The semester is over, and so is my 12-tone analysis class, which made me work harder than any class I've ever taught. I added about 18 works to my analytical repertoire, including behemoths like Mantra, Sinfonia, Le Marteau, and Threni. Even having analyzed most of the music over the summer, I still spent most weekends checking rows and poring over dense JSTOR articles. And aside from me having wanted to learn all that stuff anyway, it was a continually rewarding class. I especially enjoyed showing the row matrix from Ben Johnston's String Quartet No. 6, with a row consisting of six harmonics of D- plus six undertones of D#, comprising, if I counted right, 61 different pitches in his Just-Intonation notation:

That 11th pitch in the third row, by the way, is called F-double-sharp-down-arrow-upside-down-seven- plus. It's the 77th subharmonic of the perfect fifth above D#. But you knew that.

Babbitt was really fun to teach (which explains, I guess, why so many theory professors teach him). I demonstrated how there are 16 ways to make a rhythmic pattern within a half-note using only eighth-notes, and then showed how Babbitt assembled those 16 possibilities into a rhythmic row that covers the first eight measures of his jazz band piece All Set and then reappears elsewhere in the work, now augmented, now in the percussion - and I heard a voice major, who'd had no prior interest in 12-tone music and was only taking the class to get a theory credit, whisper under her breath, "That's incredible!" She ended up doing a final paper on Babbitt's Du, which I took as one of those rare personal triumphs a professor gets only every few years. Still, overall the students remained a little dubious about the whole 12-tone thing, which is good - interested, curious, but only intermittently convinced. The last day I played, following the scores, some pieces I love without analyzing them, including Maderna's Aura, Zimmermann's Monologe, Ligeti's Monument-Selbstportrait-Bewegung, and Xenakis's Mists, to show them where 12-tone music had led in Europe. The most recent work I played was Mikel Rouse's Quick Thrust (1983) for rock quartet which uses only one form of the row amid elegantly serialized rhythms. In playing Le Marteau I noted that my birth was historically closer to Rhapsody in Blue than the students' was to Le Marteau. The 12-tone era is now just another historical period, to which we could bring a historical perspective, and I taught it that way. The music was too old and too ensconced to engender the slightest controversy, and too distant to embody any mandate for the present. It is what it was, only now immune to partisanship in either direction.

The biggest problem was finding good examples of 12-tone analysis to serve as models. Most of the books and articles are written as though to exclude outsiders from a secret club. If you don't already understand, you can't read them. Especially irritating are the digressions into meta-analytical issues, meant to create some kind of general 12-tone theory rather than to address the piece at hand. For instance, is it ever necessary to launch into a discussion of first-, second-, third-, and fourth-order combinatoriality? Sure it determines what rows are available to combine polyphonically, but who gives a shit? The best article I found by far was Richard Toop's analysis of Mantra in his "Lectures on Stockhausen" - perhaps because they were lectures rather than articles, he was the only writer who seemed to really care that his readers got drawn into the analysis, and truly understood. As I've said before, I used the Osgood-Smith book on Sinfonia, which was thorough if indifferently lucid, and Wayne Wentzel's "Dynamic and Attack Associations in Boulez's Le marteau" (Perspectives) went a long way toward clarifying Lev Koblyakov's impenetrable Boulez book, possibly the worst-written music book in history. I regretted throwing in the towel on Sessions's Third Sonata, but I asked George Tsontakis, a Sessions protege, and he said, "Oh, don't analyze that piece, it's like two pieces happening at once"; and the published analyses were little help.

Most of all, the class meant to me - and this conditioned what it meant to them - a chance to go back through a repertoire that had seemed numinous when I was a teenager. That's the music I loved before minimalism came along and seduced me away, seeming fresher and more full of possibility. I remember clearly what it sounded like in 1971, and I needed to find out how I'd react to it now. I was bringing up demons from my youth to exorcise, and I hope I didn't often sound like Captain Ahab chasing his personal white whale. But I was told that some appreciated learning that repertoire from someone who didn't insist that they pledge allegiance to it. Now that I've gone through all that analysis and kept records of it, I may well teach it again someday.

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COOMENTS:

Rodney Lister says: I had a similar situation teaching a course on post-tonal analytic techniques, which was an enormous amount of work and from which I learned a lot. Not being as systematic or as thorough as you are, I covered less ground. Although the purpose of the course was somewhat different-thinking about analytic techniques-what the toolbox was and which of the tools were best in approaching which music. I wanted to include thinking about Britten as well as Babbitt. For some reason the piece (music)that seemed to meet with the most resistance was Lutoslawsi (Parole Tisees). Anyway, I'm sure you know Words About Music by Babbitt, which seems to me to be the clearest and most convincing discussion about why one might want to write twelve-tone music and what it might do for you. I get lost with partitions (which I suppose I shouldn't admit), but I like the rest of it.

KG replies: Words About Music is indeed an oasis of plain-talking about 12-tone issues. I should have looked through it to see whether any excerpts could have applied for my class, but didn't think of it, and I don't recall him mentioning All Set. I relied heavily on the Andrew Meade book, which is a godsend but you really have to plow through most of it to get all the benefit. I found it difficult to excerpt for students working on individual pieces, because (and also true with Joseph Straus's late Stravinsky book) the concepts are all cumulative. So it was easier to absorb them myself and feed students the ones they needed for the individual pieces. I should add that the Babbitt piece I used to always use was Post-Partitions, which they always hated. I had much better success analyzing All Set and playing them Philomel - though I also have to say that the ones with good ears picked up how miserably inaccurate the Nonesuch recording of All Set is.

Dylan Mattingly says: 'Twas a great class, Kyle. My strong desire for just the type of mathematical problem solving which goes into creating and using and altering a row was greatly appeased, and I now feel that I could talk for a long and excited time about many of these pieces, without feeling any necessity to like them. That said, "All Set", and Tenney's "Chromatic Canon" and of course "Sinfonia" will remain in my itunes playlist until further notice. Moreover, on the topic of the Ben Johnston 6th SQ, this is just about the richest set of codebreaking material I've ever encountered, they should have used this piece in WWII to communicate military secrets. Not to give too much away (before you read my paper), but when you graph the rhythmic modulations as a function (after converting them to ratios, with which they make a simple just scale with 9 notes to the octave), you can take the derivative and get a perfect parabola towards the exact center of the piece (a complete palindrome). Cool stuff, thanks for the fun times and the analytical tools, I wouldn't want to be taught 12tone by anyone else!

Eric Bruskin says: Kyle,
I have to agree with your student, and I didn't even take the course. As a veteran of teachers, books and articles, I can confidently say that I wouldn't want to be taught this stuff by anybody else. Between your scholarship and your attitude is a very sweet spot.
The great physicist Enrico Fermi published his Notes on Quantum Mechanics - simply images of his raw lecture notes. People who already know some of the basics can enjoy watching a teacher teach himself and others. (Check it out on Amazon.) Is there any chance you could offer us a peek at yours?
- Eric
KG replies: Thanks very much, Eric. But I almost never use lecture notes. I just walk into class with a score and start talking.

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