|
The Geometry Of Musical Rhythm
''The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good?'' is a book on the mathematics of rhythms and drum beats. It was written by Godfried Toussaint, and published by Chapman & Hall/CRC in 2013 and in an expanded second edition in 2020. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Author Godfried Toussaint (1944–2019) was a Belgian–Canadian computer scientist who worked as a professor of computer science for McGill University and New York University. His main professional expertise was in computational geometry, but he was also a jazz drummer, held a long-term interest in the mathematics of music and musical rhythm, and since 2005 held an affiliation as a researcher in the Centre for Interdisciplinary Research in Music Media and Technology in the Schulich School of Music at McGill. In 2009 he visited Harvard University as a Radcliffe Fellow in advancement of his rese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Geometry Of Musical Rhythm
''The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good?'' is a book on the mathematics of rhythms and drum beats. It was written by Godfried Toussaint, and published by Chapman & Hall/CRC in 2013 and in an expanded second edition in 2020. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Author Godfried Toussaint (1944–2019) was a Belgian–Canadian computer scientist who worked as a professor of computer science for McGill University and New York University. His main professional expertise was in computational geometry, but he was also a jazz drummer, held a long-term interest in the mathematics of music and musical rhythm, and since 2005 held an affiliation as a researcher in the Centre for Interdisciplinary Research in Music Media and Technology in the Schulich School of Music at McGill. In 2009 he visited Harvard University as a Radcliffe Fellow in advancement of his rese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polygon
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed. General properties ''These properties apply to all regular polygons, whether convex or star.'' A regular ''n''-sided polygon has rotational symmetry of order ''n''. All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint. Thus a regular polygon is a tangential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Music Theory
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the " rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built." Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. Because of the ever-expanding conception of what constitutes music, a more inclusive definition could be the consideration of any sonic phenomena, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Music Psychology
Music psychology, or the psychology of music, may be regarded as a branch of both psychology and musicology. It aims to explain and understand musical behaviour and experience, including the processes through which music is perceived, created, responded to, and incorporated into everyday life. Modern music psychology is primarily empirical; its knowledge tends to advance on the basis of interpretations of data collected by systematic observation of and interaction with human participants. Music psychology is a field of research with practical relevance for many areas, including music performance, composition, education, criticism, and therapy, as well as investigations of human attitude, skill, performance, intelligence, creativity, and social behavior. Music psychology can shed light on non-psychological aspects of musicology and musical practice. For example, it contributes to music theory through investigations of the perception and computational modelling of musical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Music History
Music history, sometimes called historical musicology, is a highly diverse subfield of the broader discipline of musicology that studies music from a historical point of view. In theory, "music history" could refer to the study of the history of any type or genre of music (e.g., the history of Indian music or the history of rock). In practice, these research topics are often categorized as part of ethnomusicology or cultural studies, whether or not they are ethnographically based. The terms "music history" and "historical musicology" usually refer to the history of the notated music of Western elites, sometimes called " art music" (by analogy to art history, which tends to focus on elite art). The methods of music history include source studies (esp. manuscript studies), paleography, philology (especially textual criticism), style criticism, historiography (the choice of historical method), musical analysis, and iconography. The application of musical analysis to further thes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ethnomusicology
Ethnomusicology is the study of music from the cultural and social aspects of the people who make it. It encompasses distinct theoretical and methodical approaches that emphasize cultural, social, material, cognitive, biological, and other dimensions or contexts of musical behavior, in addition to the sound component. Within musical ethnography it is the first-hand personal study of musicking as known as the act of taking part in a musical performance. Folklorists, who began preserving and studying folklore music in Europe and the US in the 19th century, are considered the precursors of the field prior to the Second World War. The term ''ethnomusicology'' is said to have been coined by Jaap Kunst from the Greek words ἔθνος (''ethnos'', "nation") and μουσική (''mousike'', "music"), It is often defined as the anthropology or ethnography of music, or as musical anthropology.Seeger, Anthony. 1983. ''Why Suyá Sing''. London: Oxford University Press. pp. xiii-xvii. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. A regular octahedron is the dual polyhedron of a cube. It is a rectified tetrahedron. It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations. An octahedron is the three-dimensional case of the more general concept of a cross polytope. A regular octahedron is a 3-ball in the Manhattan () metric. Regular octahedron Dimensions If the edge length of a regular octahedron is ''a'', the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is :r_u = \frac a \approx 0.707 \cdot a and the radius of an inscribed sphere (tangent to each of the octahedron's faces) is :r_i = \frac a \approx 0.408\cdot a while the midradius, which t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isosceles Triangle
In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids. The mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings. The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bar (music)
In musical notation, a bar (or measure) is a segment of time corresponding to a specific number of beats in which each beat is represented by a particular note value and the boundaries of the bar are indicated by vertical bar lines. Dividing music into bars provides regular reference points to pinpoint locations within a musical composition. It also makes written music easier to follow, since each bar of staff symbols can be read and played as a batch. Typically, a piece consists of several bars of the same length, and in modern musical notation the number of beats in each bar is specified at the beginning of the score by the time signature. In simple time, (such as ), the top figure indicates the number of beats per bar, while the bottom number indicates the note value of the beat (the beat has a quarter note value in the example). The word ''bar'' is more common in British English, and the word ''measure'' is more common in American English, although musicians generall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tresillo (rhythm)
Tresillo ( ; ) is a rhythmic pattern (shown below) used in Latin American music. It is a more basic form of the rhythmic figure known as the ''habanera''. : \new RhythmicStaff Tresillo is the most fundamental duple-pulse rhythmic cell in Cuban and other Latin American music. It was introduced in the New World through the Atlantic slave trade during the Colonial period. The pattern is also the most fundamental and most prevalent duple-pulse rhythmic cell in Sub-Saharan African music traditions. The cinquillo pattern is another common embellishment of tresillo. Cinquillo is used frequently in the Cuban contradanza (the "habanera") and the danzón. Triplet (formal usage) ''Tresillo'' is a Spanish word meaning " triplet"—three equal notes within the same time span normally occupied by two notes. In its formal usage, ''tresillo'' refers to a subdivision of the beat that does not normally occur within the given structure. Therefore, it is indicated by the number 3 between th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
