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Field notes: a study of fixed-pitch formations.
THIS ARTICLE INVESTIGATES a technique of pitch organization that is common in post-tonal music, involving static formations I call "pitch fields." After an introductory example and a brief, informal survey of pitch-field properties and their significance in works by Mel Powell, Elliott Carter, and Witold Lutoslawski, I develop a novel type of pitch field modeled on these precedents. Fields of this new type are generated by cyclic strings of intervals in a manner that I describe formally and relate to work in the theory of scales by Stephen Soderberg and others.
The second half of the article develops the idea of cyclically generated pitch fields, pursuing two paths. First, I examine chord formation and voice-leading in the context of this type of field. And second, I develop (in two stages) a concept of "pitch field systems," which give rise to families of related pitch fields and provide a principled means of modulating from field to field.
AN EXAMPLE FROM WEBERN
Example 1 presents the opening fourteen bars of the first movement of Webern's Symphony, op. 21. This movement proceeds as a double canon by inversion, organized in the form A :[parallel]: BA'. Its distinctive orchestration and other factors are omitted from the example, which is formatted according to the four-voice texture of the canon and runs through the first row statement of each voice: I9 answers P9 in canon 1, and P1 answers I5 in canon 2. (1)
[ILLUSTRATION OMITTED]
A well-known feature of this movement is its consistent placement of pitch classes in particular registers. This feature is evident in the excerpt given in Example 1, persists through the remainder of section A (measures 1-26), is largely absent from section B (measures 25-44), and returns--with different particulars--in section A' (measures 42-66). The registral disposition of pitch classes in the first and last of these three sections is given in Example 2 and represents in each case an instance of what I shall call a pitch field.
[ILLUSTRATION OMITTED]
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Source: HighBeam Research, Field notes: a study of fixed-pitch formations.