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Isomorphic Keyboards
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. The Ragzpole is a recently developed cylindrical MIDI controller having dimensions in fift ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Input Device
In computing, an input device is a piece of equipment used to provide data and control signals to an information processing system, such as a computer or information appliance. Examples of input devices include keyboards, mouse, scanners, cameras, joysticks, and microphones. Input devices can be categorized based on: * modality of input (e.g., mechanical motion, audio, visual, etc.) * whether the input is discrete (e.g., pressing of key) or continuous (e.g., a mouse's position, though digitized into a discrete quantity, is fast enough to be considered continuous) * the number of degrees of freedom involved (e.g., two-dimensional traditional mice, or three-dimensional navigators designed for CAD applications) Keyboard A keyboard is a human interface device which is represented as a layout of buttons. Each button, or key, can be used to either input an alphanumeric character to a computer, or to call upon a particular function of the computer. It acts as the main text ent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank Of An Abelian Group
In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group ''A'' is the cardinality of a maximal linearly independent subset. The rank of ''A'' determines the size of the largest free abelian group contained in ''A''. If ''A'' is torsion-free then it embeds into a vector space over the rational numbers of dimension rank ''A''. For finitely generated abelian groups, rank is a strong invariant and every such group is determined up to isomorphism by its rank and torsion subgroup. Torsion-free abelian groups of rank 1 have been completely classified. However, the theory of abelian groups of higher rank is more involved. The term rank has a different meaning in the context of elementary abelian groups. Definition A subset of an abelian group ''A'' is linearly independent (over Z) if the only linear combination of these elements that is equal to zero is trivial: if : \sum_\alpha n_\alpha a_\alpha = 0, \quad n_\alpha\in\mathbb, where all but finitely many coef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syntonic Temperament
A regular diatonic tuning is any musical scale consisting of " tones" (T) and "semitones" (S) arranged in any rotation of the sequence TTSTTTS which adds up to the octave with all the T's being the same size and all the S's the being the same size, with the 'S's being smaller than the 'T's. In such a tuning, then the notes are connected together in a chain of seven fifths, all the same size (TTTS or a permutation of that) which makes it a Linear temperament with the tempered fifth as a generator. Overview In the ordinary diatonic scales the T's here are tones and the S's are semitones which are half, or approximately half the size of the tone. But in the more general regular diatonic tunings, the two steps can be of any relation within the range between T=171.43 (S=T) and T=240 (S=0) cents (fifth between 685.71 and 720). Note that regular diatonic tunings are not limited to the notes of the diatonic scale which defines them. One may determine the corresponding cents of S, T, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Temperament Modulations
In psychology, temperament broadly refers to consistent individual differences in behavior that are biologically based and are relatively independent of learning, system of values and attitudes. Some researchers point to association of temperament with formal dynamical features of behavior, such as energetic aspects, plasticity, sensitivity to specific reinforcers and emotionality. Temperament traits (such as Neuroticism, Sociability, Impulsivity, etc.) are distinct patterns in behavior throughout a lifetime, but they are most noticeable and most studied in children. Babies are typically described by temperament, but longitudinal research in the 1920s began to establish temperament as something which is stable across the lifespan. Definition Temperament has been defined as "the constellation of inborn traits that determine a child's unique behavioral style and the way he or she experiences and reacts to the world." Classification schemes Many classification schemes for tempera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord Progressions
In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice era of Classical music to the 21st century. Chord progressions are the foundation of Western popular music styles (e.g., pop music, rock music), traditional music, as well as genres such as blues and jazz. In these genres, chord progressions are the defining feature on which melody and rhythm are built. In tonal music, chord progressions have the function of either establishing or otherwise contradicting a tonality, the technical name for what is commonly understood as the " key" of a song or piece. Chord progressions, such as the common chord progression I–vi–ii–V, are usually expressed by Roman numerals in Classical music theory. In many styles of popular and traditional music, chord progressions are expressed using the name a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyphonic Tuning Bends
Polyphony ( ) is a type of musical texture consisting of two or more simultaneous lines of independent melody, as opposed to a musical texture with just one voice, monophony, or a texture with one dominant melodic voice accompanied by chords, homophony. Within the context of the Western musical tradition, the term ''polyphony'' is usually used to refer to music of the late Middle Ages and Renaissance. Baroque forms such as fugue, which might be called polyphonic, are usually described instead as contrapuntal. Also, as opposed to the ''species'' terminology of counterpoint, polyphony was generally either "pitch-against-pitch" / "point-against-point" or "sustained-pitch" in one part with melismas of varying lengths in another. In all cases the conception was probably what Margaret Bent (1999) calls "dyadic counterpoint", with each part being written generally against one other part, with all parts modified if needed in the end. This point-against-point conception is opposed to "su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Controller
Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous game, a generalization of games used in game theory ** Law of Continuity, a heuristic principle of Gottfried Leibniz * Continuous function, in particular: ** Continuity (topology), a generalization to functions between topological spaces ** Scott continuity, for functions between posets ** Continuity (set theory), for functions between ordinals ** Continuity (category theory), for functors ** Graph continuity, for payoff functions in game theory * Continuity theorem may refer to one of two results: ** Lévy's continuity theorem, on random variables ** Kolmogorov continuity theorem, on stochastic processes * In geometry: ** Parametric continuity, for parametrised curves ** Geometric continuity, a concept primarily applied to the conic sectio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Tonality
Dynamic tonality is a paradigm for tuning and timbre which generalizes the special relationship between just intonation and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic timbres.Duffin, R.W., 2006''How Equal Temperament Ruined Harmony (and Why You Should Care)''/ref> This misalignment, in any tuning that is not fully Just (and hence infinitely complex), is the defining characteristic of the Static Timbre Paradigm. Instruments Many of the pseudo-just temperaments proposed during this "temperament battle" were rank-2 (two-dimensional)—such as quarter-comma meantone—that provided more than 12 notes per octave. However, the standard piano-like keyboard is only rank-1 (one-dimensional), affording at most 12 notes per octave. Piano-like keyboards affording more than 12 notes per octave were developed by Vicentino, Colonna, Mersenne, Huygens, and Newton, but were deemed cumbersome and difficult to learn. The dynamic tonality para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microtonal Music
Microtonal music or microtonality is the use in music of microtones—intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls between the keys of a piano tuned in equal temperament. In ''Revising the musical equal temperament,'' Haye Hinrichsen defines equal temperament as “the frequency ratios of all intervals are invariant under transposition (translational shifts along the keyboard), i.e., to be constant. The standard twelve-tone ''equal temperament'' (ET), which was originally invented in ancient China and rediscovered in Europe in the 16th century, is determined by two additional conditions. Firstly the octave is divided into twelve semitones. Secondly the octave, the most fundamental of all intervals, is postulated to be pure (beatless), as described by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schismatic Temperament
A schismatic temperament is a musical tuning system that results from tempering the schisma of 32805:32768 (1.9537 cents) to a unison. It is also called the schismic temperament, Helmholtz temperament, or quasi-Pythagorean temperament. Construction In Pythagorean tuning all notes are tuned as a number of perfect fifths (701.96 cents ). The major third above C, E, is considered four fifths above C. This causes the Pythagorean major third, E (407.82 cents ), to differ from the just major third, E (386.31 cents ): the Pythagorean third is sharper than the just third by 21.51 cents (a syntonic comma ). C — G — D — A — E Ellis's "skhismic temperament". instead uses the note eight fifths ''below'' C, F (384.36 cents ), the Pythagorean diminished fourth or schismatic major third. Though spelled "incorrectly" for a major third, this note is only 1.95 cents (a schisma) flat of E, and thus more in tune than the Pythagorean major third. As Ellis puts it, "the Fifths should be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syntonic Temperament
A regular diatonic tuning is any musical scale consisting of " tones" (T) and "semitones" (S) arranged in any rotation of the sequence TTSTTTS which adds up to the octave with all the T's being the same size and all the S's the being the same size, with the 'S's being smaller than the 'T's. In such a tuning, then the notes are connected together in a chain of seven fifths, all the same size (TTTS or a permutation of that) which makes it a Linear temperament with the tempered fifth as a generator. Overview In the ordinary diatonic scales the T's here are tones and the S's are semitones which are half, or approximately half the size of the tone. But in the more general regular diatonic tunings, the two steps can be of any relation within the range between T=171.43 (S=T) and T=240 (S=0) cents (fifth between 685.71 and 720). Note that regular diatonic tunings are not limited to the notes of the diatonic scale which defines them. One may determine the corresponding cents of S, T, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis (linear Algebra)
In mathematics, a set of vectors in a vector space is called a basis if every element of may be written in a unique way as a finite linear combination of elements of . The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to . The elements of a basis are called . Equivalently, a set is a basis if its elements are linearly independent and every element of is a linear combination of elements of . In other words, a basis is a linearly independent spanning set. A vector space can have several bases; however all the bases have the same number of elements, called the ''dimension'' of the vector space. This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces. Definition A basis of a vector space over a field (such as the real numbers or the complex numbers ) is a linearly independent subset of that spans . This me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
