accidental but controlled (appendix)

an early term for abstract art.) attempt to make their work accessible, interesting examples from early Twentieth Century music (Debussy, Webern, Berg, Bartok) - to illustrate these aspects of non-figurative painting -( by adding di http://t.co/pJDlQvrRKg Atonality in its broadest sense is music that lacks a tonal center, or key. Atonality, in this sense, usually describes compositions written from about 1908 to the present day where a hierarchy of pitches focusing on a single, central tone is not used, and the notes of the chromatic scale function independently of one another (Kennedy 1994). More narrowly, the term atonality describes music that does not conform to the system of tonal hierarchies that characterized classical European music between the seventeenth and nineteenth centuries (Lansky, Perle, and Headlam 2001). "The repertory of atonal music is characterized by the occurrence of pitches in novel combinations, as well as by the occurrence of familiar pitch combinations in unfamiliar environments" (Forte 1977, 1). More narrowly still, the term is sometimes used to describe music that is neither tonal nor serial, especially the pre-twelve-tone music of the Second Viennese School, principally Alban Berg, Arnold Schoenberg, and Anton Webern (Lansky, Perle, and Headlam 2001). However, "[a]s a categorical label, 'atonal' generally means only that the piece is in the Western tradition and is not 'tonal'" (Rahn 1980, 1), although there are longer periods, e.g., medieval, renaissance, and modern modal musics to which this definition does not apply. "[S]erialism arose partly as a means of organizing more coherently the relations used in the preserial 'free atonal' music. ... Thus many useful and crucial insights about even strictly serial music depend only on such basic atonal theory" (Rahn 1980, 2). Examples from mathematics to show the structures in terms of which the human brain functions, thinks and perceives -

A golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship . . pure painting - an early term for abstract art.) attempt to make their work accessible, interesting ( by adding different levels of meaning, interpretation, expression,etc) acceptable, etc by adding lines, forms, shapes, colours, figures, objects and other elements that will make their work appear as realistic, refer or point to or represent some realistic or recognizable object, place, situation, mood, feeling, etc