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Multiplication (music)
The mathematical operations of multiplication have several applications to music. Other than its application to the frequency ratios of intervals (for example, Just intonation, and the twelfth root of two in equal temperament), it has been used in other ways for twelve-tone technique, and musical set theory. Additionally ring modulation is an electrical audio process involving multiplication that has been used for musical effect. A multiplicative operation is a mapping in which the argument is multiplied. Multiplication originated intuitively in interval expansion, including tone row order number rotation, for example in the music of Béla Bartók and Alban Berg. Pitch number rotation, ''Fünferreihe'' or "five-series" and ''Siebenerreihe'' or "seven-series", was first described by Ernst Krenek in ''Über neue Musik''. Princeton-based theorists, including James K. Randall, Godfrey Winham, and Hubert S. Howe "were the first to discuss and adopt them, not only with regards to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James K
James may refer to: People * James (given name) * James (surname) * James (musician), aka Faruq Mahfuz Anam James, (born 1964), Bollywood musician * James, brother of Jesus * King James (other), various kings named James * Prince James (other) * Saint James (other) Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, a college of the University of York United States * James, Georgia, an unincorporated community * James, Iowa, an unincorporated community * James City, North Carolina * James City County, Virginia ** James City (Virginia Company) ** James City Shire * James City, Pennsylvania * St. James City, Florida Film and television * ''James'' (2005 film), a Bollywood film * ''James'' (2008 film), an Irish short film * ''James'' (2022 film), an Indian Kannada-language film * "James", a television episode of ''Adventure Time'' Music * James (band), a band from Manchester ** ''James'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Morris (composer)
Robert Daniel Morris (born October 19, 1943) is a British-born American composer and music theorist. Early life and education Born in Cheltenham, England, in 1943, Morris received his musical education at the Eastman School of Music (B.M. in composition with distinction) and the University of Michigan (M.M. and D.M.A. in composition and ethnomusicology), where he studied composition with John La Montaine, Leslie Bassett, Ross Lee Finney, and Eugene Kurtz. Career As a Margret Lee Crofts Fellow, Morris worked with Gunther Schuller. Morris has taught composition, electronic music, and music theory at the University of Hawaiʻi at Mānoa and Yale University, where he was chairman of the Composition Department and director of the Yale Electronic Music Studio. He was also director of the Computer and Electronic Studio, director of graduate (music) Studies, and associate professor of Music at the University of Pittsburgh. In 1980 Morris joined the faculty of the Eastman School ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milton Babbitt
Milton Byron Babbitt (May 10, 1916 – January 29, 2011) was an American composer, music theorist, mathematician, and teacher. He was a Pulitzer Prize and MacArthur Fellowship recipient, recognized for his serial and electronic music. Biography Babbitt was born in Philadelphia to Albert E. Babbitt and Sarah Potamkin, who were Jewish. He was raised in Jackson, Mississippi, and began studying the violin when he was four but soon switched to clarinet and saxophone. Early in his life he was attracted to jazz and theater music, and "played in every pit-orchestra that came to town". Babbitt was making his own arrangements of popular songs by age 7, "wrote a lot of pop tunes for school productions", and won a local songwriting contest when he was 13. A Jackson newspaper called Babbitt a "whiz kid" and noted "that he had perfect pitch and could add up his family's grocery bills in his head. In his teens he became a great fan of jazz cornet player Bix Beiderbecke". Babbitt's father was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert Eimert
Herbert Eimert (8 April 1897 – 15 December 1972) was a German music theorist, musicologist, journalist, music critic, editor, radio producer, and composer. Education Herbert Eimert was born in Bad Kreuznach. He studied music theory and composition from 1919 to 1924 at the Cologne Musikhochschule with Hermann Abendroth, , and August von Othegraven. In 1924, while still a student, he published an ''Atonale Musiklehre'' (Atonal Music Theory Text) which, together with a twelve-tone string quartet composed for the end-of-term examination concert, led to an altercation with Bölsche, who withdrew the quartet from the program and expelled Eimert from his composition class. In 1924, he began studies in musicology at the University of Cologne with Ernst Bücken, Willi Kahl, and Georg Kinsky, and read philosophy with Max Scheler (a pupil of Husserl) and Nicolai Hartmann. He attained his doctorate in 1931 with a dissertation titled ''Musikalische Formstrukturen im 17. und 18. Jahrh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transposition (music)
In music, transposition refers to the process or operation of moving a collection of notes ( pitches or pitch classes) up or down in pitch by a constant interval. For example, a music transposer might transpose an entire piece of music into another key. Similarly, one might transpose a tone row or an unordered collection of pitches such as a chord so that it begins on another pitch. The transposition of a set ''A'' by ''n'' semitones is designated by ''T''''n''(''A''), representing the addition ( mod 12) of an integer ''n'' to each of the pitch class integers of the set ''A''. Thus the set (''A'') consisting of 0–1–2 transposed by 5 semitones is 5–6–7 (''T''5(''A'')) since , , and . Scalar transpositions In scalar transposition, every pitch in a collection is shifted up or down a fixed number of scale steps within some scale. The pitches remain in the same scale before and after the shift. This term covers both chromatic and diatonic transpositions as follo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tritone
In music theory, the tritone is defined as a interval (music), musical interval spanning three adjacent Major second, whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. Narrowly defined, each of these whole tones must be a step in the scale (music), scale, so by this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. More broadly, a tritone is also commonly defined as any interval with a width of three whole tones (spanning six semitones in the chromatic scale), regardless of scale degrees. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B (from F to the B above it, also called augment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Of Fourths
In music theory, the circle of fifths (sometimes also cycle of fifths) is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music (12-tone equal temperament), the sequence is: C, G, D, A, E, B, F/G, C/D, G/A, D/E, A/B, F, and C. This order places the most closely related key signatures adjacent to one another. Twelve-tone equal temperament tuning divides each octave into twelve equivalent semitones, and the circle of fifths leads to a C seven octaves above the starting point. If the fifths are tuned with an exact frequency ratio of 3:2 (the system of tuning known as just intonation), this is not the case (the circle does not "close"). Definition The circle of fifths organizes pitches in a sequence of perfect fifths, generally shown as a circle with the pitches (and their corresponding keys) in clockwise order. It can be viewed in a counterclockwise direction as a circle of fourths. Harmonic progres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chromatic
Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms are also applied to musical instruments, intervals, chords, 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 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 chromatic scale in 12-tone equal temperament, which consists of all semitones. Historically, however, it had other senses, referring in Ancient Greek music theory to a particular tuning of the tetrachord, and to a rhythmic notational co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relatively Prime
In number theory, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. One says also ''is prime to'' or ''is coprime with'' . The numbers 8 and 9 are coprime, despite the fact that neither—considered individually—is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition. Notation and testing When the integers and are coprime, the standard way of expressing this fact in mathematical notation is to indicate that their greatest common divisor is one, by the formula or . In their 1989 textbook '' Concrete Mathematics'', Ronald Graham, Donald Knuth, and Oren Patashnik proposed an alter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set. A function is bijective if it is invertible; that is, a function f:X\to Y is bijective if and only if there is a function g:Y\to X, the ''inverse'' of , such that each of the two ways for composing the two functions produces an identity function: g(f(x)) = x for each x in X and f(g(y)) = y for each y in Y. For example, the ''multiplication by two'' defines a bijection from the integers to the even numbers, which has the ''division by two'' as its inverse function. A function is bijective if and only if it is both injective (or ''one-to-one'')—meaning that each element in the codomain is mappe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twelve Tone Technique
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded equally often in a piece of music while preventing the emphasis of any one notePerle 1977, 2. through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. The technique was first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed his own, better-known version of 12-tone technique, which became associated with the " Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. Over time, the technique increased greatly in popularity and eventually became widely influen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
