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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
Inclusion of the combinatorial matrix would also be a good introduction to the topic. I would also include a section on the use of the set-complex to construct a 12-tone row. For this to be effectively achieved, perhaps a seperate article that covers the second part of Forte's "The Structure of Atonal Music" is needed.
This template is intended to provide a consistent and easy display for tone rows, in all forms: prime, retrograde, inverse, retrograde inversion, and inverse retrograde; and in all transpositions.
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.
"Mirror forms", P, R, I, and RI, of a tone row (from Arnold Schoenberg's Variations for Orchestra Op. 31, "Called mirror forms because...they are identical". [1]In music, a tone row or note row (German: Reihe or Tonreihe), also series or set, [2] is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both ...
D harmonic minor & in the inverted row-form added-sixth chord with both major and minor third : I: 0 t 9 7 5 4 1 8 6 2 4 e: P: 0 2 3 6 8 t 5 7 9 e 1 4: 2 1 3 2 2 5 2 2 2 2 3: Ernst Krenek: Lamentatio Jeremiae Prophetae, Op. 93, row 2 [18] 1940–41 6-34: 6-34: RI-symmetry I: 0 t 9 6 4 2 7 5 3 1 e 8: P: 0 2 4 5 8 t 6 7 9 e 1 3
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]
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.