Diagrams for Formal Planning
From the first ensemble music I composed in the early 60s, I have used diagrammatic plans to portray in a proportional, rectilinear map, the prospects for the music I was setting out to create. Certainly, both my father's profession (architecture) and the engineering physics studies that I completed before undertaking formal musical training at the University of Michigan both influenced this. It did not stem from my teachers. Whether in formally prepared diagrams or informal sketching in notebooks, there is a geometrical cast to these beginnings. In early pages of the Angel project notebook, I am already assuming the desirability of a form that "allows for several presentations of identical or nearly identical materials/sections". The presence of the Sectional and Domain ideals is already known, and I ask myself "What about preparing a tape 'layer' that could be superimposed on either 1/2 of the 2- part overall structure, namely, whichever is last" This passage continues, "then the overall form would be either …" (cf. Ex. 9).
A few pages later, I am laying out an initial proposal for the definition of the Sectional part. It has a number of functions: Introduction, Theme, Transition, Combination, and "Other". There are, however, only three thematic elements at this stage.
Many of the features of the final plan are already in place. There is an introductory section that precedes the "Th 1". This initial theme is followed by a "TRANS 1" leading to "Th 2", which is, in turn, immediately followed by "Other". In this initial sketch, Other is surprisingly long, in proportional terms. In fact, it has an importance rather more as it actually turned out in the end (in contrast to what was proposed in the early overall plans [cf. Ex. 14 below]). Other does not have exclusivity, but coexists with a second presentation of Theme 1, and also with the beginning of a transition to Theme 3. This new transition also coexists with the first "Comb", which leads to Th 3. A second combination follows Theme 3, and appears to end the piece, although there is also a box below with unclear identity. The accompanying verbal list of elements includes a "closing" to balance the introduction, but this is not shown. If one replaces the introduction and closing posited here with thematic elements, the overall shape is closely related to later, more formal overall plans. The presence of two layers of narrow boxes in the present diagram is in keeping with the idea of stratified instrumentation (the piano contrasted with the ensemble), but, at this stage, I appear to be underestimating the potential dangers (technically, perceptually) of overlapping formal functions.
The second appearance of Theme 1 — now in the presence of Other — appealed to the psychologists, and survived in early versions of the overall plan, but was eventually discarded. Another feature of this earliest developed sketch is that, while Theme 1 occurs exclusively in the lower stratum, and Theme 2 in the upper one, Theme 3 is shared by both media. This feature was retained in the formal overall plans, but, in the end, was not accepted. In S, the fourth theme was presented by the ensemble only, and, in D, its core subsection was carried by the piano alone. Note that there is still only a general suggestion of proportion. The logarithmic series that shaped the proportions of the formal elements has not yet been evoked.
In the next notebook instantiation, more detail and precision is evident.
A listing of "TYPES of elements" at the right, includes 5 Themes, 3 Combinations, 2 Transitions, 1 Repeat, and 1 Other, and this is what the first formal overall plan included. Incidentally, one can note my realization that this number of musical segments adds up to 12 rather than to 11 (from the integer series). In the end, a repetition of Theme 2 under cover of Other was dropped and the number of formal elements reduced to 11. It became clear that the coexistence of formal elements — particularly because of the looming fact that the computer part would overlap either D or S in each performance — intensified the desirability of reducing the superimposition of ideas. An effort is made, at the bottom of Ex. 11, to resolve the proportions roughly indicated above into a more explicit form, corresponding with numbers from the proportional logarithmic series. The original "Introduction" has now become Theme 1, and other formal elements follow, more or less as before, though now the choice of specific durations for each has brought the alignment of the elements into a more refined state favoring exclusivity: one musical function followed by another. A further intensification of this tendency occurred as actual composition began, and, for example, Theme 3's appearance causes Combination 2/4 to become silent until the theme is finished. Similarly, Theme 5 replaces the indicated Combination of 1/2/3. (This combination will be discussed in more detail later.)
