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The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition.The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded equally often in a piece of music while preventing the emphasis of any one note [3] through the use of tone rows, orderings of the 12 pitch classes.
The Grandmother chord is an eleven-interval, twelve-note, invertible chord with all of the properties of the Mother chord. Additionally, the intervals are so arranged that they alternate odd and even intervals (counted by semitones) and that the odd intervals successively decrease by one whole-tone while the even intervals successively increase by one whole-tone. [13]
A 12-tone row has hexachordal combinatoriality with another 12-tone row if their respective first (as well as second, because a 12-tone row itself forms an aggregate by definition) hexachords form an aggregate. There are four main types of combinatoriality. A hexachord may be: Prime combinatorial (transposition) Retrograde combinatorial
The complement of set X is the set consisting of all the pitch classes not contained in X. [12] The product of two pitch classes is the product of their pitch-class numbers modulo 12. Since complementation and multiplication are not isometries of pitch-class space, they do not necessarily preserve the musical character of the objects they ...
In music using the twelve-tone technique, derivation is the construction of a row through segments. A derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the generator. Anton Webern often used derived rows in his pieces. A partition is a segment created from a set through partitioning.
The chromatic scale is a musical scale with twelve pitches, each a semitone, also known as a half-step, above or below its adjacent pitches. As a result, in 12-tone equal temperament (the most common tuning in Western music), the chromatic scale covers all 12 of the available pitches. Thus, there is only one chromatic scale.
If the generators are all the prime numbers up to a given prime p, we have what is called p-limit just intonation.Sometimes some irrational number close to one of these primes is substituted (an example of tempering) to favour other primes, as in twelve tone equal temperament where 3 is tempered to 2 19 ⁄ 12 to favour 2, or in quarter-comma meantone where 3 is tempered to 2 4 √ 5 to favor ...
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