Interval Array
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Interval Array
In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class.Whittall, Arnold. 2008. ''The Cambridge Introduction to Serialism'', p. 273-74. New York: Cambridge University Press. (pbk). In other words, a collection of pitches by starting with a certain note and going up by a certain interval until the original note is reached (e.g. starting from C, going up by 3 semitones repeatedly until eventually C is again reached - the cycle is the collection of all the notes met on the way). In other words, interval cycles "unfold a single recurrent interval in a series that closes with a return to the initial pitch class". See: wikt:cycle. Interval cycles are notated by George Perle using the letter "C" (for ''cycle''), with an interval class integer to distinguish the interval. Thus the diminished seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0&ndas ...
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Music
Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect of all human societies, a cultural universal. While scholars agree that music is defined by a few specific elements, there is no consensus on their precise definitions. The creation of music is commonly divided into musical composition, musical improvisation, and musical performance, though the topic itself extends into academic disciplines, criticism, philosophy, and psychology. Music may be performed or improvised using a vast range of instruments, including the human voice. In some musical contexts, a performance or composition may be to some extent improvised. For instance, in Hindustani classical music, the performer plays spontaneously while following a partially defined structure and using characteristic motifs. In modal jazz ...
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Just Intonation
In music, just intonation or pure intonation is the tuning of musical intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets * A statistical level of measurement * Interval e ... as whole number ratios (such as 3:2 or 4:3) of Frequency, frequencies. An interval (music), interval tuned in this way is said to be pure, and is called a just interval. Just intervals (and chords created by combining them) consist of tones from a single harmonic series (music), harmonic series of an implied fundamental frequency, fundamental. For example, in the diagram, if the notes G3 and C4 (labelled 3 and 4) are tuned as members of the harmonic series of the lowest C, their frequencies will be 3 and 4 times the fundamental frequency. The interval ratio between C4 and G3 is therefore 4:3, a just fourth (music), fourth. In Western musical practice ...
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Edgard Varèse
Edgard Victor Achille Charles Varèse (; also spelled Edgar; December 22, 1883 – November 6, 1965) was a French-born composer who spent the greater part of his career in the United States. Varèse's music emphasizes timbre and rhythm; he coined the term " organized sound" in reference to his own musical aesthetic. Varèse's conception of music reflected his vision of "sound as living matter" and of "musical space as open rather than bounded". He conceived the elements of his music in terms of " sound-masses", likening their organization to the natural phenomenon of crystallization. Varèse thought that "to stubbornly conditioned ears, anything new in music has always been called noise", and he posed the question, "what is music but organized noises?" Although his complete surviving works only last about three hours, he has been recognised as an influence by several major composers of the late 20th century. Varèse saw potential in using electronic media for sound production, and ...
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Alexander Scriabin
Alexander Nikolayevich Scriabin (; russian: Александр Николаевич Скрябин ; – ) was a Russian composer and virtuoso pianist. Before 1903, Scriabin was greatly influenced by the music of Frédéric Chopin and composed in a relatively tonal, late Romantic idiom. Later, and independently of his influential contemporary, Arnold Schoenberg, Scriabin developed a much more dissonant musical language that had transcended usual tonality but was not atonal, which accorded with his personal brand of metaphysics. Scriabin found significant appeal in the concept of Gesamtkunstwerk as well as synesthesia, and associated colours with the various harmonic tones of his scale, while his colour-coded circle of fifths was also inspired by theosophy. He is often considered the main Russian Symbolist composer and a major representative of the Russian Silver Age. Scriabin was an innovator as well as one of the most controversial composer-pianists of the early 20th century ...
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Béla Bartók
Béla Viktor János Bartók (; ; 25 March 1881 – 26 September 1945) was a Hungarian composer, pianist, and ethnomusicologist. He is considered one of the most important composers of the 20th century; he and Franz Liszt are regarded as Hungary's greatest composers. Through his collection and analytical study of folk music, he was one of the founders of comparative musicology, which later became ethnomusicology. Biography Childhood and early years (1881–98) Bartók was born in the Banatian town of Nagyszentmiklós in the Kingdom of Hungary (present-day Sânnicolau Mare, Romania) on 25 March 1881. On his father's side, the Bartók family was a Hungarian lower noble family, originating from Borsodszirák, Borsod. His paternal grandmother was a Catholic of Bunjevci origin, but considered herself Hungarian. Bartók's father (1855–1888) was also named Béla. Bartók's mother, Paula (née Voit) (1857–1939), also spoke Hungarian fluently. A native of Turócszentmárton ...
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Richard Wagner
Wilhelm Richard Wagner ( ; ; 22 May 181313 February 1883) was a German composer, theatre director, polemicist, and conductor who is chiefly known for his operas (or, as some of his mature works were later known, "music dramas"). Unlike most opera composers, Wagner wrote both the libretto and the music for each of his stage works. Initially establishing his reputation as a composer of works in the romantic vein of Carl Maria von Weber and Giacomo Meyerbeer, Wagner revolutionised opera through his concept of the ''Gesamtkunstwerk'' ("total work of art"), by which he sought to synthesise the poetic, visual, musical and dramatic arts, with music subsidiary to drama. He described this vision in a series of essays published between 1849 and 1852. Wagner realised these ideas most fully in the first half of the four-opera cycle ''Der Ring des Nibelungen'' (''The Ring of the Nibelung''). His compositions, particularly those of his later period, are notable for their complex textures, ...
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Gustav Mahler
Gustav Mahler (; 7 July 1860 – 18 May 1911) was an Austro-Bohemian Romantic composer, and one of the leading conductors of his generation. As a composer he acted as a bridge between the 19th-century Austro-German tradition and the modernism of the early 20th century. While in his lifetime his status as a conductor was established beyond question, his own music gained wide popularity only after periods of relative neglect, which included a ban on its performance in much of Europe during the Nazi era. After 1945 his compositions were rediscovered by a new generation of listeners; Mahler then became one of the most frequently performed and recorded of all composers, a position he has sustained into the 21st century. Born in Bohemia (then part of the Austrian Empire) to Jewish parents of humble origins, the German-speaking Mahler displayed his musical gifts at an early age. After graduating from the Vienna Conservatory in 1878, he held a succession of conducting posts of rising ...
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Chord Progression
In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice era of Classical music to the 21st century. Chord progressions are the foundation of Western popular music styles (e.g., pop music, rock music), traditional music, as well as genres such as blues and jazz. In these genres, chord progressions are the defining feature on which melody and rhythm are built. In tonal music, chord progressions have the function of either establishing or otherwise contradicting a tonality, the technical name for what is commonly understood as the "key" of a song or piece. Chord progressions, such as the common chord progression I–vi–ii–V, are usually expressed by Roman numerals in Classical music theory. In many styles of popular and traditional music, chord progressions are expressed using the name and " ...
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Generated Collection
In diatonic set theory, a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection or scale is formed. All scales with the deep scale property can be generated by any interval coprime with (in twelve-tone equal temperament) twelve. (Johnson, 2003, p. 83) The C major diatonic collection can be generated by adding a cycle of perfect fifths (C7) starting at F: F-C-G-D-A-E-B = C-D-E-F-G-A-B. Using integer notation and modulo 12: 5 + 7 = 0, 0 + 7 = 7, 7 + 7 = 2, 2 + 7 = 9, 9 + 7 = 4, 4 + 7 = 11. The C major scale could also be generated using cycle of perfect fourths (C5), as 12 minus any coprime of twelve is also coprime with twelve: 12 − 7 = 5. B-E-A-D-G-C-F. A gener ...
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Diatonic Major Scale
In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other (i.e. separated by at least two whole steps). The seven pitches of any diatonic scale can also be obtained by using a chain of six perfect fifths. For instance, the seven natural pitch classes that form the C-major scale can be obtained from a stack of perfect fifths starting from F: :F–C–G–D–A–E–B Any sequence of seven successive natural notes, such as C–D–E–F–G–A–B, and any transposition thereof, is a diatonic scale. Modern musical keyboards are designed so that the white notes form a diatonic scale, though transpositions of this dia ...
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Diatonic
Diatonic and chromatic are terms in music theory that are most often used to characterize Scale (music), scales, and are also applied to musical instruments, Interval (music), intervals, Chord (music), chords, Musical note, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the Common practice period, common practice music of the period 1600–1900. These terms may mean different things in different contexts. Very often, ''diatonic'' refers to musical elements derived from the modes and transpositions of the "white note scale" C–D–E–F–G–A–B. In some usages it includes all forms of heptatonic scale that are in common use in Western music (the major, and all forms of the minor). ''Chromatic'' most often refers to structures derived from the twelve-note chromatic scale, which consists of all semitones. Historically, however, it had other senses, referring in Ancient Greek music theory to ...
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