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Pitch Interval
In musical set theory, there are four kinds of interval: * Ordered pitch interval * Unordered pitch interval * Ordered pitch-class interval * Unordered pitch-class interval Pitch Intervals Ordered Pitch Interval The ordered pitch interval. 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. . It is thus more specific than the unordered pitch interval in that it represents the directionality of the interval. An ordered pitch interval always includes a plus or minus sign. Thus this interval type can describe a melodic as well as a harmonic interval. Unordered Pitch Interval The unordered pitch interval does not include directionality information and is thus less specific than the ordered pitch interval. It is still the distance between two pitches measured in s ... [...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. Comparison with mathematical set theory Although musical set theory is often thought to involve the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semitone
A semitone, also called a minor second, 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 (or half of a whole step), visually seen on a keyboard as the distance between two keys that are adjacent to each other. 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. f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pitch (music)
Pitch is a perception, perceptual property that allows sounds to be ordered on a frequency-related scale (music), 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 melody, melodies. Pitch is a major auditory system, auditory attribute of musical tones, along with duration (music), duration, loudness, and timbre. Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective Psychoacoustics, 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 percep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordered Pitch-class Interval
In musical set theory, there are four kinds of interval: * Ordered pitch interval * Unordered pitch interval * Ordered pitch-class interval * Unordered pitch-class interval Pitch Intervals Ordered Pitch Interval The ordered pitch interval. 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. . It is thus more specific than the unordered pitch interval in that it represents the directionality of the interval. An ordered pitch interval always includes a plus or minus sign. Thus this interval type can describe a melodic as well as a harmonic interval. Unordered Pitch Interval The unordered pitch interval does not include directionality information and is thus less specific than the ordered pitch interval. It is still the distance between two pitches measured in s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordered Pitch Interval
In Set theory (music), musical set theory, there are four kinds of interval: * Ordered pitch interval * Unordered pitch interval * Ordered pitch-class interval * Unordered pitch-class interval Pitch Intervals Ordered Pitch Interval The ordered pitch interval. is the number of semitones that separates one Pitch (music), 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. . It is thus more specific than the unordered pitch interval in that it represents the directionality of the interval. An ordered pitch interval always includes a plus or minus sign. Thus this interval type can describe a melodic as well as a harmonic interval. Unordered Pitch Interval The unordered pitch interval does not include directionality information and is thus less specific than the ordered pitch interval. It is still the distance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave And Augmented Second On C
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. 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'' (), ''8va bassa'' (, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing this mark above or below the staff. Exp ... [...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 pitc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, 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 example of modular arithmetic is the hour hand on a 12-hour clock. If the hour hand points to 7 now, then 8 hours later it will point to 3. Ordinary addition would result in , but 15 reads as 3 on the clock face. This is because the hour hand makes one rotation every 12 hours and the hour number starts over when the hour hand passes 12. We say that 15 is ''congruent'' to 3 modulo 12, written 15 ≡ 3 (mod 12), so that 7 + 8 ≡ 3 (mod 12). Similarly, if one starts at 12 and waits 8 hours, the hour hand will be at 8. If one instead waited twice as long, 16 hours, the hour hand would be on 4. This ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Rahn
John Rahn, born on February 26, 1944, in New York City, is a music theory, music theorist, composer, bassoonist, and Professor of Music at the University of Washington School of Music, Seattle. A former student of Milton Babbitt and Benjamin Boretz, he was editor of ''Perspectives of New Music'' from 1983 to 1993 and since 2001 has been co-editor with Benjamin Boretz and Robert Morris (composer), Robert Morris. Forte number and prime form There are three methods of computing Forte number and prime form (music), prime form. Allen Forte published the first in his 1973 book ''The Structure of Atonal Music'', citing a 1961 article by Milton Babbitt. The second was introduced in Rahn's ''Basic Atonal Theory'' and used in Joseph N. Straus's ''Introduction to Post-Tonal Theory'', where it was declared that the two algorithms only differed in five cases: 5-20, 6-Z29, 6-31, 7-20, and 8-26. and both list the prime forms of a set (music), set as the most left-packed possible version of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval Class
In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (; ), is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 ≡ 7 (mod 12). See modular arithmetic for more on modulo 12. The largest interval class is 6 since any greater interval ''n'' may be reduced to 12 − ''n''. Use of interval classes The concept of interval class accounts for octave, enharmonic, and inversional equivalency. Consider, for instance, the following passage: (To hear a MIDI realization, click the following: In the example above, all four labeled pitch-pairs, or dyads, share a common "intervallic color." In atonal Atonality in i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intervals (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 fre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
