Timespan Hierarchies and Posttonal Pitch Structure: A Composer's Strategies

Timespan Hierarchies and Posttonal Pitch Structure: A Composer's Strategies I *? ? ? i?? m Paul Nauert This paper describes various strategies for organizing pitch materials and coordinating them with a particular conception of rhythm and form. Beginning with the simple notions that chord changes can articu late a relatively small level of rhythmic structure, and that pitch-field changes can articulate a larger one, it next considers how a composer might create additional levels of rhythmic structure by exploiting the property of similarity. For instance, a structural level might consist of regions defined by the intervallic similarityof the chords they contain. In this scenario, the chords of any one region would have a high intervallic resemblance to one another and a lower intervallic resemblance to the chords of neighboring regions. Other scenarios might depend on the intervallic similarity between pitch fields, or between progressions from chord to chord or from field to field. Familiar theoretical models exist for Timespan Hierarchies 35 some of these cases and can be extended to cover the rest of them. In addition to these familiar (extensible) models, I argue thatmore idiosyn cratic, contextually determined notions of intervallic similarity are also relevant to composition, and I present ways tomodel these aswell. This paper begins with a brief narrative account, looking back across the evolution of my work as a composer to a time when the basic ideas outlined above first took shape. From that start, Iwill continue the narra tive for awhile in order to explain how and why my strategies grew more elaborate. Once themost important concepts are in place, Iwill shift my attention back to the present in order to describe the role these ideas play in my music today. Origins and Evolution One of the first elements to become a durable part ofmy compositional practice was the technique of restricting pitch content in a potentially long stretch ofmusic to a fixed collection of pitches?today Iwould call it a pitchfield. This device has a significant history in themusic ofAnton Webern and subsequently inworks by Luciano Berio, Pierre Boulez, Earle Brown, Elliott Carter, Witold Lutoslawski, Henri Pousseur, Mel Powell, Anton Webern, Iannis Xenakis, and other prominent composers. Elsewhere, I have traced this history in some detail and developed a technical account of pitch fields with certain types of structure.1Here it will suffice to say that a pitch field is a collection of pitches that occur, to the exclusion of other pitches, throughout some musical passage. The construction of a pitch field is distinct from that of a pitch-class set because the former consists of registrally specific pitches while the latter consists of registrallyneutral pitch classes. The phrase "throughout some musical passage" is vague in order to allow for the different practices of different composers, but its intent is to distinguish pitch-field usage from more transient presentations of pitch sets. A pitch field has aspects in common with both a scale and a chord. Like a scale, itprovides a gamut of pitches fromwhich melodic and har monic material can be fashioned; like a chord, it possesses a distinctive harmonic sonoritywhen its fullcontents are kept in circulation. This sec ond conception of a pitch field?the idea of it as a chord?was initially themore important one formy own compositional purposes. My idea in these early days was to create a piece for large ensemble by assembling a texture of densely layered complex rhythms and using this rhythmic material to "animate" a succession of pitch fields. Or from another per spective, my intentwas to use the pitch fields to "colorize" the rhythmic 36 Perspectives of New Music material. At a very general level, this strategy ofworking out the rhyth mic fabric of a whole composition and coordinating it afterwards with pitch materials has remained with me ever since. With hindsight, Iwould saymy early plans forusing pitch fields resem bled techniques that are characteristic of Lutos?awski; but at the time I was thinking a lot about themusic of Steve Reich, particularly hisMusic for 18Musicians and theworks immediately following it.Of course this music reflectsReich's interest in the concept of gradual process,2 but this concept ispursued less single-mindedly than inmany of his...