Okay, hotshot, I can hear someone out there thinking. You’ve complained about the disappearance from widespread prominence of the composer/thinker in the American concert music scene. You recently complained on facebook about the lack of any heirs apparent to Babbitt and Perle, to Boretz and Morris, who occupy the same sort of presence on the concert music stage as did they in days gone by. Fine, but what are your big ideas? What do you actually stand for in composition?
Nobody’s actually asked this, yet, but I think if I keep complaining loudly enough and persistently enough, the question would become inevitable. So here are a few ideas that I’ve developed in my theoretical writings that I also apply to my composing, and where possible, an example piece.
1. Post-Tonal Prolongation, alive and well.
My view of course is that post-tonal prolongation exists, and I vary wildly from anyone who says otherwise. I won’t totally rehash my views as expressed in the link just given, but I will say that the fact that post-tonal music is vastly more complex than tonal music means that the odds are greater, not lesser, that some kind of prolongational syntax is at work in order to make this music coherent. And don’t say that it’s not coherent; everybody loves post-tonal music and understands it just fine when it is used in film and television.
Prolongational graphs of post-tonal pieces probably are more complex than orthodox Schenker graphs of tonal works, if done well. That does not mean that these complexities are insurmountable; I certainly don’t believe that the prospect of vastly complex prolongational relationships in post-tonal music means we should throw our hands up, give up, and simply pretend that the relationships don’t exist. That’s certainly not the can-do attitude that made America great.
Moreover, I think post-tonal prolongation can be reverse-engineered to be a compositional device. (For that matter, I think functionally tonal composers can sketch in the form of an orthodox Schenker graph and realize the graph in the form of a fully composed piece. Indeed, I would urge any composer insisting on writing functional tonality to do this because there is great risk that one’s functionally tonal music can verge on superficial surface mimicry without a deeper understanding of tonal architectonics.)
My post-tonal prolongational thinking comes in two flavors: vertical and horizontal, and I do not believe these approaches are in any way mutually exclusive. I call my vertical post-tonal prolongational analytical schema projection-constructive analysis. My horizontal schema I would more traditionally call post-tonal linear-reductive analysis (no newly coined term).
Projection-constructive analysis posits that lurking in the background of most post-tonal pieces is a pitch field that represents the structural culmination of the work. Suppose that pitch field is C#2/A4/D5/E5 with the numerals representing fixed register. Projection-constructive analysis is predicated on the idea that fixed register assertion of pitches replaces functionality, which is missing in post-tonal music, as a means of asserting structural supremacy of those pitches. The C#2/A4/D5/E5 pitch field might occur toward the end of the post-tonal piece, and I would call that the Structural Tetrad (sort of like the “Structural ^4” we might encounter in a Schenker graph).
How do we know it’s the Structural Tetrad? We have to look for non-pitch parameters to determine structurality of the event. We do this in orthodox Schenkerian analysis too: in determining whether a pitch is a potential head-tone, or should be flagged, or whatever, we often ask the same contextual questions, like, does it fall on a downbeat? Is the event strongly placed metrically? Is the event agogically accented? Is the event dynamically extreme? Is it colored by orchestration in a particularly marked way? In the case of the post-tonal work, we can ask this additional question: is the set salient on the surface as well as in the deep background? Notice that our C#2/A4/D5/E5 Structural Tetrad is a  set. Do we see plenty of  sets in operation on the surface of the piece? Projection-constructive analysis shares with Schenkerian analysis the idea that there is a significant nexus between the surface events of a piece and its background, and that the two mutually reinforce one another.
Projection-constructive analysis then looks for events in the piece, one event at a time, in which the final structural x-ad assembles itself vertically. So if C#2/A4/D5/E5 is our Structural Tetrad, then we might find, for example, a prominently placed C#2 at the beginning of the work. We can label this C#2 the Structural Monad (the post-tonal equivalent of a Schenkerian head tone).
Next, we would look for a Structural Dyad. We could expect something like this: somewhere along the way, we might find a C#2 and a D5 in close proximity to one another (either vertically simultaneous or very near to one another), with both pitches contextually made prominent. Once we’ve found this, we can label the dyad our Structural Dyad. Then we would look for a Structural Triad (the term “triad” here is not used to denote tertian harmony but rather any literal three-note collection). Suppose we find at some prominent juncture of the piece, occurring after the Structural Dyad, a C#2/D5/A4 collection. So long as the three notes are contextually prominent, this would make a fine Structural Triad.
The arrival of E5 working in some prominent conjunction with C#2/A4/D5 completes the Structural Tetrad, the culminating structural point of the post-tonal work. Of course, unlike with Schenkerian analysis where we have three prescribed cardinalities of structural events possible (the 3-prong descent from ^3, the 5-prong descent from ^5 and the 8-prong descent from ^8), projection-constructive analysis posits up to twelve possible structural events (if there are twelve, then the piece culminates in a Structural Dodecad). I have not found a Structural Dodecad in a piece yet, but I have found a Structural Octad, lurking in the background of The Rite of Spring.
(The Structural Monad of The Rite of Spring is D#6 at Rehearsal 8+2; the Structural Dyad is C6/Eb6 at Rehearsal 9+4; the Structural Triad is G5/C6/Eb6 at Rehearsal 11; the Structural Tetrad is A4/G5/C6/Eb6 at Rehearsal 34 through 34+1; the Structural Pentad is E4/A4/G5/C6/Eb6 at Rehearsal 36+3 through 37; the Structural Hexad is C#4/E4/A4/G5/C6/Eb6 at Rehearsal 39+1; the Structural Septad is A#3/C#4/E4/A4/G5/C6/Eb6 at Rehearsal 70+5 and the Structural Octad is F#2/Bb3/C#4/E4/A4/G5/C6/Eb6 at Rehearsal 80+3. Note that the Structural Octad is fully octatonic, giving support to those who have maintained that The Rite is essentially an octatonic work. Once the Structural Octad is in place, those eight pitches in fixed register continue to assert themselves prominently in various combinations throughout the rest of the work, in what I call an Epilogical Dissipation.)
You would be amazed at how often one can find a projection-construction lurking in the background of any post-tonal work. I believe that projection-constructions might be tropes of post-tonal pieces, because they are the results of the way post-tonal composers hear music: they go back to the same fixed-register pitches in various combinations again and again in order to tether together the work. Webern does this very clearly. Stravinsky does this. Schoenberg does this. Samuel Adler, whose music I’ve analyzed extensively, does this. Birds do it. Bees do it. Post-tonal composers make projection-constructions— not intentionally, but by virtue of the way that post-tonal composers organize their pieces when they are listening closely to their materials.
A piece of mine that is structured in such a way is called Twelve Structures for Piano and Cello or Twelve Charming Little Pieces for Cello and Piano. Each movement is a one-minute miniature that projects one of the twelve possible trichords across the background of the movement. A performance of the piece by Viktor Valkov, piano, and Lachezar Kostov, cello, can be heard here:
The other post-tonal prolongational idea I work with is essentially linear. The big idea here is that post-tonal prolongation is predicated on post-tonal counterpoint. I have found that many pieces idiostructurally assert their own rules of post-tonal counterpoint on a piece-by-piece basis. Certainly, it takes sleuthing and analysis to find the rules of counterpoint lurking in a post-tonal piece, but again, what are we analysts to do but analyze?
Stefan Wolpe composed a short passage called Modulation as Process which aesthetically modulates from a tonal harmonic landscape to a post-tonal harmonic landscape with remarkable fluidity. Analyzing the short work, I determined these contrapuntal principles at play:
For the tonal section:
Traditional rules of counterpoint apply for the section described by diatonic intervals, with the exception of the following:
1. 7ths are allowed on strong beats if they are approached and left by step.
2. Tritones are allowed on strong beats if they are approached and left by step.
For the post-tonal section:
1. No tritones on any part of the downbeat.
2. Every beat must entail at least four distinct interval classes.
3. Interval classes 3 and 6 never appear together in a purely 4-voice sonority, unless on an upbeat.
4. Wide leaps greater than an octave must be a registral displacement of a linear motion (i.e., the only leap greater than an octave that is allowed is a leap of some kind of ic1 or ic2).
5. Tritone leaps must be followed by step in either direction.
6. Leaps from 6 to 12 semitones must be followed by another leap in the opposite direction.
Taking these idiostructures as rules for background contrapuntal skeletons, I am now composing a set of Wolpe Variations for pianist Viktor Valkov. Wolpe’s Modulation as Process provides the framework of events that I prolong; the contrapuntal principles provide the rules by which I can compose-out the prolongations.
The purposes of the Wolpe Variations are two-fold: first, to show that post-tonal music can be prolonged through contrapuntal principles; second, to show that post-tonal music and tonal music can coexist peaceably and without superficial juxtapostion as long as there are large-scale architectonic forces in governance of both.
The Wolpe Variations are not yet complete; I’m shooting for 45 minutes of music. The piece, I’m told by Viktor, will require significant amounts of editing to make it more idiomatic for piano. Nonetheless, here is a MIDI realization of what I have so far. I think piano samples are reasonably okay to listen to in order to get an idea of the work; they’re certainly better than any string samples. There is about a half hour of music here; about two-thirds of the way.
To be continued:
Vol. II: Klumpenhouwer Networks as Compositional Devices
Vol. III: Geometric Formal Proportions other than Golden Sections