Post-tonal music theory

Source: Wikipedia. Pages: 74. Chapters: Chromatic scale, Tone row, Serialism, Microtonal music, Whole tone scale, Atonality, Twelve-tone technique, Simultaneity succession, Tone cluster, Quartal and quintal harmony, Quarter tone, Tuplet, 72 equal temperament, Tristan chord, Spectral music, Set, 19 equal temperament, Octatonic scale, Dynamic tonality, Pitch class, 34 equal temperament, Modes of limited transposition, Schillinger System, Transformational theory, Modulatory space, Interval vector, Heptatonic scale, Moment form, Mystic chord, Combinatoriality, Emancipation of the dissonance, Graphic notation, Hexatonic scale, 15 equal temperament, Derived row, Formula composition, Permutation, Polymodal chromaticism, Pitch class space, Interval class, All-interval tetrachord, Identity, Prolongation, Chromatic circle, Klangfarbenmelodie, Polychord, Pitch interval, Cyclic set, Fundamental structure, Synthetic chord, Synthetic scale, Psalms chord, All-interval hexachord, Unified field, Partiels, Mixed-interval chord, Reinterpretation, Ausmultiplikation, Time-point. Excerpt: A tone cluster is a musical chord comprising at least three consecutive tones in a scale. Prototypical tone clusters are based on the chromatic scale, and are separated by semitones. For instance, three adjacent piano keys (such as C, C, and D) struck simultaneously produce a tone cluster. Variants of the tone cluster include chords comprising consecutive tones separated diatonically, pentatonically, or microtonally. On the piano, such clusters often involve the simultaneous striking of successive white or black keys. The early years of the twentieth century saw tone clusters elevated to central roles in pioneering works by ragtime artists Jelly Roll Morton and Scott Joplin. In the 1910s, two classical avant-gardists, composer-pianists Leo Ornstein and Henry Cowell, were recognized as making the first extensive explorations of the tone cluster. During the same period, Charles Ives employed them in several compositions that were not publicly performed until the late 1920s or 1930s. Composers such as Béla Bartók and, later, Lou Harrison and Karlheinz Stockhausen became proponents of the tone cluster. Today, tone clusters play a significant role in the work of free jazz musicians such as Cecil Taylor and Matthew Shipp, as well as the work of many modern classical composers. In most Western music, tone clusters tend to be heard as dissonant. Clusters may be performed with almost any individual instrument on which three or more notes can be played simultaneously, as well as by most groups of instruments or voices. Keyboard instruments are particularly suited to the performance of tone clusters because it is relatively easy to play multiple notes in unison on them. The modern keyboard is designed for playing diatonic scales on the white keys and pentatonic scales on the black keys. Chromatic scales involve both. Three immediately adjacent keys produce a basic chromatic tone cluster.Prototypical tone clusters are chords of three or more adjacent notes on a chromatic scale,