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Chordal Space
Music theorists have often used graphs, tilings, and geometrical spaces to represent the relationship between chords. We can describe these spaces as ''chord spaces'' or ''chordal spaces'', though the terms are relatively recent in origin. History of chordal space One of the earliest graphical models of chord-relationships was devised by Johann David Heinichen in 1728; he proposed placing the major and minor chords in a circular arrangement of twenty-four chords arranged according to the circle of fifths; reading clockwise, ... F, d, C, a, G, ... (Capital letters represent major chords and small letters represent minor.) 1737, David Kellner proposed an alternate arrangement, with the 12 major chords and 12 minor chords placed on concentric circles. Each chord was vertically aligned with its relative major or minor. F. G. Vial and Gottfried Weber suggested a grid graph or square lattice model of chordal space; Weber's graph, centered on C major, is: This was first propos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a Set (mathematics), set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' m ... [...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, one 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 follows. Chromatic transpo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pitch Class Space
In music theory, pitch-class space is the circular space representing all the notes (pitch classes) in a musical octave. In this space, there is no distinction between tones that are 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 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 graphs, using height to represent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 placed farther apart. Depending on the complexity of the relationships under consideration, the models may be multidimensional. Models of pitch space are often graphs, groups, 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 space model is the real line. A fundamental frequency ''f'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Cohn
Richard Cohn (born 1955) is a music theorist and Battell Professor of Music Theory at Yale. He was previously chair of the department of music at the University of Chicago. Early in his career, he specialized in the music of Béla Bartók, but more recently has written about Neo-Riemannian theory, metric dissonance, equal divisions of the octave, and chromatic harmony. In 1994, he won the Society for Music Theory's Outstanding Publication Award for his article, "Transpositional Combination of Beat-Class Sets in Steve Reich’s Phase-Shifting Music," and he won it again in 1997 for "Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions." Cohn was the founding editor (2004–14) of ''Oxford Studies in Music Theory'', and is the current editor of ''Journal of Music Theory The ''Journal of Music Theory'' is a peer-reviewed academic journal specializing in music theory and analysis. It was established by David Kraehenbuehl (Yale Univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tonnetz
In musical tuning and harmony, the (German for 'tone network') 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). The ''Tonnetz'' was rediscovered in 1858 by Ernst Naumann, and was disseminated in an 1866 treatise of Arthur von Oettingen. Oettingen and the influential musicologist Hugo Riemann (not to be confused with the mathematician Bernhard Riemann) explored the capacity of the space to chart harmonic motion between chords and modulation between keys. Simil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 placed farther apart. Depending on the complexity of the relationships under consideration, the models may be multidimensional. Models of pitch space are often graphs, groups, 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 space model is the real line. A fundamental frequency ''f'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relative Triad
In music, relative keys are the major and minor scales that have the same key signatures (enharmonically equivalent), meaning that they share all the same notes but are arranged in a different order of whole steps and half steps. A pair of major and minor scales sharing the same key signature are said to be in a relative relationship. The relative minor of a particular major key, or the relative major of a minor key, is the key which has the same key signature but a different tonic. (This is as opposed to ''parallel'' minor or major, which shares the same tonic.) For example, F major and D minor both have one flat in their key signature at B♭; therefore, D minor is the relative minor of F major, and conversely F major is the relative major of D minor. The tonic of the relative minor is the sixth scale degree of the major scale, while the tonic of the relative major is the third degree of the minor scale. The minor key starts three semitones below its relative major; for example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Chord
In music theory, a major scale and a minor scale that have the same tonic note are called parallel keys and are said to be in a parallel relationship. Forte, Allen (1979). ''Tonal Harmony'', p.9. 3rd edition. Holt, Rinehart, and Wilson. . "When a major and minor scale both begin with the same note ... they are called ''parallel''. Thus we say that the parallel major key of C minor is C major, the parallel minor of C major is C minor." The parallel minor or tonic minor of a particular major key is the minor key based on the same tonic; similarly the parallel major has the same tonic as the minor key. For example, G major and G minor have different modes but both have the same tonic, G; so G minor is said to be the parallel minor of G major. In contrast, a major scale and a minor scale that have the same key signature (and therefore different tonics) are called relative keys. A major scale can be transformed to its parallel minor by lowering the third, sixth, and seventh scale d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Schoenberg
Arnold Schoenberg or Schönberg (, ; ; 13 September 187413 July 1951) was an Austrian-American composer, music theorist, teacher, writer, and painter. He is widely considered one of the most influential composers of the 20th century. He was associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School. As a Jewish composer, Schoenberg was targeted by the Nazi Party, which labeled his works as degenerate music and forbade them from being published. He immigrated to the United States in 1933, becoming an American citizen in 1941. Schoenberg's approach, bοth in terms of harmony and development, has shaped much of 20th-century musical thought. Many composers from at least three generations have consciously extended his thinking, whereas others have passionately reacted against it. Schoenberg was known early in his career for simultaneously extending the traditionally opposed German Romantic styles of Brahms and Wagner. Later, hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugo Riemann
Karl Wilhelm Julius Hugo Riemann (18 July 1849 – 10 July 1919) was a German musicologist and composer who was among the founders of modern musicology. The leading European music scholar of his time, he was active and influential as both a music theorist and music historian. Many of his contributions are now termed as Riemannian theory, a variety of related ideas on many aspects of music theory. Biography Riemann was born at Grossmehlra, Schwarzburg-Sondershausen. His first musical training came from his father Robert Riemann, a land owner, bailiff and, to judge from locally surviving listings of his songs and choral works, an active music enthusiast. Hugo Riemann was educated by Heinrich Frankenberger, the Sondershausen Choir Master, in Music theory. He was taught the piano by August Barthel and Theodor Ratzenberger (who had once studied under Liszt). He studied law, and finally philosophy and history at Berlin and Tübingen. After participating in the Franco-Prussian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
