I mentioned that I find myself working Sudoku puzzles lately. My other spare-time hobby, relentless nerd that I am, is analyzing the 12-tone pieces I'm using for my 12-tone analysis class in the fall. The two activities - tone-row searching and Sudoku - are kind of alarmingly similar, so much so that I can forget at times which I'm doing. (Is that "aggregate" filled up yet? Am I looking for 12 of something, or 9 of something?) I do like understanding things, though, so that I get a real childlike kick out of teasing out the structure of a piece I've been listening to for decades. In other words it's more like summer fun for me than it would be, I imagine, for most people.

I'm also honing in on the repertoire for the course. Looking for Schoenberg 12-tone pieces I can stomach, I've come up with the Waltz, Op. 23 No. 5, the first 12-tone piece he published, with a row that never transposes; the Op. 24 Serenade sonnet with the 11-syllable lines that go out of phase with the row; and the magnificent first scene of Moses und Aron. For Webern I am almost criterion-less, because they all make the same point, and I already use my favorites - Opp. 21, 27, and 29 - in other courses. Using the Concerto feels like such a cliche, but I guess my students need to know the cliches. I'm afraid I'm at the point of dropping poor Aaron Copland from the list. Connotations and Inscape are big, unwieldy pieces, and I just don't think they're that good, and I don't want to end up weakly defending them. Copland's imagination seemed constrained by the technique. If I'm going to venture into a large orchestral work (in addition to Sinfonia), I'd much rather use Rochberg's Second Symphony, which is the most exciting, memorable, and followable orchestral 12-tone work by any American I know of - also more to my taste, frankly, than anything the Second Vienna School ever produced. I'm already using Rochberg's Serenata d'Estate, which has been fun to take apart.

I have to do much of this at the beginning of the summer, because I need to order scores for students, and I have to make sure I don't get in over my head. I don't want to omit Boulez, and I'll attempt Le Marteau rather than more attractive examples only because there's a published analysis. Yes, I'm slowly working my way through Lev Koblyakov's oddly titled Pierre Boulez: A World of Harmony, a stunning work of analysis, and an equally stunning piece of dismal writing. If he could have stuck with even one musical passage long enough to show how Boulez derived it from beginning to end, it would be immensely more illuminating, but instead he goes concept by concept and jumps all over the piece with each new concept. He's certainly concise - too much so, in fact - and I admire his achievement, but he could have made his findings infinitely easier to digest.

(Time magazine hasn't yet added it to their online archive, but I clearly remember around 1980 when they ran an article breaking the news that a music-analyst, Koblyakov, had cracked the code to Le marteau. Amazing to think that mainstream media actually cared about such things a mere 30 years ago.)

Nevertheless, I get that Boulez divides up his row into five segments in five possible ways based on a rotating number series:

and so on. I also get that he "multiplies" each of those five segments by all five of them to build up derived unordered pitch sets - the process of "chord multiplication" being to transpose one chord to all the pitches of the other chord and add all the pitches together. And you can see how (if you take the trouble) each gesture is drawn from the pitches of these chord-multiplication products:

I also get how Boulez chose the order of chord multiples by making little diagonal patterns through his chart of available sets. Sounds like fun.

Well, that's great, sir, you're a Lebowski, I'm a Lebowski. What I can't see is why this method of generating pitches has any significant advantage over Cage's chance processes, which Boulez so vehemently rejected. I can't see what they have to do with the ostensive unifying purpose of the 12-tone row, and since Boulez plays around within them as unordered collections, plus has two of them going at any given time in extremely rapid succession (any one collection rarely occupying more than two beats at quarter = 168), I can't see what purpose this incredibly convoluted process serves in the least. Stephen Heinemann in "Pitch-Class Set Multiplication in Theory and Practice" (Music Theory Spectrum Vol. 20, No. 1, Spring 1998) promises to reveal a "process-based listening strategy" for Le Marteau based on all this, but by the time one's waded through all his math, the results aren't much. He shows how in "Domain 5" (one of the five harmonic areas) a certain octatonic partitioning tends to occur, but then writes

the other domains do not parse as easily as Domain 5, and... such an analytical approach is not without its obstacles. The aural "processing" in terms of interval class 3 and octatonic structuring is complicated... by the sheer rapidity of change...

If this is the best assurance we can get from someone who understands Le Marteau well enough to correct Koblyakov's misconceptions about it, I'm ready to give up on anyone ever making detailed aural sense of the piece. As Fred Lerdahl famously wrote (and Taruskin quotes it in his history),

Boulez's Le Marteau sans Maitre (1954) was widely hailed as a masterpiece of post-war serialism. Yet nobody could figure out, much less hear, how the piece was serial. From hints in Boulez (1963), Koblyakov (1977) at last determined that it was indeed serial, though in an idiosyncratic way. In the interim, listeners made what sense they could of the piece in ways unrelated to its construction. Nor has Koblyakov's decipherment subsequently changed how the piece is heard.... The serial organization of Le Marteau would appear, 30 years later, to be irrelevant. The story is, or should be, disturbing. ("Cognitive Constraints on Compositional Systems," in Generative Processes in Music, Oxford, 1988)

I agree. I'm disturbed by it. And yet...

* * * * * * * * * * * * * * * * * * * * * *

- and yet, just as I couldn't decipher Le Marteau on my own without Koblyakov's almost grudging help, neither had I been able to tease any detailed sense out of Stravinsky's Requiem Canticles before Joseph Straus's Stravinsky's Late Music appeared. (Koblyakov proudly asserts that he analyzed Le Marteau without seeing Boulez's sketches, which are apparently lost, but I gather Straus had access to Stravinsky's notes.) In my youth I struggled vainly to relate the luscious quadruple flute chords from the Interlude (so proto-Feldmanesque, although Feldman was already doing similar things) to any kind of pitch order drawn from the first movement:

What a relief it was to learn that the chords are drawn from the first two-note columns in an array of four rows, prime, retrograde, inversion, and retrograde inversion:

And, going on, the two chords in the fifth measure are drawn from columns 3 and 4, respectively. The relationship of this fat A-flat 9 chord, drawn from two notes each from four different row forms, with duplications, to any sense of this work's 12-tone content is just as tenuous as the order of Boulez's chord multiplications. Here and elsewhere, it's almost like Stravinsky wrote out his row forms in some interesting logical order and then just glanced around for groups of pitches he liked that happened to be adjacent on the page. Of course, that gorgeous chord locked in the choice of other chords following it, quasi-randomly determined, with little musical function of their own but to resolve back to the initial one. The approach seems more charmingly intuitive, almost accidental or even opportunistic, than theoretical. I'm reminded of Bill Duckworth's piece from the 1970s Pitch City, in which the players are given a map for improvising their way through a row matrix.

(I was also amused to read in Straus's book about Boulez's and Stravinsky's relationship. Despite the flattering interest Stravinsky showed in the young Boulez, Boulez led a disastrous 1958 performance of Stravinsky's Threni, and frequently made public his contempt for all of Stravinsky's post-1923 music. In 1970 Stravinsky said, "I have not had any contact with M. Boulez myself since, shortly after visiting me in Hollywood three years ago, he talked about my latest compositions... with unforgivable condescension, then went on to play them at a prestigious concert in Edinburgh. This was not the first proof of disingenuousness I had had of that arch-careerist, but it will be the last in which I have any personal connection." (Stravinsky's Late Music, p. 34, n. 66) I'm not sure "arch-careerist" is the precise term for someone who bites the hand that could feed him, but I do feel certain that, even with my stunted sense of political advantage-taking, I would have returned the solicitations of Igor Stravinsky more graciously than that.)

In neither the case of Le Marteau nor Requiem Canticles does the technique seem to have any perceptible relation to the unifying idea of a 12-tone row. In the case of Requiem Canticles, though, it doesn't matter to me, because I've always loved the piece and I always will; it and Threni are among my favorite Stravinsky works, which I guess makes me a pretty rare breed of Stravinsky fan. (Straus goes concept-by-concept too, but with his broad hints I've been able to trace the rows through half of Threni.) I'm curious to find out how Requiem Canticles was composed, but the knowledge won't influence the way I listen to it, and I didn't care what the process "turned out" to be. In Le Marteau's case, however, I have always been baffled by the music, was never able to learn to love it or even like it or remember any of it, and finding out what total disregard for perceptibility it was written with is more likely to reinforce my dismissive attitude toward it than to make me listen more sympathetically. (I'm with this guy.) And yet I do love some of Boulez's later music, particularly Pli selon pli and Rituel.

Going further into all this is bracing me for the big philosophical question I'm expecting from the students this fall: Why use 12-tone method? What was the point? I don't expect to have an answer by then. Already when I mentioned in modernism class that some composers deviate from strict use of the row, they became indignant; if you believe in the theory, they said, you should trust it devoutly, and if not you should abandon it. (Young people can afford to be so pure.) The music itself will have to convince them that it's not so black and white: that the row is sometimes a unifying factor, sometimes a melody, sometimes a note generator, sometimes a pretext, sometimes an ideological weapon, sometimes a bad idea entertained for too long, sometimes even a Rorschach test. But I think I can convince them some beautiful music happened in spite of it, if not always because of it.

COMMENTS:

Joseph L. says: June 21, 2010 at 6:44 pm - Amazing to think that mainstream media actually cared about such things a mere 30 years ago. Around that time, the Harvard Lampoon produced a parody of Newsweek, in which the results of a "readers' survey" appeared. One of the survey questions was: "Who is your favorite twelve-tone composer?" "‘Arnold Shoenberg!' scream our readers." Fourth and last was "the emphatically flat Pierre Boulez, proving that music is not the universal language."

jodru says: June 21, 2010 at 6:57 pm - "if you believe in the theory, they said, you should trust it devoutly, and if not you should abandon it. (Young people can afford to be so pure.)" I will never forget a young, ‘pure' student leaping to his feet, convinced that he'd caught a mistake in ‘Lichter Wasser', and asking Stockhausen if he realized he had repeated a note that broke with his tone row (at that point, Stockhausen called them ‘formulas'). Stockhausen had spent hours upon hours drilling into our heads how his formulas shaped every moment in the music, how all of the music germinated from the formulas. When confronted with evidence that he hadn't quite followed his own strict pattern, Stockhausen shrugged and said, "I wanted to repeat that note..." By that point, Stockhausen had been deviating from his own patterns for 5 decades. He knew the limits of any system, and he cared about pleasing his sense of drama more than any system he'd devised. So, if the Grand Poobah of total serialization can laugh it off when he wants to, I'd say your students can too.

Samuel Vriezen says: June 21, 2010 at 9:36 pm - Ah, what a fine good old subject! If I may attempt some answers of my own to the question of "Why serialism"... First, I'd suggest the difference with Cageian chance is that chance ends up being more wild, or more honestly so. Cage is not going to avoid any octaves and triads, but the serial system can and will usually be skewed towards the appearance of certain favorite interval distribution patterns. Secondly, in some composers the use of symmetries and the like was very expressive. Third, the most important thing in serialism is I believe not the series, but the way it made people aware of the single pitch and the single interval, and the parametrization of music. The best work in the style shows a great awareness of precision for the sake of precision, which you can hear in the tiniest note and which can sound exhilarating when done well. By giving every note its own place in the structure, it seems as if every note is saying something - even if it is not in a "language" you can actually understand, and that's great - a music that almost entirely consists of articulations, but not of "words". Early Stockhausen in this regard is to my ears vastly preferable to Boulez. Finally, of course it really started taking off when higher order textural concerns were being studied at their proper level of structural abstraction. Hence Xenakis, who I would say is easily the greatest of all the European composers of that generation.
KG replies: I never meant to imply that European serialism didn't bring about a welcome revolution in the area of musical texture. But as your non-12-tone example of Xenakis definitively clinches, why did it require a 12-tone row?

Dan Schmidt says: June 21, 2010 at 9:43 pm - I don't even think of Rituel and Pli selon pli as being particularly late Boulez! Rituel is a great piece, but also unlike any other Boulez I've heard in being so understandable (in marked opposition to everything else I've heard of his). The only real early music of Boulez I've heard are the piano sonatas, which I can't get a grip on at all. It's amazing that it's the same composer who wrote such lushly beautiful pieces as ...explosante-fixe... It's hard for me to think of any twelve-tone piece in which perceiving anything interesting about the way that it was put together is actually possible without a score and a few pencils. Maybe Berg's violin concerto? And I guess some Webern - he's so minimal that his scores sometimes read more like the architectural scaffolding of actual pieces.
KG replies: I didn't mean they were late Boulez, just later than Le Marteau.

Samuel Vriezen says: June 22, 2010 at 7:19 am - Kyle: with the example of Xenakis, the argument I would make is that the twelve-tone row was the instrument to get to parametric thinking. Would other instruments have been thinkable? Probably. Of course the case can still be made that Messiaen's "Mode" was more influential than anything else. But they seem to have needed the row to make the transition in terms of form. The problem of course being that parametric thought does not have any kind of internal temporal logic, like tonality does. I'd say the row as a transitional instrument was useful because it combines a parametric view of materials, which is "a-temporal", with temporal organization. That is again a reason why row composition is different from Cageian chance composition, of course, Cage understanding parametric thought and its implications in the time domain more profoundly than Boulez. (But, of course, Cage's major inventions in this area were influenced by European serialism to some degree) So the row combines an atemporal way of looking at materials with a temporalizing logic, and also it does so on the basis of a sense of harmonic completeness (you manipulate every pitch, interval, etc. in the gamut). I do think it's a very clumsy tool, however, and perhaps Boulez' intricacies are symptoms of his recognition of this fact. (Appropriately, the spambot-filter words I have to type for this comment are "by clock")
KG replies: I can see all that. Talking about European 12-tone music and American 12-tone music, you know, are like talking about two almost entirely different animals. In America it became such an ideological article of faith, and you strayed from the letter of the law at your spiritual peril. In the '60s Berio and Zimmermann and Ligeti wandered away from serialism with a nonchalance unknown in America; here every individual apostasy brought a threat of academic execution. One of the challenges is going to be teaching both these conceptions of the style in one class.

michael chant says: June 22, 2010 at 9:41 am - Chris Hobbs has a CD of Sudoku pieces.
KG replies: Way ahead of you: http://www.artsjournal.com/postclassic/2007/09/ europostclassicality_does_exis.html

Samuel Vriezen says: June 22, 2010 at 11:05 am - In that respect, Kyle, how do you see Carter's work? He was never really serial. Isn't it that in the States, serialism has primarily meant Schoenberg's influence, whereas in Europe, he was conveniently absent? (Still, there have been scandals about things like octaves - oooo! - in Darmstadt around the time of the later 50s!) Perhaps a unified narrative works something like this? There was a pre-war European modernism that continued in the States as academic music, mostly coming out of Schoenberg and Stravinsky. But in Europe, the absence of this tradition because of the war opened the way to truly experimental approaches. These, however, were soon brought to blossom in the States most clearly by Cage and his tradition - Cage being uniquely positioned, having (1) studied with Schoenberg; (2) corresponded with Boulez in the late 40s; (3) been able to connect it all to an existing, very American tradition that includes people like Ives, Cowell and Varèse (and (4) also been able to connect it all to what was happening in the other arts in post-war NYC). Cage then would be the American "serialist" in the European sense of the word, whereas the American sense of the word simply does not have any real representatives in Europe post-WW II, Boulez & Stockhausen already trying to get away from the strictures of the row almost from the moment they first started using it. You'd have the row as subjective language (pre-war European developments, with Webern at its high apex: integration of atonal harmony with 16th century contrapuntal models), as disciplining structure (American academicism) and as "line of flight" (experimentalism, using the row as a ladder to be thrown away). That makes for a nice tripartite dialectical model! KG replies: That sounds pretty good. I guess Carter's works have a more expressionist, European profile, but I think he cares as little as Babbitt does whether you can hear what he's doing or not. Americans may be more satisfied with what's on paper.

Ryan Tanaka says: June 22, 2010 at 1:50 pm - There was a point in time when I was really into the 12-tone method, but I've always enjoyed the 2nd Vienese School's music much more than any of the post-war serialists that came afterwards. Like your analysis above, it bothered me that the pitch choices of the latter pieces seemed largely arbitrary, and that if you were clever enough you could probably justify almost anything if you wanted to. Even "traditional" methods of transposition, inversion, and retrogrades I couldn't see what the point was, since you can't hear what was happening anyway.

The impetus behind the method has always been to give each pitch equal weight. In that case, the most diciplined thing to do would be to repeat the row over and over without straying at all, which is something you can actually hear. I wrote a piece using that idea, giving each instrument its own tone-row to give "character" (and idea I stole from Carter, where he assigns intervals to each instrument) and it turned out pretty comical:

Fantasies for a Quintet (Intro)

Like 5 people talking to each other, but not really communicating since they're all completely unwaivering. After that piece I pretty much gave up on the method altogether because I couldn't really use it without it turning into a parody of itself. If you want to hit "all the pitches" you can do that intuitively (like a lot of improvisers do) or use rules of harmonic modulation if you want some sort of theoretical justification behind what you're doing. And these sort of things you can actually hear, which is why I think Schoenberg's "free atonal" style tends to resonate with people much better than his later, more formalized works.

Boulez and Stockhausen et al. took that formalized process to the next level, but the premise itself was shoddy so I don't think it can really be justified from an intellectual point of view. Boulez probably disliked Cage mostly because the latter composer illuminated arbitrariness behind these types of structures and posed a threat to the music-theory castle that the former had built for himself. If you're just writing whatever you want, why create an overly elaborate pretense?

Now that I've been out of school for a while why nobody wants to listen to that kind of stuff seems pretty obvious. Advocates say that it makes more "sense" the more you study and listen to it, but I think that any honest inquiry will lead anybody towards the opposite direction. It's hard to realize that from the inside, though.

Evan says: June 22, 2010 at 10:29 pm - But then I have to say I can't figure out how J. S. Bach wrote the B-Minor Mass or the Art of Fugue either.

Richard says: June 23, 2010 at 8:59 am - Riegger employed a loodey-goosey 12 tone technique in his 3rd symphony, so there has been an american tradition of non-ideological "serialism". I do believe that the Germanic need for "Ordnung" is behind Schoenberg's "discovery". German speaking folks fear chaos, we thrive on it.
KG replies: I was listening to that piece last night as a possible replacement for the Copland, and angry because I forgot to bring the score home from my office. I'm also looking into his 2nd Quartet, but I forget whether it's 12-tone.

Stephen says: June 23, 2010 at 1:36 pm - Come on, Derive II and Sur Incises are lovely, sensuous works. Take your point on the rest of it though.
KG replies: Since I complimented some Boulez works after Le Marteau, I have no idea what the "come on" is in response to.

Frank J. Oteri says: June 24, 2010 at 2:18 pm - Kyle, since you've dropped the Copland 12-tone pieces from your syllabus, how about adding Irving Fine, either the Symphony or-my personal favorite-his Fantasia for String Trio. Very exciting and discernible use of rows most of the time as well as tuneful and rhythmically inventive all the time.... FJO
KG replies: Don't know either piece. !!!

Rob Davidson says: June 24, 2010 at 6:58 pm - The Time news story about "Le Marteau" (which has been looping in my iPod this week - gorgeous stuff) is pretty fascinating. But I wonder why it was newsworthy - why did the piece need to have its code cracked? Surely Koblyakov could just have asked Boulez what he did - why was there a puzzle to be worked out when it was the result of a deliberate, conscious process? Unless it's set up like a Rubik's cube, Rubik and Boulez keeping their solutions secret. Pardon my ignorance if I've missed something. It's a general feeling I have about analysis of serial-related music - why are analysts even necessary (beyond systematising and organising) when the processes in the music were decided consciously? It's not like they are revealing the structure behind intuitive choices.
KG replies: The method of Le Marteau is so complicated no one could ever figure it out. Boulez threw out a couple of hints in On Music Today, but withheld crucial information, and by the '70s he was saying that the sketches were lost and he didn't remember what he did. Who knows?

Richard Friedman says: June 26, 2010 at 2:29 am - In the same vein, here's a discussion of fractal techniques as applied to music construction: http://plus.maths.org/issue55/features/kormann/index.html

W. Thompson says: June 26, 2010 at 3:44 pm - The brilliant Leonard B. Meyer explained beautifully why Cage's and Boulez' music has the same effect on the listener in his "Emotion and Meaning in Music" (1957). I wouldn't be fair to him to try to summarize here his reasoning, so I encourage everyone to give the book a read.

Samuel Vriezen says: June 27, 2010 at 8:05 am - Funny. The music of Boulez and that of Cage doesn't remotely have the same effect on me when I listen. Not even when I compare the 2nd Sonata and Music of Changes.

michael chant says: June 28, 2010 at 9:06 am - Re: Hobbs/Sudoku - Great! Not the only line of descent of the Scratch composers though!

Carlton Wilkinson says: July 5, 2010 at 11:01 pm - Funny you mentioned Pli Selon Pli and Rituel. I would have picked them as my favorites as well, along with Le Soliel des Eaux and ... explosante fixe .... But I also have to agree with some of the comments here that maybe we're just not taking into account enough of B.s output. There's actually very little beyond Le Marteau that matches its coldness. I remember reading Boulez's book, rereading the same passage on "multiplication" many times, over a course of days. (I didn't have a teacher who cared to explain this stuff to me, even if they understood.) I finally had to discard most of his explanation and sit down at the keyboard and analyze the musical examples he gives. When it finally sank in what he meant by "multiplication" I picked up the book and threw it against the wall-triumphant and disgusted. Then I went and composed several pieces using multiplication.

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