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Ordered Pitch Interval
In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward.Schuijer, Michiel (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', Eastman Studies in Music 60 (Rochester, NY: University of Rochester Press, 2008), p. 35. . They are notated as follows: :PI(''a'',''b'') = ''b'' − ''a'' For example C 4 to D4 is 3 semitones: :PI(0,3) = 3 − 0 While C4 to D5 is 15 semitones: :PI(0,15) = 15 − 0 However, under octave equivalence these are the same pitches (D4 & D5, ), thus the #Pitch-interval class may be used. Pitch-interval class In musical set theory, a pitch-interval class (PIC, also ordered pitch class interval and directed pitch class interval) is a pitch interval modulo twelve. The PIC is notated and related to the PI thus: :PIC(0,15) = PI(0,15) mod 12 = (15 − 0) mod 12 = 15 mod 12 = 3 Equations Using integer notation and modulo 12, ordered pitch interval, ''ip'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augmented Second On C
Augment or augmentation may refer to: Language *Augment (Indo-European), a syllable added to the beginning of the word in certain Indo-European languages *Augment (Bantu languages), a morpheme that is prefixed to the noun class prefix of nouns in certain Bantu languages *Augment, a name sometimes given to the verbal ''ō-'' prefix in Nahuatl grammar Technology *Augmentation (obstetrics), the process by which the first and/or second stages of an already established labour is accelerated or potentiated by deliberate and artificial means *Augmentation (pharmacology), the combination of two or more drugs to achieve better treatment results *Augmented reality, a live view of a physical, real-world environment whose elements are ''augmented'' by computer-generated sensory input *Augmented cognition, a research field that aims at creating revolutionary human-computer interactions *Augment (Tymshare), a hypertext system derived from Douglas Engelbart's oN-Line System, renamed "Augment" b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory (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 involve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale. For example, C is adjacent to C; the interval between them is a semitone. In a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones (e.g. a whole tone or major second is 2 semitones wide, a major third 4 semitones, and a perfect fifth 7 semitones. In music theory, a distinction is made between a diatonic semitone, or minor second (an interval encompassing two different staff positions, e.g. from C to D) and a chromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. from C to C). These are enharmonically equivalent when twelve-tone equal temperament is used, but are not the same thing in meantone temper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pitch (music)
Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound. Historically, the study of pitch and pitch perception has been a central problem in psychoacoustics, and has been instrumental in forming and testing theories of sound representation, processing, and perception in the auditory system. Perception Pitch and frequency Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the frequency of vibration. Pitch is closely related to frequency, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music," the use of which is "common in most musical systems." The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' ( it, all'ottava), ''8va bassa'' ( it, all'ottava bassa, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave Equivalence
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music," the use of which is "common in most musical systems." The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' ( it, all'ottava), ''8va bassa'' ( it, all'ottava bassa, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pitch-interval Class
In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward.Schuijer, Michiel (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', Eastman Studies in Music 60 (Rochester, NY: University of Rochester Press, 2008), p. 35. . They are notated as follows: :PI(''a'',''b'') = ''b'' − ''a'' For example C 4 to D4 is 3 semitones: :PI(0,3) = 3 − 0 While C4 to D5 is 15 semitones: :PI(0,15) = 15 − 0 However, under octave equivalence these are the same pitches (D4 & D5, ), thus the #Pitch-interval class may be used. Pitch-interval class In musical set theory, a pitch-interval class (PIC, also ordered pitch class interval and directed pitch class interval) is a pitch interval modulo twelve. The PIC is notated and related to the PI thus: :PIC(0,15) = PI(0,15) mod 12 = (15 − 0) mod 12 = 15 mod 12 = 3 Equations Using integer notation and modulo 12, ordered pitch interval, ''ip'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordered Pitch-class Interval
In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward.Schuijer, Michiel (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', Eastman Studies in Music 60 (Rochester, NY: University of Rochester Press, 2008), p. 35. . They are notated as follows: :PI(''a'',''b'') = ''b'' − ''a'' For example C 4 to D4 is 3 semitones: :PI(0,3) = 3 − 0 While C4 to D5 is 15 semitones: :PI(0,15) = 15 − 0 However, under octave equivalence these are the same pitches (D4 & D5, ), thus the #Pitch-interval class may be used. Pitch-interval class In musical set theory, a pitch-interval class (PIC, also ordered pitch class interval and directed pitch class interval) is a pitch interval modulo twelve. The PIC is notated and related to the PI thus: :PIC(0,15) = PI(0,15) mod 12 = (15 − 0) mod 12 = 15 mod 12 = 3 Equations Using integer notation and modulo 12, ordered pitch interval, ''ip'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordered Pitch Interval
In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward.Schuijer, Michiel (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', Eastman Studies in Music 60 (Rochester, NY: University of Rochester Press, 2008), p. 35. . They are notated as follows: :PI(''a'',''b'') = ''b'' − ''a'' For example C 4 to D4 is 3 semitones: :PI(0,3) = 3 − 0 While C4 to D5 is 15 semitones: :PI(0,15) = 15 − 0 However, under octave equivalence these are the same pitches (D4 & D5, ), thus the #Pitch-interval class may be used. Pitch-interval class In musical set theory, a pitch-interval class (PIC, also ordered pitch class interval and directed pitch class interval) is a pitch interval modulo twelve. The PIC is notated and related to the PI thus: :PIC(0,15) = PI(0,15) mod 12 = (15 − 0) mod 12 = 15 mod 12 = 3 Equations Using integer notation and modulo 12, ordered pitch interval, ''ip'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave And Augmented Second On C
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music," the use of which is "common in most musical systems." The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' ( it, all'ottava), ''8va bassa'' ( it, all'ottava bassa, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book ''Disquisitiones Arithmeticae'', published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in , but clocks "wrap around" every 12 hours. Because the hour number starts over at zero when it reaches 12, this is arithmetic ''modulo'' 12. In terms of the definition below, 15 is ''congruent'' to 3 modulo 12, so "15:00" on a 24-hour clock is displayed "3:00" on a 12-hour clock. Congruence Given an integer , called a modulus, two integers and are said to be congruent modulo , if is a divisor of their difference (that is, if there is an integer such that ). Congruence modulo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Notation
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to musical set theory, a pitch class is "all pitches related to each other by octave, enharmonic equivalence, or both." Thus, using scientific pitch notation, the pitch class "C" is the set : = . Although there is no formal upper or lower limit to this sequence, only a few of these pitches are audible to humans. Pitch class is important because human pitch-perception is periodic: pitches belonging to the same pitch class are perceived as having a similar quality or color, a property called "octave equivalence". Psychologists refer to the quality of a pitch as its "chroma". A ''chroma'' is an attribute of pitches (as opposed to ''tone height''), just like hue is an attribute of color. A ''pitch class'' is a set of all pit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
