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Transformation (music)
In music, a transformation consists of any operation or process that may apply to a musical variable (usually a set or tone row in twelve tone music, or a melody or chord progression in tonal music), or rhythm in composition, performance, or analysis. Transformations include multiplication, rotation, permutation (i.e. transposition, inversion, and retrograde), prolation ( augmentation, diminution) and combinations thereof. Transformations may also be applied to simpler or more complex variables such as interval and spectrum or timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica .... See also * Identity (music) * Operation (music) * Permutation (music) * Transformational theory References Musical techniques {{Music-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transposition Example From Koch
Transposition may refer to: Logic and mathematics * Transposition (mathematics), a permutation which exchanges two elements and keeps all others fixed * Transposition, producing the transpose of a matrix ''A''T, which is computed by swapping columns for rows in the matrix ''A'' * Transpose of a linear map * Transposition (logic), a rule of replacement in philosophical logic * Transpose relation, another name for converse relation Games * Transposition (chess), different moves or a different move order leading to the same position, especially during the openings * Transposition table, used in computer games to speed up the search of the game tree Biology * Transposition (birth defect), a group of congenital defects involving an abnormal spatial arrangement of tissue or organ ** Transposition of the great vessels, cardiac transposition, a congenital heart defect with malformation of any of the major vessels ** Transposition of teeth ** Penoscrotal transposition * Tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation (music)
In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more ''operations'', such as transposition, inversion, retrogradation, circular permutation (also called ''rotation''), or multiplicative operations (such as the cycle of fourths and cycle of fifths transforms). These may produce reorderings of the members of the set, or may simply map the set onto itself. Order is particularly important in the theories of composition techniques originating in the 20th century such as the twelve-tone technique and serialism. Analytical techniques such as set theory take care to distinguish between ordered and unordered collections. In traditional theory concepts like voicing and form include ordering; for example, many musical forms, such as rondo, are defined by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operation (music)
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music, drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that. One branch of musical set theory deals with collections ( sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, melodic inversion, and complementation. Some theorists apply the methods of musical set theory to the analysis of rhythm as well. Mathematical set theory versus musical set theory Although musical set theory is often thought to involv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity (music)
In post-tonal music theory, identity is similar to identity in universal algebra. An identity function is a permutation or transformation which transforms a pitch or pitch class set into itself. Generally this requires symmetry. For instance, inverting an augmented triad or C4 interval cycle, 048, produces itself. Performing a retrograde operation upon the tone row 01210 produces 01210. Doubling the length of a rhythm while doubling the tempo produces a rhythm of the same durations as the original. In addition to being a property of a specific set, identity is, by extension, the "family" of sets or set forms which satisfy a possible identity. These families are defined by symmetry, which means that an object is invariant to any of various transformations; including reflection and rotation. George Perle provides the following example:Perle, George (1995). ''The Right Notes: Twenty-Three Selected Essays by George Perle on Twentieth-Century Music'', p.237-238. . :"C-E, D-F, E- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timbre
In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables listeners to distinguish different instruments in the same category (e.g., an oboe and a clarinet, both woodwind instruments). In simple terms, timbre is what makes a particular musical instrument or human voice have a different sound from another, even when they play or sing the same note. For instance, it is the difference in sound between a guitar and a piano playing the same note at the same volume. Both instruments can sound equally tuned in relation to each other as they play the same note, and while playing at the same amplitude level each instrument will still sound distinctively with its own unique tone color. Experienced musicians are able to distinguish between different instruments of the same typ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Series (music)
A harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a ''fundamental frequency''. Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series. The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or air c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval (music)
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In Western music, intervals are most commonly differences between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diminution
In Western music and music theory, diminution (from Medieval Latin ''diminutio'', alteration of Latin ''deminutio'', decrease) has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of shorter, usually melodic, values (also called " coloration"; Ger. ''Kolorieren''). Diminution may also be the compositional device where a melody, theme or motif is presented in shorter note-values than were previously used. Diminution is also the term for the proportional shortening of the value of individual note-shapes in mensural notation, either by coloration or by a sign of proportion. A minor or perfect interval that is narrowed by a chromatic semitone is a diminished interval, and the process may be referred to as diminution (this, too, was sometimes referred to as " coloration"). Diminution as embellishment Diminution is a form of embellishment or melodic variation in which a long note or a series of long notes is divi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augmentation (music)
In Western music and music theory, augmentation (from Late Latin ''augmentare'', to increase) is the lengthening of a note or the widening of an interval. Augmentation is a compositional device where a melody, theme or motif is presented in longer note-values than were previously used. Augmentation is also the term for the proportional lengthening of the value of individual note-shapes in older notation by coloration, by use of a sign of proportion, or by a notational symbol such as the modern dot. A major or perfect interval that is widened by a chromatic semitone is an augmented interval, and the process may be called augmentation. Augmentation in composition A melody or series of notes is ''augmented'' if the lengths of the notes are prolonged; augmentation is thus the opposite of diminution, where note values are shortened. A melody originally consisting of four quavers (eighth notes) for example, is augmented if it later appears with four crotchets (quarter notes) instead. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prolation Canon
In music, a prolation canon (also called a mensuration canon or proportional canon) is a type of canon, a musical composition wherein the main melody is accompanied by one or more imitations of that melody in other voices. Not only do the voices sing or play the same melody, they do so at different speeds (or ''prolations'', a mensuration term that dates to the medieval and Renaissance eras). Accompanying voices may enter either simultaneously or successively. If voices extend the rhythmic values of the leader (for example, by doubling all note values), a procedure known as augmentation, the resulting canon can be called an augmentation canon or canon by augmentation (''canon per augmentationem'') or sloth canon (recalling the slow movement of the sloth). Conversely, if they reduce the note values in diminution, it can be called a diminution canon or canon by diminution (''canon per diminutionem''). Examples Prolation canons are among the most difficult canons to write, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retrograde (music)
A melodic line that is the reverse of a previously or simultaneously stated line is said to be its retrograde or cancrizans ("walking backward", medieval Latin, from ''cancer'', crab). An exact retrograde includes both the pitches and rhythms in reverse. An even more exact retrograde reverses the physical contour of the notes themselves, though this is possible only in electronic music. Some composers choose to subject just the pitches of a musical line to retrograde, or just the rhythms. In twelve-tone music, reversal of the pitch classes alone—regardless of the melodic contour created by their registral placement—is regarded as a retrograde. In modal and tonal music In treatises Retrograde was not mentioned in theoretical treatises prior to 1500.Newes, p. 218. Nicola Vicentino (1555) discussed the difficulty in finding canonic imitation: "At times, the fugue or canon cannot be discovered through the systems mentioned above, either because of the impediment of rest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melodic Inversion
In music theory, an inversion is a type of change to intervals, chords, voices (in counterpoint), and melodies. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory. Intervals An interval is inverted by raising or lowering either of the notes by one or more octaves so that the positions of the notes reverse (i.e. the higher note becomes the lower note and vice versa). For example, the inversion of an interval consisting of a C with an E above it (the third measure below) is an E with a C above it – to work this out, the C may be moved up, the E may be lowered, or both may be moved. : The tables to the right show the changes in interval quality and interval number under inversion. Thus, perfect intervals remain perfect, major intervals become minor and vice versa, and augmented intervals become diminished and vice versa. (Doubly diminished intervals become doubly augmen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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