Crippled symmetry and proportion in Feldman’s Projection 2

Dating to the early 1950s, Feldman’s graphic scores stand at the dawn of compositional practices based on indeterminacy. Although Feldman’s experiences in this field were destined to remain partly in the shadow of Cage’s, his contribution is fundamental and in many ways profoundly different from that of his composer friend. The widespread belief that Feldman’s compositional method is entirely unsystematic and consequently lacks general compositional principles, which could be brought to light by an analytical type of study, has been contradicted by recent research (Noble, 2013 and Cline, 2016). It has been shown that it is not in the least impossible to carry out a comparative study of Feldman’s different works, aimed at identifying structural relations responding to the same principles. These comparative studies have revealed the importance of the graphic component in the score and the significant presence of proportional relationships characterized by a certain degree of symmetry. In particular, the central concept of “crippled symmetry”, i.e., the creation of patterns of musical elements linked by relationships of symmetry and proportionality, yet characterized by a certain degree of imperfection and disproportion, has been repeatedly emphasized. The aim of this essay is to apply these different analytical methodologies to one of Feldman’s compositions that inaugurated his compositional phase characterized by the earliest experiments in the field of indeterminate music and the use of graphic scores: Projection 2.