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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&nbs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Of Fifths
In music theory, the circle of fifths (sometimes also cycle of fifths) is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music (12-tone equal temperament), the sequence is: C, G, D, A, E, B, F/G, C/D, G/A, D/E, A/B, F, and C. This order places the most closely related key signatures adjacent to one another. Twelve-tone equal temperament tuning divides each octave into twelve equivalent semitones, and the circle of fifths leads to a C seven octaves above the starting point. If the fifths are tuned with an exact frequency ratio of 3:2 (the system of tuning known as just intonation), this is not the case (the circle does not "close"). Definition The circle of fifths organizes pitches in a sequence of perfect fifths, generally shown as a circle with the pitches (and their corresponding keys) in clockwise order. It can be viewed in a counterclockwise direction as a circle of fourths. Harmonic progres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentatonic Scale
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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifthsBruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: McGraw-Hill). Vol. I: p. 56. which are " pure" or perfect, with ratio 3:2. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio 2:1), and hence is the next most consonant "pure" interval, and the easiest to tune by ear. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i.e., the untempered perfect fifth), which is ≈ 702 cents wide. The system dates back to Ancient Mesopotamia;. (See .) It is named, and has been widely misattributed, to Ancient Greeks, notably Pythagoras (six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance Model
In music a distance model is the alternation of two different intervals to create a non-diatonic musical mode such as the 1:3 distance model, the alternation of semitones and minor thirds: C-E-E-G-A-B-C. This scale is also an example of polymodal chromaticism as it includes both the tonic and dominant as well as "'two of the most typical degrees from both major and minor' (E and B, E and A, respectively) ( árpáti 1975p.132)". The most common distance model is the 1:2, also known as the octatonic scale ( set type 8-28), followed by 1:3 and 1:5, also known as set type 4-9, which is a subset of the 1:2 model. Set type 4-9 has also been referred to as a "Z-Cell." See also *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 s ... References Modes (music) [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclic Group
In abstract algebra, a cyclic group or monogenous group is a Group (mathematics), group, denoted C_n (also frequently \Z_n or Z_n, not to be confused with the commutative ring of P-adic number, -adic numbers), that is Generating set of a group, generated by a single element. That is, it is a set (mathematics), set of Inverse element, invertible elements with a single associative binary operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation to g or its inverse. Each element can be written as an integer Exponentiation, power of g in multiplicative notation, or as an integer multiple of g in additive notation. This element g is called a ''Generating set of a group, generator'' of the group. Every infinite cyclic group is isomorphic to the additive group \Z, the integers. Every finite cyclic group of Order (group theory), order n is isomorphic to the additive group of Quotient group, Z/''n''Z, the in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
833 Cents Scale
The 833 cents scale is a musical tuning and scale (music), scale proposed by Heinz Bohlen based on combination tones, an interval (music), interval of 833.09 cent (music), cents, and, coincidentally, the Fibonacci number, Fibonacci sequence.Bohlen, Heinz (last updated 2012).An 833 Cents Scale: An experiment on harmony, ''Huygens-Fokker.org''. The golden ratio is \varphi = \frac = 1.6180339887\ldots, which as a musical interval is 833.09 cents (). In the 833 cents scale this interval is taken as an alternative to the octave as the interval of octave-repeating scale, repetition,833 Cent Golden Scale (Bohlen) , ''Xenharmonic Wiki''. however the golden ratio is not regarded as an equivalence class (music), equivalent interval (notes 833.09 cents apart are not "the same" in the 833 cents scale the way notes 1200 cents ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bisector (music)
In diatonic set theory, a bisector divides the octave approximately in half (the equal tempered tritone is exactly half the octave) and may be used in place of a generated collection, generator to derive Set (music), collections for which structure implies multiplicity is not true such as the ascending melodic minor, harmonic minor, and octatonic scales. Well formed generated collections generators and bisectors coincide, such as the perfect fifth (circle of fifths) in the diatonic collection. The term was introduced by Jay Rahn (1977), who considers any division between one and two thirds as approximately half (major third to minor sixth or 400 to 800 cents) and who applied the term only the equally spaced collections. Clough and Johnson both adapt the term to apply to generic interval, generic scale steps. Rahn also uses ''aliquant bisector'' for bisectors which may be used to generate every note in a collection, in which case the bisector and the number of notes must be coprime. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Whole-tone Scale
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or '' hexatonic'' scales. A single whole-tone scale can also be thought of as a "six-tone equal temperament". : : The whole-tone scale has no leading tone and because all tones are the same distance apart, "no single tone stands out, ndthe scale creates a blurred, indistinct effect". This effect is especially emphasised by the fact that triads built on such scale tones are all augmented triads. Indeed, all six tones of a whole-tone scale can be played simply with two augmented triads whose roots are a major second apart. Since they are symmetrical, whole-tone scales do not give a strong impression of the tonic or tonality. The composer Olivier Messiaen called the whole-tone scale his first mode of limited transposition. The composer and music t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-gap Theorem
In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places points on a circle, at angles of , , , ... from the starting point, then there will be at most three distinct distances between pairs of points in adjacent positions around the circle. When there are three distances, the largest of the three always equals the sum of the other two. Unless is a rational multiple of , there will also be at least two distinct distances. This result was conjectured by Hugo Steinhaus, and proved in the 1950s by Vera T. Sós, , and Stanisław Świerczkowski; more proofs were added by others later. Applications of the three-gap theorem include the study of plant growth and musical tuning systems, and the theory of light reflection within a mirrored square. Statement The three-gap theorem can be stated geometrically in terms of points on a circle. In this form, it states that if one places n points on a circle, at angles of \theta, 2\theta, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microtonal Music
Microtonality is the use in music of microtones — intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls "between the keys" of a piano tuned in equal temperament. Terminology Microtone ''Microtonal music'' can refer to any music containing microtones. The words "microtone" and "microtonal" were coined before 1912 by Maud MacCarthy Mann in order to avoid the misnomer " quarter tone" when speaking of the srutis of Indian music. Prior to this time the term "quarter tone" was used, confusingly, not only for an interval actually half the size of a semitone, but also for all intervals (considerably) smaller than a semitone. It may have been even slightly earlier, perhaps as early as 1895, that the Mexican composer Julián Carrillo, writing in Spanish or Frenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erv Wilson
Ervin Wilson (June 11, 1928 – December 8, 2016) was a Mexican/ American (dual citizen) music theorist. Early life Ervin Wilson was born iColonia Pacheco a small village in the remote mountains of northwest Chihuahua, Mexico, where he lived until the age of fifteen. His mother taught him to play the reed organ and to read musical notation. He began to compose at an early age, but immediately discovered that some of the sounds he was hearing mentally could not be reproduced by the conventional intervals of the organ. As a teenager, he began to read books on Indian music, developing an interest in concepts of raga. While he was in the Air Force in Japan, a chance meeting with a total stranger introduced him to musical harmonics, which changed the course of his life and work. Influenced by the work of Joseph Yasser, Wilson began to think of the musical scale as a living process—like a crystal or plant. Works Despite his avoidance of academia, Wilson has been influential on th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Clampitt
David (; , "beloved one") was a king of ancient Israel and Judah and the third king of the United Monarchy, according to the Hebrew Bible and Old Testament. The Tel Dan stele, an Aramaic-inscribed stone erected by a king of Aram-Damascus in the late 9th/early 8th centuries BCE to commemorate a victory over two enemy kings, contains the phrase (), which is translated as "House of David" by most scholars. The Mesha Stele, erected by King Mesha of Moab in the 9th century BCE, may also refer to the "House of David", although this is disputed. According to Jewish works such as the ''Seder Olam Rabbah'', ''Seder Olam Zutta'', and ''Sefer ha-Qabbalah'' (all written over a thousand years later), David ascended the throne as the king of Judah in 885 BCE. Apart from this, all that is known of David comes from biblical literature, the historicity of which has been extensively challenged,Writing and Rewriting the Story of Solomon in Ancient Israel; by Isaac Kalimi; page 32; Cambr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
