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Generic 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, and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximal Evenness Seconds
Maximal may refer to: *Maximal element, a mathematical definition *Maximal (Transformers), a faction of Transformers *Maximalism, an artistic style *Maximal set *Maxim (magazine), ''Maxim'' (magazine), a men's magazine marketed as ''Maximal'' in several countries See also *Minimal (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Fourth
A fourth is a 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 and 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 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 cents (), while in equal temperament a perfect fourth is equal to five semitones, or 500 cents (see additive s ... [...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 Willard Van Orman Quine in 1949. He was professor at SUNY Buffalo from 1966 until his death in 1987. He also taught at several other universities. 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 with 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 to determine whether a given Turing machine computes a function with property ''P''. The Myhill isomorphism theorem is a computability-theoretic analogue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerald Myerson
Gerald is a male Germanic given name meaning "rule of the spear" from the prefix ''ger-'' ("spear") and suffix ''-wald'' ("rule"). Variants include the English given name Jerrold, the feminine nickname Jeri and the Welsh language Gerallt and Irish language Gearalt. Gerald is less common as a surname. The name is also found in French as Gérald. Geraldine is the feminine equivalent. Given name People with the name Gerald include: Politicians * Gerald Boland, Ireland's longest-serving Minister for Justice * Gerald Ford, 38th President of the United States * Gerald Gardiner, Baron Gardiner, Lord Chancellor from 1964 to 1970 * Gerald Häfner, German MEP * Gerald Klug, Austrian politician * Gerald Lascelles (other), several people * Gerald Nabarro, British Conservative politician * Gerald S. McGowan, US Ambassador to Portugal * Gerald Wellesley, 7th Duke of Wellington, British diplomat, soldier, and architect Sports * Gerald Asamoah, Ghanaian-born German football player * Ge ... [...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 the heptatonic scale, which has 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. 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 scales do not contain semitones. (For example, in Japanese music the anhemitonic ''yo'' scale is contrasted with the hemitonic ''in'' scale.) Hemitonic pentatonic scales are also called "ditonic scales", because the largest interval in them is the ditone (e.g., in the scale C–E–F–G–B–C, the interval found between C–E and G–B). (This should not be confu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diatonic Scale
In music theory, a diatonic scale is any heptatonic 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, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are Maximal evenness, maximally separated from each other (i.e. separated by at least two whole steps). 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 des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Well Formed Generated Collection
In diatonic set 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 (in twelve-tone equal temperament) twelve. (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 modulo 12: 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 = 5. B-E-A-D-G-C-F. A gener ... [...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. This is that for 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 patterns (adjacently, rather than around the circle of fifths) formed by diatonic transpositions of that series. Structure being the intervals in relation to the circle of fifths, multiplicity being 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 three interval patterns: M2-M2, M2-m2, m2-M2. On the circle of fift ... [...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 Gera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musical Scale
In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. 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, there is no need for scale steps to be equal within any scale and, particularly as demonstrated by microtonal music, there is no limit to how many notes can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Seventh
In music from Western culture, a seventh is a musical interval encompassing seven staff positions (see 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 and 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 Contemporary Musician'', p.69. . For example, the most commonly cited example of a melod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Sixth
In music from Western culture, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
