 6-Z17. Its complement is 6-Z43 and they share the interval vector of . It appears in pieces by Robert Morris and Elliott Carter. Carter uses all-interval twelve-tone sets consisting of all-trichord hexachords in his '' Symphonia: sum fluxae pretium spei''.Schiff (1998), p. 41. See also All-combinatorial hexachord All-interval tetrachord * All-interval twelve-tone row References Further reading Boland, Marguerite (1999). "The All-trichord Hexachord: Compositional Strategies in Elliott Carter's ''Con leggerezza pensosa'' and ''Gra'' and a Folio of Original Compositions". MA Thesis, La Trobe University (Alegant 2010, p. 307n4). . Boland, Marguerite (2006). "'Linking' and 'Morphing': Harmonic Flow in Elliott Carter's ''Con Leggerezza Pensosa''". ''Tempo'' 60, no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	All-interval Twelve-tone Row In music, an all-interval twelve-tone row, series, or chord, is a twelve-tone tone row arranged so that it contains one instance of each interval within the octave, 1 through 11 (an ordering of every interval, 0 through 11, that contains each (ordered) pitch-interval class, 0 through 11). A "twelve-note ''spatial set'' made up of the eleven intervals etween consecutive pitches"Schiff, David (1998). ''The Music of Elliott Carter'', second edition (Ithaca: Cornell University Press), pp. 34–36. . Labels added to image. There are 1,928 distinct all-interval twelve-tone rows. These sets may be ordered in time or in register. "Distinct" in this context means in transpositionally and rotationally normal form (yielding 3856 such series), and disregarding inversionally related forms. These 1,928 tone rows have been independently rediscovered several times, their first computation probably was by Andre Riotte in 1961, see. Since the sum of numbers 1 through 11 equals 66, an al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	George Perle George Perle (6 May 1915 – 23 January 2009) was an American composer and music theorist. As a composer, his music was largely atonal, using methods similar to the twelve-tone technique of the Second Viennese School. This serialist style, and atonality in general, was the subject of much of his theoretical writings. His 1962 book, ''Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern'' remains a standard text for 20th-century classical music theory. Among Perle's awards was the 1986 Pulitzer Prize for Music for his Wind Quintet No. 4. Life and career Perle was born in Bayonne, New Jersey. He graduated from DePaul University, where he studied with Wesley LaViolette and received private lessons from Ernst Krenek. Later, he served as a technician fifth grade in the United States Army during World War II. He earned his doctorate at New York University in 1956. Perle composed with a technique of his own devising called "twelve-tone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Elliott Carter Elliott Cook Carter Jr. (December 11, 1908 – November 5, 2012) was an American modernist composer. One of the most respected composers of the second half of the 20th century, he combined elements of European modernism and American "ultra-modernism" into a distinctive style with a personal harmonic and rhythmic language, after an early neoclassical phase. His compositions are performed throughout the world, and include orchestral, chamber music, solo instrumental, and vocal works. The recipient of many awards, Carter was twice awarded the Pulitzer Prize. Born in New York City, Carter had developed an interest in modern music in the 1920s. He was later introduced to Charles Ives, and he soon came to appreciate the American ultra-modernists. After studying at Harvard University with Edward Burlingame Hill, Gustav Holst and Walter Piston, he studied with Nadia Boulanger in Paris in the 1930s, then returned to the United States. Carter was productive in his later years, pub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Tetrachord In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency proportion (approx. 498 cents)—but in modern use it means any four-note segment of a scale or tone row, not necessarily related to a particular tuning system. History The name comes from ''tetra'' (from Greek—"four of something") and ''chord'' (from Greek ''chordon''—"string" or "note"). In ancient Greek music theory, ''tetrachord'' signified a segment of the greater and lesser perfect systems bounded by ''immovable'' notes ( ); the notes between these were ''movable'' ( ). It literally means ''four strings'', originally in reference to harp-like instruments such as the lyre or the kithara, with the implicit understanding that the four strings produced adjacent (i.e., conjunct) notes. Modern music theory uses the octave as the basic u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]

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