Tone Rows
			In general terms, a 12-tone row is a string of notes that can be shaped, molded, and arranged into motives or themes. Rows can be can be presented singly or in combination; they can be transformed, concatenated, inverted (turned upside down), or reversed; they can be juxtaposed, superimposed, and intertwined. The 12-tone system is remarkably fertile: it can be used to create an infinite variety of textures, densities, and patterns. Theorists have developed quite sophisticated tools and techniques to describe the associations among and between rows. Like traditional 12-tone composers, Dallapiccola often uses rows in a linear fashion, presenting them as one-dimensional strings. Existing analyses of Dallapiccola's music concentrate exclusively on the derivation of rows used in a given work and the correspondences and relationships between their melodic components. In effect, these analyses show how row "threads" form the fabric of a composition. But Dallapiccola is equally fond of projecting rows as two-dimensional configurations; I call these "cross-partitions." The use of cross-partitions in his music has not been addressed, largely because theorists have not yet developed adequate tools for the analysis of such structures.
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