Formal conception: Its elements

There were three primary formal components. Thematic elements are brief compositions with their own formal shape: beginning, defining their terrain, evolving, and ending. They are complete musical textures, not single-line musical themes. Transitions involve a gradual change in emphasis from one state (e.g., the identity of a musical theme) to another. They are continuous and organic in nature, including a sense of long-term directionality or motion in contrast to thematic elements that are more concentrated and expository. Combinations place two or more thematic elements in interaction with one another. They are not thought of as directional, but function in the way that traditional development sections do, exploring the relationships between thematic essences, and enlarging their potential.

Proportionality is a basic consideration in planning form. Where does the composer look if s/he is interested in going beyond the familiar binary relationships (2, 4, 8, 16, …) and traditional symmetries (aba, abab, abcab, etc.)? When I first began composing, I laid out musical structures on the basis of numerical proportions drawn from features of the rows with which I was working. But I came to feel that there was an unacceptable arbitrariness to this. After reading Paul Fraisse's The Psychology of Time, I sought a source of proportionality that did not have an additive character — brick-like building blocks — but was rather a nonlinear reference. I settled upon logarithmic series of numbers, which either enlarge or diminish in a way that parallels the experience of deceleration or acceleration in music. The differences in magnitude from one event to the next (from one duration to the next) have a directional influence themselves. One feels that elements are becoming more frequent, and that the degree of their convergence is itself changing. Using log-linear graph paper, I find a series of numbers that have attractive properties and can be used to shape formal opportunity as I expect it to arise in the piece. In the case of Angel, the series is: 14.5, 23.5, 38, 61.5, 99.5, 161, etc. (See the section on "Logarithmic Number Series".)

The fact that each successive value is the sum of the preceding two is useful in that one finds it easy to devise multilayered structures where the subsections of the various layers are distinct from one another but nevertheless can be aligned conveniently into larger groups of equivalent length. It is like having a set of children's' blocks that at first appear to be of uneven size (as contrasted with brick-like conformity). Then one finds that the walls that one is building always seem to come out in accord with one another. In addition to their modular compatibility, the structures I design with such gradated durational variation do, indeed, carry the sense of expansion or concentration I wish the overall form to project.

The emerging requirements of The Angel of Death, involved the desire to traverse a single landscape of opportunity in two contrasted ways. There were two processual ideals. The Sectional mode presents materials (whether thematic, transitional, or combinations) in a way meant to maximize the listener's awareness of their identity, of the articulation of structural landmarks, of the differences between kinds of sectional definition (thematic versus nonthematic). Because of these criteria, the consistency and identifiability of each subsectional component is crucial, particularly with the thematic elements. I want the listeners to feel (before intellectually analyzing) that a certain musical purpose (expository, cadential, transitional) is foremost, and to be able to enlist their attention in the appropriate spirit. Even if a detailed comprehension of process is not possible from the outset, the outline — a sense of "being somewhere" — can be clear. But neither art nor music always intends to be clear. Ambiguity and doubt are essential to any aesthetic project. If the listener were always certain which path the musical argument would follow, if s/he were never in doubt about the weighting (or significance) of relationships between musical materials or the grouping of musical ideas, the potential richness of inference would be seriously dampened. Also, from the point of view of my psychologist collaborators, there were advantages to the idea that parallel musical materials could be presented in ways that might elicit differing reactions. Without abandoning the ideal of discriminable function, it seemed feasible to compose a body of music in which elements were understood as radiating sources of influence rather than clearly bounded segments. The ideal for the Domain mode in my compositional design, then, was more continuous, more organic. It would not be featureless, but its contours would be less sharp, its articulating silences, or sudden redefinitions rarer and softer-edged. Its content in a given passage would be less unitary. These two modes each inhabit one half of the whole piece and will be referred to as S and D.

The two participating media — two comprehensive carriers of musical information (the solo piano and the chamber orchestra) — were thought of as inhabiting distinctive layers. A set of musical elements were arrayed over time so that their functions sometimes co-existed (in the two layers), and were differentiated, in part, by their contrasted timbral character. The existence of parts conceived in relation to two procedural modes (two media and two strata for each part or half of the total composition) suggested a complementarity, as previously mentioned, whereby pianist and ensemble trade roles from one part to the other.¹

Initially, I planned that the work would consist essentially of two parts, each about 10-12 minutes in duration. I assumed that there would be a break of some sort between the two halves, but it also seemed that there should be structural silences within each part. In keeping with the idea of parallel traversals, these articulating silences would occur at identical positions in the temporal unfolding of each. They were to be of specific and appropriate duration (long enough to attract attention but not so long as to allow the musical continuity to be completely disrupted). They were to be evaluative occasions, placed so as to provide the listener with an opportunity to recall, reconsider, anticipate, etc. Thought of as formal articulators, in relation to the remarks about the Sectional mode above, they not only behave in this way (as metaphoric punctuation such as that which clarifies how the words that appear on this page are to be parsed and therefore better comprehended), but also as "gaps", unexpectedly long pauses.

There is a further member of the repertoire of elements in the overall plan. The themes are thought of as miniature compositions. Each has a shape, character, inner delineation, and — even if on a very small time scale — a trajectory of its own. I felt the plan also needed an element that would not conform to this material model, that would be a unique occurrence, not referenced elsewhere. I termed this element "Other", and conceived it, originally, as a superimposition of 11 ostinati misaligned in time, a texture that, while constantly changing, offers the listener no sense of direction. Other was to serve as an oasis. In order to give it a stronger overall profile, I also added long sweeping, upward or downward glissandi at 11 points during its course. These, while becoming a signature characteristic, nevertheless occur only at irregular intervals and cannot be anticipated.

As is normally the case, I used a project notebook for Angel, writing comments, suggesting possible directions, and so on, as my thinking evolved. But, as a result of the continuing discussions with my collaborators, it is evidently the case that the genesis of this work was somewhat more "self-conscious" than is normal for me. I do not think that this was in any significant way problematic, however. I normally begin by sketching out a possible outline for the shape of the piece to be. Although the exposition in this article suggests a more linear and rational process than that which actually occurred, I did in fact begin to make the first formal sketches on the basis of the elements already discussed (Ex. 1). These first sketches include the duality of modes (S and D), the presence of multiple themes, of derived sections with different functions, and "Other". The earliest characterization (Ex. 1) contained only the idea of two versions of one underlying design to be presented in either order, the second accompanied by computer sound (C).

As digital signal processing and spatialization can produce a surreal result, it follows that the technologically derived components of my works often carry with them an "extra-normal" expressive cast. In Ariadne's Thread, for example, synthesized computer sound takes the metaphoric role of the maze: a superhuman authority, implacable, immovable, irresistible. In The Angel of Death, though I did not originally plan this at a conscious level, it dawned on me one day that the computer was, in a sense, "the angel". From the beginning, in drawings and notebook entries (Ex. 2), I thought of the entire span of the computer element as beginning in the highest register and then descending as a shadow over the live instrumental performance of the second half of the piece, ending in the lowest register. The computer element, it was clear, would have to participate in a special meta-contrapuntal process if it were gong to effectively coexist with either the S or D forms of the live instrumental material. (I will return to this point later.)

I assumed that the computer component would begin at the close of the first part and continue after the end of whichever part were performed second, but I became dissatisfied with the prospect of ending a long and complex work without the participation of the live musicians. The solution, which came somewhat later, was to compose an Epilog for the piano soloist that would be a reflective and consoling response to the final computer summation. The Epilog, emerging as a necessity only as the nature of the entire work evolved, appears on none of the plans.