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Specific Interval
In diatonic set theory a generic interval is the number of scale steps between notes of a collection or scale. The largest generic interval is one less than the number of scale members. (Johnson 2003, p. 26) A specific interval is the clockwise distance between pitch classes on the chromatic circle ( interval class), in other words the number of half steps between notes. The largest specific interval is one less than the number of "chromatic" pitches. In twelve tone equal temperament the largest specific interval is 11. (Johnson 2003, p. 26) In the diatonic collection the generic interval is one less than the corresponding diatonic interval: * Adjacent intervals, seconds, are 1 * Thirds = 2 * Fourths = 3 * Fifths = 4 * Sixths = 5 * Sevenths = 6 The largest generic interval in the diatonic scale being 7 − 1 = 6. Myhill's property Myhill's property is the quality of musical scales or collections with exactly two specific intervals for every generic interval ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximal Evenness Seconds
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Maximal may refer to: *Maximal element, a mathematical definition *Maximal set * Maximal (''Transformers''), a faction of Transformers *Maximalism, an artistic style * ''Maxim'' (magazine), a men's magazine marketed as ''Maximal'' in several countries See also *Minimal (other) Minimal may refer to: * Minimal (music genre), art music that employs limited or minimal musical materials * "Minimal" (song), 2006 song by Pet Shop Boys * Minimal (supermarket) or miniMAL, a former supermarket chain in Germany and Poland * Minim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Fourth
A fourth is a interval (music), musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished fourth, Diminished and Tritone, augmented fourths span the same number of staff positions, but consist of a different number of semitones (four and six, respectively). The perfect fourth may be derived from the Harmonic series (music), harmonic series as the interval between the third and fourth harmonics. The term ''perfect'' identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor. A perfect fourth in just intonation corresponds to a pitch ratio of 4:3, or about 498 cent (music), cents (), while in equal temperam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Myhill
John R. Myhill Sr. (11 August 1923 – 15 February 1987) was a British mathematician. Education Myhill received his Ph.D. from Harvard University under the supervision of Willard Van Orman Quine in 1949. He was a professor at SUNY Buffalo from 1966 until his death in 1987. He also taught at several other universities during his career. His son, also called John Myhill, is a professor of linguistics in the English department of the University of Haifa in Israel. Contributions In the theory of formal languages, the Myhill–Nerode theorem, proven by Myhill and Anil Nerode, characterizes the regular languages as the languages that have only finitely many inequivalent prefixes. In computability theory, the Rice–Myhill–Shapiro theorem, more commonly known as Rice's theorem, states that, for any nontrivial property ''P'' of partial functions, it is undecidable whether a given Turing machine computes a function with property ''P''. The Myhill isomorphism theorem is a comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerald Myerson
Gerald is a masculine given name derived from the Germanic languages prefix ''ger-'' ("spear") and suffix ''-wald'' ("rule"). Gerald is a Norman French variant of the Germanic name. An Old English equivalent name was Garweald, the likely original name of Gerald of Mayo, a British Roman Catholic monk who established a monastery in Mayo, Ireland in 670. Nearly two centuries later, Gerald of Aurillac Gerald of Aurillac (or Saint Gerald) ( 855 – c. 909) is a French saint of the Roman Catholic Church, also recognized by other religious denominations of Christianity. Life Gerald was born into the Gallo-Roman nobility, counting Cesarius of Ar ..., a French count, took a vow of celibacy and later became known as the Roman Catholic patron saint of bachelors. The name was in regular use during the Middle Ages but declined after 1300 in England. It remained a common name in Ireland, where it was a common name among the powerful FitzGerald dynasty. The name was revived in the Anglosp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentatonic Collection
A pentatonic scale is a musical scale with five notes per octave, in contrast to heptatonic scales, which have seven notes per octave (such as the major scale and minor scale). Pentatonic scales were developed independently by many ancient civilizations and are still used in various musical styles to this day. As Leonard Bernstein put it: "The universality of this scale is so well known that I'm sure you could give me examples of it, from all corners of the earth, as from Scotland, or from China, or from Africa, and from American Indian cultures, from East Indian cultures, from Central and South America, Australia, Finland ...now, that is a true musico-linguistic universal." There are two types of pentatonic scales: Those with semitones (hemitonic) and those without (anhemitonic). Types Hemitonic and anhemitonic Musicology commonly classifies pentatonic scales as either ''hemitonic'' or ''anhemitonic''. Hemitonic scales contain one or more semitones and anhemitonic sca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diatonic Scale
In music theory a diatonic scale is a heptatonic scale, heptatonic (seven-note) scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps. In other words, the half steps are maximally separated from each other. The seven pitch (music), pitches of any diatonic scale can also be obtained by using a Interval cycle, chain of six perfect fifths. For instance, the seven natural (music), natural pitch classes that form the C-major scale can be obtained from a stack of perfect fifths starting from F: :F–C–G–D–A–E–B. Any sequence of seven successive natural notes, such as C–D–E–F–G–A–B, and any Transposition (music), transposition thereof, is a diatonic scale. Modern musical keyboards are designed so that the white-key notes form a diatonic scale, though transpositions of this diatonic scale require one or more black keys. A diaton ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Well Formed Generated Collection
In music theory, a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection or scale is formed. All scales with the deep scale property can be generated by any interval coprime with the number of notes per octave. (Johnson, 2003, p. 83) The C major diatonic collection can be generated by adding a cycle of perfect fifths (C7) starting at F: F-C-G-D-A-E-B = C-D-E-F-G-A-B. Using integer notation and 12-tone equal temperament, the standard tuning of Western music: 5 + 7 = 0, 0 + 7 = 7, 7 + 7 = 2, 2 + 7 = 9, 9 + 7 = 4, 4 + 7 = 11. The C major scale could also be generated using cycle of perfect fourths (C5), as 12 minus any coprime of twelve is also coprime with twelve: 12 − 7 =& ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structure Implies Multiplicity
In diatonic set theory structure implies multiplicity is a quality of a collection or scale (music), scale. For collections or scales which have this property, the interval series formed by the shortest distance around a diatonic circle of fifths between members of a series indicates the number of unique interval (music), interval patterns (adjacently, rather than around the circle of fifths) formed by diatonic transpositions of that series. Structure refers to the intervals in relation to the circle of fifths; multiplicity refers to the number of times each different (adjacent) interval pattern occurs. The property was first described by John Clough and Gerald Myerson in "Variety and Multiplicity in Diatonic Systems" (1985). () Structure implies multiplicity is true of the diatonic collection and the pentatonic scale, and any subset. For example, cardinality equals variety dictates that a three member diatonic subset of the C major scale, C-D-E transposed to all scale degrees gives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinality Equals Variety
The musical operation of scalar transposition shifts every note in a melody by the same number of scale steps. The musical operation of chromatic transposition shifts every note in a melody by the same distance in pitch class space. In general, for a given scale S, the scalar transpositions of a line L can be grouped into categories, or transpositional set classes, whose members are related by chromatic transposition. In diatonic set theory cardinality equals variety when, for any melodic line L in a particular scale S, the number of these classes is equal to the number of distinct pitch classes in the line L. For example, the melodic line C-D-E has three distinct pitch classes. When transposed diatonically to all scale degrees in the C major scale, we obtain three interval patterns: M2-M2, M2-m2, m2-M2. Melodic lines in the C major scale with ''n'' distinct pitch classes always generate ''n'' distinct patterns. The property was first described by John Clough and Geral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Scale
In music theory, a scale is "any consecutive series of notes that form a progression between one note and its octave", typically by order of pitch or fundamental frequency. The word "scale" originates from the Latin ''scala'', which literally means "ladder". Therefore, any scale is distinguishable by its "step-pattern", or how its intervals interact with each other. Often, especially in the context of the common practice period, most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature. Due to the principle of octave equivalence, scales are generally considered to span a single octave, with higher or lower octaves simply repeating the pattern. A musical scale represents a division of the octave space into a certain number of scale steps, a scale step being the recognizable distance (or interval) between two successive notes of the scale. However, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Seventh
In music from Western culture, a seventh is a interval (music), musical interval encompassing seven staff positions (see Interval (music)#Number, Interval number for more details), and the major seventh is one of two commonly occurring sevenths. It is qualified as ''major'' because it is the larger of the two. The major seventh spans eleven semitones, its smaller counterpart being the minor seventh, spanning ten semitones. For example, the interval from C to B is a major seventh, as the note B lies eleven semitones above C, and there are seven staff positions from C to B. Diminished seventh, Diminished and Augmented seventh, augmented sevenths span the same number of staff positions, but consist of a different number of semitones (nine and twelve). The easiest way to locate and identify the major seventh is from the octave rather than the unison, and it is suggested that one sings the octave first.Keith Wyatt, Carl Schroeder, Joe Elliott (2005). ''Ear Training for the Contempora ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Sixth
In music theory, a sixth is a musical interval encompassing six note letter names or staff positions (see Interval number for more details), and the major sixth is one of two commonly occurring sixths. It is qualified as ''major'' because it is the larger of the two. The major sixth spans nine semitones. Its smaller counterpart, the minor sixth, spans eight semitones. For example, the interval from C up to the nearest A is a major sixth. It is a sixth because it encompasses six note letter names (C, D, E, F, G, A) and six staff positions. It is a major sixth, not a minor sixth, because the note A lies nine semitones above C. Diminished and augmented sixths (such as C to A and C to A) span the same number of note letter names and staff positions, but consist of a different number of semitones (seven and ten, respectively). A commonly cited example of a melody featuring the major sixth as its opening is " My Bonnie Lies Over the Ocean".Blake Neely, ''Piano For Dummies'', se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
