Thematic Source Composition

As in most of my works, it is assumed from the outset that there will be a relatively small thematic resource out of which all else will be derived. There are fundamental resources — I refer to them here as "materials" — that shape these themes. They (the number sets, the pitch resources, the instrumental choices) are more fundamental than the themes in the sense that they are not yet committed to a particular musical context. What I will call "thematic elements" instantiate in explicit ways, the underlying normatives provided by the materials just mentioned. The conviction that large things (musical forms) can, and perhaps should be derived from small cells has biological resonances, but it also stems from my belief in the importance of clarity of focus in every regard. The more explicit the points from which I set out on a musical project are, the stronger is the impact of preparatory thinking in customizing the outcome of the compositional process. The methodologies and strategies I use to elaborate, extend, and combine the thematic resource, which is composed in the early stages of the work, assume that the principled transformation of something already in existence is called for. As I believe that this sort of parsimony pays dividends, I normally begin with the careful planning and composing of small-scale thematic units, which are, as it were, ideal, strongly characterized instantiations of the underlying material resources. They are neither as general, as uncommitted as the more basic materials, nor are they so extensive or definitive as to finally determine what use the whole work will make of them. They do not preclude even seemingly far-fetched developments, but they give me something specific to build upon.

As the thematic elements carry so much formative weight, their every aspect is carefully considered. I have said that even the "number of numbers" needs to be thought about. In this case, it seemed that five was the right magnitude. This is slightly larger than I might normally use for a work of 10-12 minutes (the proposed duration of each of the two parts). The larger number was chosen, partially, because of the formative decision that there would be transitions and combinations in the overall form as well as themes, and that the derived formal elements would resemble traditional formal functions (transitional and developmental). Two transitions, for example, would ideally bridge 2 different sets of themes, and this would require four. I was also imagining from the outset a quasi-narrative path that would be traversed in several ways (Sectional and Domain). Five themes provided a more distinctive and detailed succession of musical ideas than, for example, using only 3 would have. It is not that I had any "story", however abstract, in mind. Rather, the idea was that a musical discourse would occur, metaphorically, as a journey through a landscape of distinctive features. In this case, the influence of the integer series, which would have proposed either 4 or 7 themes, was overruled: 4 would have been too few, 7 too many.

One of the themes would begin the piece and have a clearly initiatory nature. Another, perhaps the most extended, would end the piece in a more reflective mood. As this musical landscape would be traversed twice, a strongly articulated close might have the effect of breaking the piece too decisively into two parts. This, of course, would undesirably disrupt the continuity of experience in relation to the larger form of the work. I knew that the thematic elements needed to be as distinct from one another as possible, since — parsimony being one of my basic considerations — there was no good purpose for adding a redundant "genetic" factor. My aim was to create a dynamic thematic resource. I knew also that I wanted a strikingly virtuosic element as well as a subtle and evocative one. And there was "Other", which was larger in scale than the thematic elements, and provided relief from the otherwise ongoing nature of the piece with its inherently "thematic" nature. The primary source of Other's distinction would come from the use of eleven superimposed and out-of-phase ostinati.

The guiding number in relation to thematic variety became 5, and it was then necessary to design the inner structure of each. I knew that I did not want a simple, symmetrical or repetitive structure (an "aba" or "abab" design). Each needed an appropriate, idiosyncratic design. Use of the logarithmic number series was a natural way for me to proceed, since the durations of the themes were going to be indebted to this series as the overall plan was finalized. The complexity of their inner design varied from the relative simplicity of Theme 3's four-part structure, to the more complicated (and extended) Theme 1, which has 9 subsections. At, or near, the center of each, I planned a section that would epitomize its character: the "core" element. It serves, in part, as an instrument of synchronization between the Sectional and Domain parts, which place the core subsections of each theme at precisely the same position in their chronologies.

In early discussion with my psychologist colleagues, it had been noted that I sometimes verbally characterized my themes. This was a potentially valuable factor in relation to psychological testing. As ideas for the overall shape evolved, and the ordering and functions of the five themes became clearer, I settled (not without a certain discomfort) on the following:

• Theme I: Equilibrium in Extremis
• Theme 2: Contradictory Assertion
• Theme 3: Tremulous Uncertainty
• Theme 4: Jagged Rips
• Theme 5: Flamboyant Line

In fact, as the music developed, I realized that the line I had devised for the final theme was less assertive than I had originally conceived it to be; it was renamed "Interior Line".⁵

My discomfort was not over whether or not verbal characterizations of music can be made. As occurs for me in relation to the selection of a title, an effort to achieve verbal characterization frequently has the effect of clarifying and concentrating what it is that (I discover) I am actually trying to do. I sometimes find that, while the bases of the music are clear (I know what I am going to do and how), and even, though perhaps to a lesser extent, the expressive intent is known, I cannot find a way to honestly characterize a passage or an idea with words. The word "honestly" is invoked here because it is important that, if I am asking words to stand in for music, they do so with a deeply rooted validity. While it may be relatively easy to describe a passage with a longer phrase, or several sentences, this goes against the grain of my commitment to parsimony. Thus, the task was not only to bring about a faithful characterization of a thematic element, but to do so with useful aptness, with a very few words … in this case, two.⁶

Normally, the thematic elements composed as a basis for completing a larger formal plan were conceived exclusively for a specific instrumentation. With Angel, I had to consider that, as a result of the decisions already made about alternative possibilities, I was going to have to conceive materials that would serve all of the functions that are being described here. But, also, they would have to do so in such a way that they might have as close to identical descriptions as possible in two radically differing media: solo piano, and chamber orchestra. The piano has, in spite of its incomparable registral span and flexibility of access, a significant set of boundary conditions established by the geometry of human hands. I began by conceiving the thematic textures in terms of a pianistic medium, keeping in mind that certain actions that are relatively trivial on the keyboard can be very problematic for an ensemble of 16 musicians (e.g., the rapidly and irregularly changing chords of Theme 2, or the multi-octave "rips" in Theme 4). In short, the condition that two radically different media needed to idiomatically carry the same musical messages was interesting and challenging.⁷

Textural sketching, planning the nature of the musical textures in each section and subsection of a theme, helped to avoid serious miscalculations such as musical ideas that were not suited to parallel representation in differing media. Let us examine the textural sketch of the simplest of the thematic elements, the third.

The following description was entered into the notebook: "alternating, out of phase, dyadic tremolos, irregularly changing, occasional arpeggiation [an unstable world]". This design is unique in that it includes little specification of intra-subsectional articulation. There are four sections ranging from 3.5 to 9 seconds in length. And this subdivision is asymmetrical, the longest section preceding the core (identified by a heavy surrounding box), and two shorter sections following it. One can see immediately that there are two features, an ostinatic incessancy ("tremulousness") and, in the core, a melting convergence which manifests the "uncertainty" of the title. The general character of each subsection is indicated graphically, and the textures described are very close to the first sketch in the notebook, where I had laid out preliminary ideals for the textural identity of the themes.

The 9-second segment is expository, more extended than the others, and contains features that persist. The core section is iconic, with its symmetrical convergence. The third part provides a slight rebuke, the speed of the tremulousness abruptly increases. Finally, the last section has a thinning, descending, cadential nature. It should be emphasized that no pitches had yet been determined, nor had the timings or numbers of events internal to each subsection yet been set. I did not know at this stage what the exact pitch range of these figurations would be either, though the sketch suggests constraint. There is a boxed admonishment (Ex. 15) telling me that "tremolos should be gauged to instrumental capabilities". (The pitch choice and ranges used were determined keeping in mind the timbral and other character of those instruments that will have to carry these roles — easily managed by the pianist — in the ensemble version.)

The outlined boxes below the theme texture (Ex. 15) indicate the contexts in which I expect Theme 3 to occur when it is completed (and therefore forewarn me about potential meta-contrapuntal difficulties). This page has both "formal" indications (proportions, durations, an implied trajectory such as the one described above), and also "informal" indications such as the words just to the left of the primary diagram: FEATURE, ESSENCE, PERSISTENCE, DISRUPTION. These terms — while not a part of the explicit formal plan, nor previously mentioned in relation to numeric or pitch materials — represent a concern parallel to that of the formative impetus that I need to have for any work. Looking at the early sketches (informal ones in the project notebook as well as more formalized drawings including the textural diagram we are now examining), I began to observe aspects of my thinking that could contribute to the consistency of the work's identity. These four words provide me with an opportunity to actively seek, not only to intermittently observe, such features in the case of all 5 themes. In this project, the set of perspectives posited here were carefully thought through and employed in shaping my ideas about each of the themes, even though they do not appear in the other textural diagrams. For example, in Theme 2 (discussed below), PERSISTENCE is represented by the 11 continually iterating chords and DISRUPTION by the dyadic, machine-like, connecting runs. (These are referred to in the notebook as "the inevitable alternative".) I understand these "informal" admonishments as indicators to my intuitive self that certain criteria might turn out to be useful. If they are, well and good, if not, they fall by the wayside.

There are also "informal" comments surrounding the diagrammatic center. These comprise a record of my interior dialog regarding what I am observing as I proceed. They can be written at the time I am creating the diagram, or be added days even months later. The diagram becomes a reference (along with pitch charts, number series, and the overall plan) to which I frequently refer while actually composing. Such "references" do not tell me what I must do, but constantly nudge me one way or another. Not infrequently, they come into conflict with one another. Resolving such dissension becomes a provocation that can itself prove productive. At the top of the page is a reminder of the integer series in case a decision needs to be made in some realm over which it has influence.

Let us now look at the first sketch page for Theme 3.

At the top of the page, there are rhythmic indications on a stave's center line. This corresponds to the temporal layout of beats at MM 60 in relation to the sectional proportions specified in the plan: 9 seconds = three, tied-together dotted half notes, whereas 5.5" is represented by a dotted quarter tied to a whole note. A metrical structure is laid out, providing specification of time at the given tempo. I decided to begin with a retrograde form of the 18-note row on the transpositional level of "F". On the 5th and 6th stave lines, I sketched out a two-line harmonic realization (briefly considering, to the left, the possibility of an inverted relationship), then used this as a source to be expanded into the actual durational situation established by the subsectional proportions. The harmonies of the two converging lines for the core section ("CI") were also worked through below, before being entered into the primary continuity above (staves 2 and 3). There are two admonitions at the lower left. One, again, suggesting attention to the issue of the instrumental recasting that will have to be made, the other noting that there should be some "out-of-phase" rhythmic relationships between the two hands on either side of the strictly note-against-note nature of the core. A 3:4 ratio is suggested at the end of the preliminary sketch (staves 5 and 6) and later incorporated at two points in the theme's first subsection. It is absent from the third subsection, to heighten the cadential effect of the loss of coordination during the last three beats of the final section. Some of the jottings here are no longer meaningful to me after the passage of five years, but the general picture is clear. A pre-established time frame is laid out in the appropriate tempo. A tentative metrical definition is given (This is sometimes revised, depending upon the way the actual music emerges.), harmonic possibilities are posited, corrected, and then become the basis for an actual realization. In most situations, the rhythmic definition would also be sketched out at the same stage as harmonic exploration occurred. This will be seen in the case of Theme 1 below.

The description already given of the content of Theme 3's four subsections suggests a formal agenda, though of the most general sort: a behavior is posited; it is restated in an idealized form, as a convergence; there is a momentary "disruption" or flurry in response; and then a closing gesture. These stages could just as well describe the course of a much larger segment of a piece, even of a whole movement. The collection of functions cited (expository, condensation, response, close) and their order (which can have only one form) describe a plausible sequence.

Let us look at Theme 1 from the same perspective (Ex. 18). It has 9 subsections, and two of them have further internal sub-divisions. Their durations, as with Theme 3, are taken directly from the proportional logarithmic series. A notebook entry proposes the following nature for this theme: "Two lines, often complementary; extreme behavior by one elicits another extremity [an adaptive world]". Evidently, this diagram is, quite apart from its greater extent, more pictorially variegated. The word "equilibrium" in the title raises the question, "Between which entities is equilibrium sought?" And, examining the textural plan, one sees that the whole is an expanded "X". One line begins in the highest register and descends over the first four subsections into the core, altering its nature as it goes from flurries of repeated notes to rapid scalar contours. A much slower moving line begins in the bass and rises gradually gaining articulative strength as it comes into the core section and becomes chordal. Equilibrium is continually redefined as the two participating lines converge on the core. And, while they are at their closest point of registral convergence, their natures (line against chord) are in the strongest contrast. From a dramaturgical perspective, the core seems to bring about some conciliation, and the subsection immediately following shows an equilibrium between similar elements, not "in extremis" at all. This ameliorated climate is maintained through the ninth subsection, although the initial registral differentiation is recovered. So there is a circularity to the overall course of this theme. We "return" at the end, but conditions have changed. I trace the structural shape of these themes to stress that they are, as has been claimed earlier, miniature movements that aspire to completeness as well as independence.

Interestingly, the first notebook sketch for the textural essence of Theme 1 is considerably more principled and consistent than the version that was actually arrived at after consideration of all contributing factors. The other proposals at this stage were more in keeping with the later, more formal textural sketches. The divergence is due to the practical requirement of subsectional delineation in the actual theme's design. The original sketch has no responsibilities beyond positing essential character.

An examination of the first bars of the sketch from Theme 1 shows immediately that the primary concerns were totally different than those for Theme 3.

Here, the mirror retrograde of the 18-note row on F is designated as the pitch reference (for the base line through the early sections) and the Ab retrograde form of the 56-note series for the upper line, there is virtually no preliminary harmonic exploration. The majority of effort goes into determining the rhythmic identity of the materials. At MM 120, 7 quarters constitute 3.5 seconds of time. If the basic unit is taken as the sixteenth-note, then there will be 28 (7 x 4 = 28) rhythmic units in the first 3.5-second section. They, in turn, will be distributed among a certain number of events whose durations are established as possible multipliers (from the integer series) of the basic unit.

The first proposal for the distribution of these 28 units is above the stave: 28 = 1, 4, 2, 7, 1, 1, 4, 1, 2, 1, 4. Note that these terms, irrespective of their freely determined orderings, are all members of the integer series. This sequence seemed too square, so, below the double stave there is another try: 28 = 1, 4, 2, 7, 4, 1, 1, 1, 4, 2, 1. Although this allowed the incorporation of a mid-beat eighth-note triplet (within the third "4"), it too was ultimately rejected in favor of a final form to be found in the sketched continuity of the first two bars. Other explorations (combining fidelity to the underlying proportionality with more volatile rhythmic drive) in relation to the rhythms of the top line (beginning at measure 5) are visible at the lower left.

Having three rather than two stages in the temporal delineation engenders greater flexibility: at the top level is the number of beats at the given tempo necessary to establish the proportional durations for the subsection. After a basic unit is chosen, one can determine how many of these "units" there are within a subsection and propose a "rough" apportionment. At the lower left of the sketch under examination: 44 = 4 + 7 + 7 + 4 + 11 + 7 + 4. Each of these intermediate units is then subdivided in a relatively flexible way. 4 = 1, 1, 1, 1, or 4 might be articulated by the first four of a group of quintuplet sixteenths, and 7 can equal 2 + 4 + 1 or 4 + 2 + 1 and so on. This is an example of what one might call "principled flexibility" in my methodologies. I try to keep the primary issues dominant (here, temporal proportionality), but do not allow restrictiveness to undermine the needed musical dimensionality . If I go outside the explicit control of my basic assumptions and materials, it will be because of musical necessity. Then, instead of simply "doing what I wish to", I will adapt a principle within some alternative perspective. Finally, note, also, that I was thinking about the future need for ensemble instrumentation (the notations in the last two bars of this page), and, therefore, making notes about how the available resources will handle these musical ideas when it comes to the instrumental recasting.

Other is one musical component of the two major parts of The Angel of Death that has not yet been discussed. It turned out to have special significance. For the moment I will only describe briefly how it was composed and why. Implicit in the foregoing discussion of thematic elements is the "sectional" perspective. The identity of sections is important, and attention is given to the explicit servicing of initiatory, cadential and other significant formal features of the theme's design. Their temporal scale is also limited, in order to ensure a highly focused, iconic impression. Thus, when considering Other, I wanted to avoid any features that would tend to ally it with the themes. It needed to be extended, devoid of directionality, unitary, and placid. My solution was to construct an 11-layered set of ostinati. The initial textural idea from my notebook showed the complexity that could arise even if only three distinctive patterns of repeating notes were used.

This graphic representation cautioned me that the individual ostinatic layers must be rather simple. Further consideration leads to simplification: the planned 11 layers were reduced to 7, and their pitch content was drastically limited (Ex. 22). Each layer has a unique pattern in time. The top one is 141 seconds (divided 7 + 11 + 29 + 47 + 29 + 11 + 7), the bottom one 65, subdivided 18 + 47. Overall, there is a variety of number and a uniqueness of pitch content in each layer:

• 1 has 7:: C, C#, D, C#, Gb, F, E
• 2 has 11: G, Eb, E, F, Ab, A, Bb, B, A, Ab, G
• 3 has 7: Ab, A, Bb, B, A, Ab, G
• 4 has 7: Gb, F, E, G, Eb, E, F
• 5 has 4: Ab, A, Bb, B
• 10 has 2: C, C#
• 11 has 2: D, C#

When the web of these relationships was laid out, it became clear that the technical demands of the wide spacing and extremely rapid lateral movement required to perform such patterns at the planned tempo were formidable. There could be only very limited ornamental identity given to the various strata, and the overall impression might become too pale. I decided to add, in places where hand position allowed, 11 very wide-ranging keyboard glissandi. Thus, although the surface of this element was constantly, subtly varied, it was also given a signature feature that occurs unpredictably. The whole is played as softly as possible.

It was clear that there would be difficulty in realizing this element even in the relatively stable context of a single performer's rhythmic confidence. And the identity of Other would depend upon the precision with which it was realized. Realizing its design for ensemble performance — even if I were able to devise a way of writing such a version of these materials — would be prohibitively time-consuming in rehearsal, so there is only a keyboard version of this element.

We have examined two of the "core" elements and can now better realize what is meant by the earlier statement that they epitomize the nature of the theme. The core cannot fully describe its host, but it can represent, even interpret a given theme's aspirations. The core element of Theme 4 is perhaps the most vigorous in its summary manifestation.

The variety of slope, range, and forms of disruption (jaggedness) is greater in the core (the 5th subsection) than in any of the other six. A unique intricacy of design is required because both a pianist and an ensemble must realize precisely the same pattern of pitch in time. Because both the words "jagged" and "rip" are strongly graphic, the implications of this diagram are more immediate than those of others. The virtuosity I wanted as an aspect of the thematic resource for Angel is provided here. But it should also be noted that the effect of the strongly directional gestures, so visceral with the compressed time scale of a 23.5-second miniature, is completely altered when they are greatly augmented, as in the longest transitional section (TR2 to 4), which builds towards the first complete appearance of the Theme 4 element.⁸

The importance of time scale to Theme 4's character has just been cited. The range of durations used by the five themes is narrow: from 23.5 (Themes 3 and 4) to 99.5 seconds (Theme 5). Such epigrammatic nature requires that, as I have been stressing, a high degree of discipline and consistency be exercised. The total duration of all five together is only around four minutes, roughly one-quarter of the duration of a major part. Larger durations would be problematic in that it would be difficult to maintain a high enough level of concentration, of essentiality. On the other hand, given a 12-15 minute duration for a major part of the overall form, it would be difficult to use units smaller than 23.5 seconds. (What is important, here, of course, is not the precise value of 23.5 seconds, but its order of magnitude value — a third of a minute.) I originally planned that Theme 3 would be only 14.5 seconds, but decided that this would not be perceptually viable.

As has been indicated, both my normal compositional practice, and the needs of the perceptual psychologists suggested that the thematic elements could and should be written before the entire piece was begun. Multi-purpose considerations in relation to thematic material had a role in shaping the textural sketches, and so although the ensemble versions were actually composed first, the pianistic medium was nevertheless a strong influence. As a result of the frequent self-admonition to remain alert to possible difficulties, I encountered none in the transfer from one medium to the other. Two issues emerged, however. The first was continuity of line over wide registral excursions. It was not infrequently the case that a particularly beguiling figure would arise easily out of the materials with which I was working. But I would realize that it crossed over the range restrictions of, say, the flue or violin and thereby would either have to be shared by two instruments, or slightly reconceived to accommodate the realities of the ensemble's capacities. Secondly, when one plays the piano, one subconsciously tends to employ the sustaining pedal to smooth, and to harmonically color the result. As I often tried out on the piano materials being conceived for the ensemble version, the pedal's influence intruded, and I needed to keep this fact in mind, so that its effects could be sensitively simulated in the ensemble writing. The adaptations, which I had to make in changing media, were not the result of altered relationships of pitch, time, contour or register. They were rather addressed to compensating for the absence of certain features of the pianistic medium: the unitary command of the individual pianist over the instrument and the ability to subtly control the mixing and retention of sonorities for harmonic or colorative purpose.⁹