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Diatonic Hexachord
The diatonic, Guidonian, or major hexachord (6-32) is a hexachord consisting of six consecutive pitches from the diatonic scale that are also a consecutive segment of the circle of fifths: F C G D A E = C D E F G A = "do-re-mi-fa-sol-la". It is the thirty-second hexachord as ordered by Forte number, and its complement is the diatonic hexachord at the tritone. If the circle of fifths transformation is applied to the diatonic hexachord the chromatic hexachord results. It is source set C. Hugo Riemann points out that the hexachord consists of three overlapping (diatonic) tetrachords: Lydian, Phrygian, and Dorian; as well as two overlapping pentatonic scales (which are major pentatonic and mixolydian pentatonic). Richard Crocker made the case that, in the words of Stefano Mengozzi, "the Guidonian hexachord was the most important diatonic unit for practical musicians from the Carolingian era to the seventeenth century".Crocker, R.L. (1968 and 1972). "Perchè Zarlino diede una nuov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root (chord)
In music theory, the concept of root is the idea that a chord (music), chord can be represented and named by one of its Musical note, notes. It is linked to Harmony (music), harmonic thinking—the idea that vertical aggregates of notes can form a single unit, a chord. It is in this sense that one speaks of a "C chord" or a "chord on C"—a chord built from C and of which the note (or pitch) C is the root. When a chord is referred to in Classical music or popular music without a reference to what type of chord it is (either major or minor, in most cases), it is assumed a major triad, which for C contains the notes C, E and G. The root need not be the bass note, the lowest note of the chord: the concept of root is linked to that of the Inverted chord, inversion of chords, which is derived from the notion of Invertible Counterpoint, invertible counterpoint. In this concept, chords can be inverted while still retaining their root. In tertian harmonic theory, wherein chords can be con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Of Fifths
In music theory, the circle of fifths is a way of organizing the 12 chromatic pitches as a sequence of perfect fifths. (This is strictly true in the standard 12-tone equal temperament system — using a different system requires one interval of diminished sixth to be treated as a fifth). If C is chosen as a starting point, the sequence is: C, G, D, A, E, B (=C), F (=G), C (=D), A, E, B, F. Continuing the pattern from F returns the sequence to its starting point of C. This order places the most closely related key signatures adjacent to one another. It is usually illustrated in the form of a circle. 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 a clockwise progression. Musicians and composers often use the circle of fifths to describe the musical relationships between pitches. Its design is helpful in composing and harmonizing melodies, building chords, and ... [...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 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] |
Tetrachord
In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency proportion (approx. 498 cents)—but in modern use it means any four-note segment of a scale or tone row, not necessarily related to a particular tuning system. History The name comes from ''tetra'' (from Greek—"four of something") and ''chord'' (from Greek ''chordon''—"string" or "note"). In ancient Greek music theory, ''tetrachord'' signified a segment of the greater and lesser perfect systems bounded by ''immovable'' notes ( ); the notes between these were ''movable'' ( ). It literally means ''four strings'', originally in reference to harp-like instruments such as the lyre or the kithara, with the implicit understanding that the four strings produced adjacent (i.e., conjunct) notes. Modern music theory uses the octave as the basic u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugo Riemann
Karl Wilhelm Julius Hugo Riemann (18 July 1849 – 10 July 1919) was a German musicologist and composer who was among the founders of modern musicology. The leading European music scholar of his time, he was active and influential as both a music theorist and music historian. Many of his contributions are now termed as Riemannian theory, a variety of related ideas on many aspects of music theory. Biography Riemann was born at Grossmehlra, Schwarzburg-Sondershausen. His first musical training came from his father Robert Riemann, a land owner, bailiff and, to judge from locally surviving listings of his songs and choral works, an active music enthusiast. Hugo Riemann was educated by Heinrich Frankenberger, the Sondershausen Choir Master, in Music theory. He was taught the piano by August Barthel and Theodor Ratzenberger (who had once studied under Liszt). He studied law, and finally philosophy and history at Berlin and Tübingen. After participating in the Franco-Prussian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Source Set
In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates (all twelve tones). Whittall, Arnold. 2008. ''The Cambridge Introduction to Serialism. Cambridge Introductions to Music'', p. 272. New York: Cambridge University Press. (hardback) (pbk). Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively." Combinatoriality is a side effect of derived rows, where the initial segment or set may be combined with its transformations (T,R,I,RI) to create an entire row. "Derivation refers to a process whereby, for instance, the ini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milton Babbitt
Milton Byron Babbitt (May 10, 1916 – January 29, 2011) was an American composer, music theorist, mathematician, and teacher. He is particularly noted for his Serialism, serial and electronic music. Biography Babbitt was born in Philadelphia to Albert E. Babbitt and Sarah Potamkin, who were Jewish. He was raised in Jackson, Mississippi, and began studying the violin when he was four but soon switched to clarinet and saxophone. Early in his life he was attracted to jazz and theater music, and "played in every pit-orchestra that came to town". Babbitt was making his own arrangements of popular songs by age 7, "wrote a lot of pop tunes for school productions", and won a local songwriting contest when he was 13. A Jackson newspaper called Babbitt a "whiz kid" and noted "that he had perfect pitch and could add up his family’s grocery bills in his head. In his teens he became a great fan of jazz cornet player Bix Beiderbecke." Babbitt's father was a mathematician, and Babbitt inten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chromatic Hexachord
In music theory, the chromatic hexachord is the hexachord consisting of a consecutive six-note segment of the chromatic scale. It is the first hexachord as ordered by Forte number, and its complement is the chromatic hexachord at the tritone. For example, zero through five and six through eleven. On C: *C, C, D, D, E, F and *F, G, G, A, A, B. This is the first of the six hexachords identified by Milton Babbitt as all-combinatorial source sets, a "source set" being "a set considered only in terms of the content of its hexachords, and whose combinatorial characteristics are independent of the ordering imposed on this content" . In the larger context of thirty-five source hexachords catalogued by Donald Martino, it is designated "Type A" . Applying the circle of fifths transformation to the chromatic hexachord produces the diatonic hexachord . As with the diatonic scale, the chromatic hexachord is, "hierarchical in interval makeup," and may also be produced by, or contains, 3-1, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication (music)
The mathematical operations of multiplication have several applications to music. Other than its application to the frequency ratios of Interval (music), intervals (for example, Just intonation, and the twelfth root of two in equal temperament), it has been used in other ways for twelve-tone technique, and set theory (music), musical set theory. Additionally ring modulation is an electrical audio process involving multiplication that has been used for musical effect. A multiplicative operation is a Map (mathematics), mapping in which the Argument of a function, argument is multiplied. Multiplication originated intuitively in interval expansion, including tone row order number Rotation (mathematics), rotation, for example in the music of Béla Bartók and Alban Berg. Pitch number rotation, ''Fünferreihe'' or "five-series" and ''Siebenerreihe'' or "seven-series", was first described by Ernst Krenek in ''Über neue Musik''. Princeton-based theorists, including James K. Randall, Godf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tritone
In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. Narrowly defined, each of these whole tones must be a step in the scale, so by this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. More broadly, a tritone is also commonly defined as any interval with a width of three whole tones (spanning six semitones in the chromatic scale), regardless of scale degrees. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B (from F to the B above it, also called augmented fourth) and B–F (from B to the F abo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complement (music)
In music theory, ''complement'' refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism. In interval complementation a complement is the interval which, when added to the original interval, spans an octave in total. For example, a major 3rd is the complement of a minor 6th. The complement of any interval is also known as its ''inverse'' or ''inversion''. Note that the octave and the unison are each other's complements and that the tritone is its own complement (though the latter is "re-spelt" as either an augmented fourth or a diminished fifth, depending on the context). In the aggregate complementation of twelve-tone music and serialism the complement of one set of notes from the chromatic scale contains all the ''other'' notes of the scale. For example, A-B-C-D-E-F-G is ''complemented'' by B-C-E-F-A. Note that ''musical set theory'' broadens the definition of both senses somewhat. Interval complementation Rule of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forte Number
In musical set theory, a Forte number is the pair of numbers Allen Forte assigned to the prime form of each pitch class set of three or more members in ''The Structure of Atonal Music'' (1973, ). The first number indicates the number of pitch classes in the pitch class set and the second number indicates the set's sequence in Forte's ordering of all pitch class sets containing that number of pitches. In the 12-TET tuning system (or in any other system of tuning that splits the octave into twelve semitones), each pitch class may be denoted by an integer in the range from 0 to 11 (inclusive), and a pitch class set may be denoted by a set of these integers. The prime form of a pitch class set is the most compact (i.e., leftwards packed or smallest in lexicographic order) of either the normal form of a set or of its inversion. The normal form of a set is that which is transposed so as to be most compact. For example, a second inversion major chord contains the pitch classes 7, 0, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
