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Distributionally Even Scale
In scale (music) theory, a maximally even set (scale) is one in which every generic interval has either one or two consecutive integers specific intervals-in other words a scale whose notes (pcs) are "spread out as much as possible." This property was first described by John Clough and Jack Douthett. Clough and Douthett also introduced the maximally even algorithm. For a chromatic cardinality ''c'' and Pitch class, pc-set cardinality ''d'' a maximally even set is D = where ''k'' ranges from 0 to ''d'' − 1 and ''m'', 0 ≤ ''m'' ≤ ''c'' − 1 is fixed and the bracket pair is the floor function. A discussion on these concepts can be found in Timothy Johnson's book on the mathematical foundations of diatonic scale theory. Jack Douthett and Richard Krantz introduced maximally even sets to the mathematics literature. A scale is said to have Myhill's property if every generic interval comes in two specific interval sizes, and a scale with Myhill's property is said to be a well-f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Maximal Evenness Seconds
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Maximal may refer to: *Maximal element, a mathematical definition *Maximal set * Maximal (''Transformers''), a faction of Transformers *Maximalism, an artistic style * ''Maxim'' (magazine), a men's magazine marketed as ''Maximal'' in several countries See also *Minimal (other) Minimal may refer to: * Minimal (music genre), art music that employs limited or minimal musical materials * "Minimal" (song), 2006 song by Pet Shop Boys * Minimal (supermarket) or miniMAL, a former supermarket chain in Germany and Poland * Minim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Whole-tone Scale
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or '' hexatonic'' scales. A single whole-tone scale can also be thought of as a "six-tone equal temperament". : : The whole-tone scale has no leading tone and because all tones are the same distance apart, "no single tone stands out, ndthe scale creates a blurred, indistinct effect". This effect is especially emphasised by the fact that triads built on such scale tones are all augmented triads. Indeed, all six tones of a whole-tone scale can be played simply with two augmented triads whose roots are a major second apart. Since they are symmetrical, whole-tone scales do not give a strong impression of the tonic or tonality. The composer Olivier Messiaen called the whole-tone scale his first mode of limited transposition. The composer and music t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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] [Amazon] |
Diatonic
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 notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Neo-Riemannian Theory
Neo-Riemannian theory is a loose collection of ideas present in the writings of music theory, music theorists such as David Lewin, Brian Hyer, Richard Cohn, and Henry Klumpenhouwer. What binds these ideas is a central commitment to relating harmony, harmonies directly to each other, without necessary reference to a tonic (music), tonic. Initially, those harmonies were major chord, major and minor chord, minor triads; subsequently, neo-Riemannian theory was extended to standard consonance and dissonance, dissonant sonorities as well. Harmonic proximity is characteristically gauged by efficiency of voice leading. Thus, C major and E minor triads are close by virtue of requiring only a single semitone, semitonal shift to move from one to the other. Motion between proximate harmonies is described by simple transformations. For example, motion between a C major and E minor triad, in either direction, is executed by an "L" transformation. Extended progressions of harmonies are character ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Concentric Circles
In geometry, two or more objects are said to be ''concentric'' when they share the same center. Any pair of (possibly unalike) objects with well-defined centers can be concentric, including circles, spheres, regular polygons, regular polyhedra, parallelograms, cones, conic sections, and quadrics. Geometric objects are ''coaxial'' if they share the same axis (line of symmetry). Geometric objects with a well-defined axis include circles (any line through the center), spheres, cylinders, conic sections, and surfaces of revolution. Concentric objects are often part of the broad category of ''whorled patterns'', which also includes ''spirals'' (a curve which emanates from a point, moving farther away as it revolves around the point). Geometric properties In the Euclidean plane, two circles that are concentric necessarily have different radii from each other.. However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dynamical
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Pitch Space
In music theory, pitch spaces model relationships between pitches. These models typically use distance to model the degree of relatedness, with closely related pitches placed near one another, and less closely related pitches farther apart. Depending on the complexity of the relationships under consideration, the models may be dimension, multidimensional. Models of pitch space are often Graph (discrete mathematics), graphs, group (mathematics), groups, lattice (music), lattices, or geometrical figures such as helixes. Pitch spaces distinguish octave-related pitches. When octave-related pitches are not distinguished, we have instead pitch class spaces, which represent relationships between pitch classes. (Some of these models are discussed in the entry on modulatory space, though readers should be advised that the term "modulatory space" is not a standard music-theoretical term.) Chordal spaces model relationships between chords. Linear and helical pitch space The simplest pitch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fred Lerdahl
Alfred Whitford (Fred) Lerdahl (born March 10, 1943) is an American music theorist and composer. Best known for his work on musical grammar, Music cognition, cognition, Rhythm, rhythmic theory, and pitch space, he and the linguist Ray Jackendoff developed the Chomsky-inspired generative theory of tonal music. Lerdahl has written numerous orchestral and chamber works, three of which were finalists for the Pulitzer Prize for Music: ''Time after Time'' in 2001, String Quartet No. 3 in 2010, and ''Arches (Lerdahl), Arches'' in 2011. He is a Professor Emeritus of Musical Composition at Columbia University. Life Alfred Whitford "Fred" Lerdahl was born on March 10, 1943, in Madison, Wisconsin. His maternal uncle was the astronomer Albert Whitford (astronomer), Albert Whitford. Lerdahl studied with James Ming at Lawrence University, where he earned his BMus in 1965, and with Milton Babbitt, Edward Cone, Edward T. Cone, and Earl Kim at Princeton University, where he earned his MFA in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Diatonic Collection
In music theory a diatonic scale is a heptatonic (seven-note) 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. In other words, the half steps are maximally separated from each other. 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-key notes form a diatonic scale, though transpositions of this diatonic scale require one or more black keys. A diatonic scale can be also described as two tetrachords separated by a whole tone. In musical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Not Maximal Evenness Seconds
Not or NOT may also refer to: Language * Not, the general declarative form of "no", indicating a negation of a related statement that usually precedes * ... Not!, a grammatical construction used as a contradiction, popularized in the early 1990s Science and technology * Negation, a unary operator in logic depicted as ~, ¬, or ! * Bitwise NOT, an operator used in computer programming * NOT gate, a digital logic gate (commonly called an inverter) * Nordic Optical Telescope, an astronomical telescope at Roque de los Muchachos Observatory, La Palma, Canary Islands Other uses * Nottingham railway station (station code NOT) * Polish Federation of Engineering Associations (''Naczelna Organizacja Techniczna'') * Not, Missouri Not is an unincorporated community in Shannon County, Missouri, United States. History A post office called Not was established in 1886, and remained in operation until 1917. The community was so named on account of the knot A knot is an in ..., an uninc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Well-formed Scale
In music theory, a generated collection is a set (music), collection or scale (music), scale formed by repeatedly adding a constant interval (music), 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 Common tone (scale)#Deep scale property, deep scale property can be generated by any interval coprime with the number of notes per octave. (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 12-tone equal temperament, the standard tuning of Western music: 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 mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
