The internal representation of information in the form of hierarchies.

An issue of considerable interest to perceptual and cognitive psychology concerns the internal representation of information in the form of hierarchies. Strong evidence has accumulated for the encoding of visual scenes as hierarchies of subscenes (Bower & Glass, 1976; Hanson & Riseman, 1978; Navon, 1977; Palmer, 1977; Winston, 1973). Sophisticated hierarchical models of the representation of sentence structure have been advanced (Chomsky, 1963; Miller & Chomsky, 1963; Yngve, 1960). The hierarchical structure of tonal music has been the subject of considerable analysis (Lerdahl & Jackendoff, 1977; Meyer, 1956, 1973; Narmour, 1977; Salzer, 1962; Schenker, 1956, 1973). It has been shown that, when presented with hierarchically organized serial patterns, subjects’ encodings of these patterns reflect pattern structure (Bjork, 1968; Kotovsky & Simon, 1973; Restle, 1970; Restle & Brown, 1970; Simon & Kotovsky, 1963; Simon & Sumner, 1968; Vitz & Todd, 1967, 1969). In considering how hierarchically structured information is internally represented, models utilizing hierarchies of operators have proved particularly useful (Greeno & Simon, 1974; Restle, 1970). Recently, I, together with the mathematician John Feroe, have proposed a model for the internal representation of pitch sequences in tonal music that utilizes this approach (Deutsch & Feroe, 1981). This model, which is also briefly described in Deutsch (1980), has recently been seriously misdescribed by Jones (1981). The major purpose of the present note is to dispel any misconceptions about the model that may have arisen as a result of this erroneous description.1 In the model of Deutsch and Feroe (1981), pitch sequences are assumed to be represented as hierarchical networks. At each level of the hierarchy, elements are organized as structural units in accordance with laws of figural goodness such as proximity and good continuation. Elements at each hierarchical level are elaborated by further elements so as to form structural units at the next-lower level, until the lowest level is attained. At each level of the hierarchy, there exists a set of