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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] |
Pitch Class Space
In music theory, pitch-class space is the circular space representing all the Musical note, notes (pitch classes) in a musical octave. In this space, there is no distinction between tones separated by an integral number of octaves. For example, C4, C5, and C6, though different pitches, are represented by the same point in pitch class space. Since pitch-class space is a circle, we return to our starting point by taking a series of steps in the same direction: beginning with C, we can move "upward" in pitch-class space, through the pitch classes C♯, D, D♯, E, F, F♯, G, G♯, A, A♯, and B, returning finally to C. By contrast, pitch space is a linear space: the more steps we take in a single direction, the further we get from our starting point. Tonal pitch-class space , and Generative theory of tonal music, Lerdahl and Jackendoff (1983) use a "reductional format" to represent the perception of pitch-class relations in tonal contexts. These two-dimensional models resemble bar g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Von Oettingen
Arthur Joachim von Oettingen ( – 5 September 1920) was a Baltic German physicist and music theorist. He was the brother of theologian Alexander von Oettingen (1827–1905) and ophthalmologist Georg von Oettingen (1824–1916). Biography He studied astronomy and physics at the University of Dorpat, and furthered his education of physics in Paris in the laboratories of Antoine César Becquerel (1788–1878) and Henri Victor Régnault (1810–1878), and afterwards at Berlin in the laboratories of Heinrich Gustav Magnus (1802–1870), Johann Christian Poggendorff (1796–1877) and Heinrich Wilhelm Dove (1803–1879). In 1868 he became a professor at Dorpat, where he founded a meteorological observatory. In 1893 he moved to the University of Leipzig, where he remained until 1919 as a teacher and honorary professor. In 1898 and 1904 he published the third and fourth volumes of Poggendorff's ''Biographisch-Literarisches Handwörterbuch der exakten Naturwissenschaften''. Oe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isomorphic Keyboard
An isomorphic keyboard is a musical input device consisting of a two-dimensional grid of note-controlling elements (such as buttons or keys) on which any given sequence and/or combination of musical intervals has the "same shape" on the keyboard wherever it occurs – within a key, across keys, across octaves, and across tunings. Examples Helmholtz's 1863 book '' On the Sensations of Tone'' gave several possible layouts. Practical isomorphic keyboards were developed by Bosanquet (1875), Janko (1882), Wicki (1896), Fokker (1951), Erv Wilson (1975–present), William Wesley (2001), and Antonio Fernández (2009). Accordions have been built since the 19th century using various isomorphic keyboards, typically with dimensions of semitones and tones. The keyboards of Bosanquet and Erv Wilson are also known as generalized keyboards. The keyboard of Antonio Fernández is also known as Transclado. Invariance Isomorphic keyboards can expose, through their geometry, two invariant prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chromatic Circle
The chromatic circle is a clock diagram for displaying relationships among the equal-tempered pitch classes making up a given equal temperament tuning's chromatic scale on a circle. Explanation If one starts on any equal-tempered pitch and repeatedly ascends by the musical interval of a semitone, one will eventually land on a pitch with the same pitch class as the initial one, having passed through all the other equal-tempered chromatic pitch classes in between. Since the space is circular, it is also possible to descend by semitone. The chromatic circle is useful because it represents melodic distance, which is often correlated with physical distance on musical instruments. For instance, assuming 12-tone equal temperament, to move from any C on a keyboard to the nearest E, one must move up four semitones, corresponding to four clockwise steps on the chromatic circle. One can also move ''down'' by eight semitones, corresponding to eight counterclockwise steps on the pitch cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudo-octave
In music theory, a pseudo-octave, pseudooctave, or paradoxical octave is an interval whose ratio of frequencies is not exactly expected for perfectly harmonic pitches, but slightly wider or narrower in pitch – for example , , or even as large as The pseudo-octave is never-the-less perceived as if it were equivalent to the conventional 2:1 harmonic ratio, and consequently is treated the same: Pitches separated by a pseudo-octave appropriate for a given instrument are considered equivalent to each other just as with normal ''"pitch classes"'' (which are typically explained only in terms of the idealized 2:1 octave). Stretched octave The stretched octave, for example rather than (an 8.6 cent pitch difference), sounds ''out of tune'' when played with ideal harmonic overtones, but ''in tune'' when played with lower notes whose overtones are themselves naturally stretched by an equivalent amount. In piano tuning, stretched octaves are commonly encou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamelan
Gamelan (; ; , ; ) is the traditional musical ensemble, ensemble music of the Javanese people, Javanese, Sundanese people, Sundanese, and Balinese people, Balinese peoples of Indonesia, made up predominantly of percussion instrument, percussive instruments. The most common instruments used are metallophones (played with mallets) and a set of hand-drums called ''kendang'', which keep the beat (music), beat. The ''kemanak'', a banana-shaped idiophone, and the ''gangsa'', another metallophone, are also commonly used gamelan Musical instrument, instruments on Bali. Other notable instruments include xylophones, bamboo flutes (similar to the Indian ''bansuri''), a bowed string instrument called a ''rebab'' (somewhat similar to the ''gadulka'' of Bulgaria), and a zither-like instrument called a ''siter'', used in Javanese gamelan. Additionally, vocalists may be featured, being referred to as ''sindhen'' for females or ''gerong'' for males.Sumarsam (1998)''Introduction to Javanese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Tenzer
Michael Tenzer (born 1957) is a composer, performer, and music educator and scholar. Career Tenzer was born in New York City and studied music at Yale University (BA. 1978) and University of California, Berkeley (Ph.D. 1986). After teaching at Yale from 1986 to 1996, he moved to University of British Columbia where he teaches ethnomusicology, composition, music theory and gamelan performance, and co-directs the doctoral program in ethnomusicology. Tenzer's compositions for chamber, solo and orchestral media have been performed in North America, Europe, and Asia, featuring performers such as Pandit Swapan Chaudhuri (tabla), Alex Klein (oboe) and Evan Ziporyn (clarinet). His publications have been recognized with the Society for Ethnomusicology's Alan P. Merriam Prize (best book of 2000) and the 34th annual ASCAP-Deems Taylor award, and his research has been supported with grants from the National Endowment for the Humanities and Fulbright. Among his composition prizes are a Libr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helix
A helix (; ) is a shape like a cylindrical coil spring or the thread of a machine screw. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word ''helix'' comes from the Greek word , "twisted, curved". A "filled-in" helix – for example, a "spiral" (helical) ramp – is a surface called a '' helicoid''. Properties and types The pitch of a helix is the height of one complete helix turn, measured parallel to the axis of the helix. A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis. A circular helix (i.e. one with constant radius) has constant band curvature and constant torsion. The slope of a circular helix is commonly defined as the ratio of the circumference of the circular cylinder that it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Tenney
James Tenney (August 10, 1934 – August 24, 2006) was an American composer and music theorist. He made significant early musical contributions to plunderphonics, sound synthesis, algorithmic composition, process music, spectral music, microtonal music, and tuning systems including extended just intonation. His theoretical writings variously concern musical form, texture, timbre, consonance and dissonance, and harmonic perception. Biography James Tenney was born in Silver City, New Mexico, and grew up in Arizona and Colorado. He attended the University of Denver, the Juilliard School of Music, Bennington College (B.A., 1958) and the University of Illinois (M.A., 1961). He studied piano with Eduard Steuermann and composition with Chou Wen-chung, Lionel Nowak, Paul Boepple, Henry Brant, Carl Ruggles, Kenneth Gaburo, John Cage, Harry Partch, and Edgard Varèse. He also studied acoustics, information theory and tape music composition under Lejaren Hiller. In 1961, Te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative numbers, signed distances to the point from two fixed perpendicular oriented lines, called ''coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the ''Origin (mathematics), origin'' and has as coordinates. The axes direction (geometry), directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice (group)
In geometry and group theory, a lattice in the real coordinate space \mathbb^n is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point. Closure under addition and subtraction means that a lattice must be a subgroup of the additive group of the points in the space, and the requirements of minimum and maximum distance can be summarized by saying that a lattice is a Delone set. More abstractly, a lattice can be described as a free abelian group of dimension n which spans the vector space \mathbb^n. For any basis of \mathbb^n, the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice, and every lattice can be formed from a basis in this way. A lattice may be viewed as a re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonnetz
In musical tuning and harmony, the (German for 'tone net') is a conceptual lattice diagram representing tonal space first described by Leonhard Euler in 1739. Various visual representations of the ''Tonnetz'' can be used to show traditional harmonic relationships in European classical music. History through 1900 The ''Tonnetz'' originally appeared in Leonhard Euler's 1739 . Euler's ''Tonnetz'', pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a major third above F). Gottfried Weber, , discusses the relationships between keys, presenting them in a network analogous to Euler's ''Tonnetz'', but showing keys rather than notes. The ''Tonnetz'' itself was rediscovered in 1858 by Ernst Naumann in his ., and was disseminated in an 1866 treatise of Arthur von Oettingen. Oettingen and the influential musicologist Hugo Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
