Ludus Supertonalis is a structured improvisation, inspired by (but much smaller in scale than) La Monte Young's The Well-Tuned Piano. All of the material stems from the overtone series of a single low F on the piano, except for the bass notes, which slowly proceed through all 12 chromatic pitches in a fixed order. The changing bass notes continually reframe the otherwise static harmonic content, drawing both performer and listener towards different sets of pitches at different times. The tone row in the bass begins on a low F, the fundamental of the overtone series, and subsequent pitches provide a departure from this home base. The final note of the bass row is C, the dominant to F and the pitch most closely related to F in the overtone series. Now the higher notes suggest C minor rather than F major; we have almost returned home, but not quite. The title, makeshift Latin for "play of overtones," is more than a passing nod at Paul Hindemith's Ludus Tonalis, as the central idea of Ludus Supertonalis is unintentionally quite similar to Hindemith's conception of chromatic tonality as related to the overtone series.
Ludus Supertonalis may be performed on a regular equal-tempered keyboard, or on a piano or synthesizer that has been retuned in just intonation. The notes of the keyboard should all be tuned to harmonics of F:
| pitch | overtone | deviation* |
| F | 1 | 0 |
| F# | 17 | +5 |
| G | 9 | +3.9 |
| Ab | 19 | -2.5 |
| A | 5 | -13.7 |
| Bb | 21 | -39.2 |
| B | 11 | -48.7 |
| C | 3 | +2 |
| C# | 25 or 13** | -27.4 or +40.5 |
| D | 13** or 27 | -59.5 or +5.9 |
| Eb | 7 | -31.2 |
| E | 15 | -11.7 |
* Deviation is measured in cents with respect to 12-tone equal-tempered tuning
** One of C# or D should be tuned to the 13th harmonic.
Alternately, if you are performing Ben Johnston's Suite for Microtonal Piano, you may use the same tuning to perform Ludus Supertonalis, transposed down a perfect fourth or up a perfect fifth, so that you use the overtone series of C. The idea of duplicating the alternate tuning of an existing piece sprung from an earlier (but as of yet unrealized) idea, to write music for prepared piano, using the same preparations as some other well-known piece, such as John Cage's Sonatas and Interludes. Retuning a piano, like preparing one, is a difficult and time-consuming enterprise, so piggybacking on the alterations involved in an another work offers many practical advantages.
If you listened to the recording, you might be tempted to say that in naming this piece Song and Dance: Panic and Repose, I got the subtitle backwards. After all, the "Song" is calm and relaxed for the most part, while the "Dance" is nervous and agitated. That's because the subtitle refers not to the mood of the music, but rather to the mood of the composer.
In the spring of 2004, during my second semester at Tufts, I was working on a piano sonatina, to be played at a concert in April. I made a promising start, but as the concert got nearer, my progress slowed down. In fact, when I had my weekly composition with my professor, John McDonald, about two weeks before the concert, I had not written a single note since the previous meeting, and wasn't even close to finishing one movement of the sonatina. I had two weeks to somehow triple or quadruple my output from the previous month. Less than two weeks, really, since I'd need to give the pianist a chance to rehearse everything. I considered cancelling my lesson since I didn't have anything to show for my efforts, but in the end I decided to go and tell my professor about my predicament.
John's response was quite refreshing. "Forget about the sonatina," he said. "Put it away. If it's in you, you'll go back to it and finish it another time." Well, that's nice to hear, but what about the upcoming concert? "You don't have to have anything for the concert, although I agree it would be nice if you did. Why don't you try writing something that you can play on the piano yourself, so you don't have to worry about giving a performer enough time to practice?" In two weeks? I couldn't write a single note all last week! "Well, let's see. Maybe I can help you get started."
John took a blank sheet of staff paper, and wrote down a few notes. One chord at the beginning of the top system, two chords near the middle of the page, and one more chord close to the bottom. He then urged me to fill in the rest of the page myself, starting right then. I had never had to compose written music on the spot -- though I have done a lot of improvisation, in many different contexts -- and although I was sitting at a piano, I decided to compose without touching the keyboard. By the end of the lesson, I had filled about a third of the page, and only then did I play back what I had written. It sounded pretty good.
Encouraged by this start, I went to a practice room to keep writing. By the time I went to the NME rehearsal later that afternoon, I had filled almost the whole page, and though my notation was rough and incomplete, I had a good enough idea of the piece in my head that I could play it all the way through. It was a complete movement -- not as long as the planned sonatina, but enough to stand on its own. In a few hours, I may not have quadrupled my output from the previous month, but I'm pretty sure I exceeded it. A heavy weight had been lifted my shoulders. I was so relieved that, in the next weekend, I composed a companion movement, using a theme I had jotted down in the laundromat a few weeks earlier, but had ignored in favor of the now-forgotten sonatina. This second movement was fast and rhythmic, a bit off-kilter but definitely dancelike. I decided that the first movement, being slow and freely moving, was therefore a song, obviously lacking words, and perhaps less tuneful than Mendelssohn's Lieder ohne Worte, but a song nonetheless. The song was written while I was stressing out over not having anything for the upcoming concert, while the dance was written precisely because I was no longer worried. So there it is: song and dance. Panic and repose. It makes perfect sense when you look at it from my perspective, though of course I also relish the apparent chiasmus of the title.
Trinkle Dance arose out of an assignment from a composition class with Anthony Kelley. The assignment was to write a dance, in giving the instructions for the assignment, Anthony said something a long the lines of
If you want to use an existing dance rhythm, that's fine, or if you come up with your own dance rhythm, and call it a "trinkle" dance, that's okay too.
I came up with my own dance rhythms, and, in search of a name, took my professor's advice and dubbed it a "trinkle." One of my classmates, Ben Crawford, turned around and paid tribute to my new dance style with his composition for the same assignment, Dance in Arch Form, With Homage on B-A-C-H, and a Bad-Ass Trinkle B Section. At least, I think that's the title of it. And then I incorporated a trinkle into another composition, Ude, Ude O. So the "trinkle" is not merely a one-off production, but an established form. Take that!
So, what is a "trinkle" dance? Well, it's built on top of a motoric ostinato in 6/8 or 12/8 time. It's got lots of cross-rhythms against the time, and periodic interruptions. With these characteristics in mind, I was able to go back in time and retcon some trinkles into the established literature, going at least as far back as the "Witches' Trinkle Dance" from the final movement of Symphony Fantastique. Who knew Berlioz was that hip? Anyway, back to Earth-616.
After writing two trinkles in a period of six months or so, I thought I was going to make the trinkle one of my trademarks, but that never really seemed to happen. I had a couple of sketches for trinkle ground rhythms, but nothing that coalesced into a longer piece. With my recent interest in metametrics, though, the cross-rhythms of the trinkle seem like a nice starting point for further rhythmic explorations. Maybe it's time to revisit the idea?
I did subsequently reuse the original Trinkle Dance as the last movement of my Bass Trombone Sonata, merely adding an introduction for a better segue from the second movement. This is the version heard in the recording above; the original version starts right when the piano begins to repeat the basic pattern in the left hand. I have to admit that Trinkle Dance is rather hard on the pianist, as the left hand never gets a break, but the relentless pattern in the bass is one of the essential features of the trinkle. My getting slightly lost in the trio section is not one of the essential features.
By my own reckoning, Midnight Blue is one of the most successful pieces I have composed. I feel like I achieved everything I set out to accomplish in the piece, in terms of both form and expression. Audience response to Midnight Blue has been enthusiastic, and it is also the piece that earned me my first groupie. And isn't that why anyone goes into music in the first place?
The many splendors of Midnight Blue are the end result of an experiment which took a year and a half to carry out. It began in the spring of 2002, during my studies at Duke with Anthony Kelley. We had examined some compositions which employed additive structures -- forms in which new material is progressively added to a preexisting seed -- paying particular attention to "Call to Prayer" from In This House On This Morning by Wynton Marsalis, and to measures 7-30 of The Yellow Pages by Michael Torke. Although the additive structures in these two works are both clearly audible, they are developed in different ways. In "Call to Prayer," Marsalis starts with a very basic three-note riff, and elongates it, by adding extra notes at the end of the riff, and prepending a sequence of chords leading into the riff. In "The Yellow Pages," Torke starts out with a sparse melody in 16th-notes -- more rests than notes, initially -- and gradually fills in the gaps with more notes in an apparently haphazard fashion over successive repetitions of the two-bar cell. In both of these cases, it is easy to hear how the musical material evolves over time, and I decided I wanted to be a bit more subtle in my presentation of the structure.
The particular structure I chose to use, though clearly related to both Marsalis' and Torke's structures, was most directly inspired by a completely different sort of artist: comics artist, writer, and theorist Scout McCloud. Although he is an accomplished creator of mainstream comics, McCloud is perhaps best known for his works, both written and drawn, exploring the formal possibilities of online comics, employing what he refers to as the "infinite canvas". Though not particularly adventurous artistically, his variable-length strip Original Recipe Carl uses a clear additive structure for narrative purposes: beginning with a very basic two-panel comic, additional panels are inserted, one at a time, at various points in the middle of the strip, until we arrive at the 52-panel story of Carl's demise. While the story is hardly profound, I was intrigued at the way that the reader's perception of time can change through the many iterations of the strip. As more panels are added, impression of the passage of time, both globally -- from the first panel to the last -- and locally -- from one panel to the next -- are constantly revised, and both global and local markers have the potential to stretch or shrink -- or stay the same. In other words, the shape and proportions of the story, even the parts we are already familiar with from previous iterations, are always in flux. In contrast, the additive structures of Marsalis' and Torke's compositions both leave the shape of previous iterations intact; at any point in the evolution of either piece, you could take a highlighter to the score and reveal the seed, or any other preceding stage of the structure, in its original form.
At this point, you can probably guess the sort of musical structure I had in mind to reflect McCloud's narrative structure. I started with a simple musical idea, a 14-note melody that outlines the harmonies of the 12-bar blues form in the most skeletal way. I then inserted notes, a small handful at a time, in between existing notes, so that the skeletal line blossomed into a 35-note melody, now dancing around the blues changes. But unlike The Yellow Pages, where each iteration of the structure is limited to the same 2-bar timeframe, the boundaries of the melody grow with time. At the same time, the durations of individual notes in the melody are free to grow or shrink, to better fit the slowly swinging cadence of the blues.
It took me rather little time to work out how this melody would grow from 14 notes to 35, and even less time to work out chords supporting the melody in the piano. But successively elaborated repetitions of this melody would not be sufficient to carry the piece; I need something more. Look again to the blues tradition for inspiration, I decided that a call-and-response form would allow me to contrast different melodies, and different structures as well. I started sketching a melody for the most noble of instruments, the bass trombone. While the initial melody in the piano had a very narrow compass in both rhythm and register, the bass trombone would be largely free of such constraints. And while the piano's additive structure interpolated notes in every nook and cranny, the bass trombone would be much more straightforward: first two bars of its melody, then four, then eight, and so on. At this point, having written eight bars of melody for the bass trombone, I realized that these eight bars could easily be fit to the first eight bars of the blues form, so I added four more bars to fill out the form.
Now I had a full-blown melody for both the bass trombone and piano, and I was going to progressively build up to both melodies in alternation. But what should I do in between? The bass trombone melody was quite soulful, and could easily stand unaccompanied. But in comparison, the piano melody, even at its most complex stage, was rather weak; it couldn't stand up to the trombone on its own. So maybe I could use it as accompaniment, and write other material for the trombone on top of it. Now, just because I'm using the piano melody as accompaniment doesn't mean it's not important -- think of how a Gospel choir lays down a tune, with a soloist going to town on top. Without the tune, the soloist doesn't have anything to play off of. If I could get that kind of dynamic going in my piece, I'd really be happy.
So, I want to come up with something for the bass trombone to play on top of the piano, but at the same time I want it to be a part of the additive structures I've been building up. I notice that, as the bass trombone's unaccompanied melody goes on, it introduces new pitches not previously heard at key points. While this is not particularly striking on its own -- if you take a close look at this now long-winded description I've been writing, you'll find that each paragraph includes new words I haven't used previously -- it still seemed like something I could use. The bass trombone, when it plays on top of the piano, is at first limited to the very first note of its melody -- D -- and with each additional segment of the unaccompanied melody that it plays, the new pitches that are introduced can be used as well. Thus, the available pitches for the bass trombone to play on top of the piano keep growing: D, then A and C after two bars, B and F after four bars, G, G#, and F# after eight bars, and E and C# after the whole 12-bar melody has been stated in its entirety. And this also suggests an ending for the piece: a cadenza in which Bb and Eb, the two missing notes, finally become available to the trombone. I go nuts writing this cadenza, adding numerous flourishes to the basic 12-bar melody I had already sketched out. Then a cascade of all 12 chromatic pitches, tumbling across the full register of the trombone, and then borrowing the chords from the piano's initial statement-- wait. Chords? I can play some two-note chords on my horn, but the chords I want are fuller and more agile than I can manage with my multiphonic technique. Maybe this isn't a bass trombone piece after all. Maybe it's...*sigh*...a cello piece. Guess I'll have to write something else if I want to be the star.
But, yes. Cello. And piano. I've got the piano part all worked out. I've got the concept of the cello part all down, but the details need to be worked out. I'll start with the full twelve bars of the cello melody, unaccompanied, just to let everyone know where this is headed. This melody ends on D, the same note that it starts on, so I'll treat that as the first bar of the melody for structural purposes, and when the piano comes in with the skeletal form of its melody, the cello is limited to that D. I've allowed myself to use any octave, so it isn't too monotonous, but there's only so much I can do in this context with just Ds. The first stage of the structure is complete. Then the piano lays out again and I write the first 2 bars of the cello melody, with a little elaboration, but there's only so much elaboration I can put into two bars, especially as I want to stick to the pitches in the first two bars of the original melody, of which there are 3. Then the piano comes in, and with 3 notes to pick from, the cello can have a little more fun on top. That's stage two. Then four bars of cello solo, and we're up to five pitches. Piano comes in, cello plays with those five pitches, getting even more intricate.
At this point, I run into a wall. After three iterations of the various processes underlying the piece, and with only five available pitches in the cello part, I'm running up against the limits of what I can hear in my head and write down. Well, the cadenza I have planned for the end is even wilder than what I just wrote, but that's unaccompanied. Whatever I do with the cello part up to that part has to work with the piano part, which in turn is getting more active and more syncopated. It's taken me two or three weeks to get to this point, and it would take more than a year before I could go further. By now I've graduated from Duke, and am beginning my studies at Tufts with John McDonald. My unfinished sketch for this piece -- still unnamed -- was one of the things that got me into the M.A. program, so one of my first projects is to finish the darn thing. Somehow, I manage it. Maybe it's the impetus of having it performed that semester, maybe my mind's ear is sharper now, but some way or another, I pick up where I left off and see it through. I flesh out two more iterations of the process, each one wilder than before. As the pitch inventory of the cello grows, so do my options -- I can arpeggiate chords both "inside" and "outside" the piano harmonies, I can emphasize the blue notes, I can throw in trills and mordants and other classic figurations. And I go absolutely wild with my rhythms -- syncopations within syncopations, or hemiolas against a beat which is only implied in the piano. I want this music to swing and sing, and I go through a lot of effort to meticulously notate the desired rhythmic nuances, so the cello can swing even if the cellist can't. But I was lucky to have a great cellist, Emmanuel Feldman, premiering the piece, and he did a great job with it.
I wound up calling the piece Midnight Blue, for a few reasons. First, the title alludes to the blues form that I love so much, and which forms the backbone of the piece. It also describes the instrumental color of the piece; the combination of cello and the lower register of the piano (the piano never goes higher than the E above middle C, and spends most of its time and octave or two below that) is very dark and rich. And Midnight Blue, especially with the melodic outpourings of the cello, has an emotional urgency which, for some reason, I associate with the middle of the night. Like there's something on your mind keeping you awake at night, and it gets so heavy that you just have to get up, find the highest spot you can, whether it's a mountaintop or the roof of your apartment building, and just shout out loud. That's what Midnight Blue is to me.
Midnight Blue is not a perfect piece. It's got things I'm not entirely happy with. A few days before the premiere, I realized that I broke one of the rules of my additive structure -- that the cello would always be limited to the pitches from the last segment of its melody -- in two or three places, using notes that hadn't been properly introduced yet. If I had caught those "mistakes" while writing the piece, I would have written something else, but it was too late to change anything for the premiere, and, frankly, I couldn't come up with anything that sounded as good using the "right" notes. Even more troubling is the way I go to town with the cello part -- for all that I am suspicious of showy displays of virtuosity, Midnight Blue is the showiest piece I have ever written. Maybe that's part of why it has gone over so well with audiences. But even if it doesn't fully align with my own musical standards, it's still a fine piece, and I'm proud to have my name on it.
Early in 2006, Rachel Tanenhaus made an online journal post titled, "A Very Wibbly News Flash". That post was brief, but emphatic:
CUTE PEOPLE ARE CUTE
WIBBLE WIBBLE WIBBLE
KTHXBYE
When I first read this post, a commenter had noted that it was almost a haiku, and had edited it to produce the desired syllable count and nature reference. I, however, preferred the original post to those edited versions. For one thing, utterances in English tend to have fewer syllables than in Japanese, so 17 syllables in English is actually quite verbose, compared to a classical Japanese haiku. For another thing, any attempt to wedge a "spring brook" or the like into Rachel's carefully worded message would only dull its effect. "WIBBLE WIBBLE WIBBLE" is a potent distillation of joy and eagerness, while perhaps nothing expresses the urgency of the moment better than "KTHXBYE".
So, adding a couple of extra words to Rachel's post ruins the whole thing, but stretching out those 14 syllables into a two-and-a-half-minute song? That's brilliant. Or silly. I forget which. This was in fact my first successful foray into composing for voice. Once upon a time, I was as besotted with Eliot's "The Love Song of J. Alfred Prufrock" and Poe's "The Bells" as any sullen, pretentious teenager, but my efforts at setting those poems were thwarted by my then-inept compositional hand, and their prodigious length. "Prufrock" goes on for, what, three pages? Way too long for me. A not-quite-haiku is much more suited to my attention span. I have since set a few longer poems, but nothing longer than a sonnet at this point. Many thanks go to Rachel, who graciously gave me permission to set her post to music, even though she might not have known I was serious at the time. A Very Wibbly News Flash also exists in a version for voice and string quartet.
Recombinant is a little musical Frankenstein's monster. To compose this piece, I took a handful of blues "heads", threw them against the wall, and then glued the pieces back together. Or rather, I let fragments of those heads float around in my brain, bumping into one another and sticking together to form a not necessarily cohesive whole. As a result, the piece fluctuates wildly between extremes, from percussive to lyrical, from driving syncopation to free-floating syncopation. There's a lot of syncopation, actually. But it's simple, really; you start with a basic 7/8 pulse, then you lose a 16th note in the middle of the measure and gain it back at the end. Or did you mean measure 56?
Metrical irregularities aside, I was not wholly haphazard in my construction of Recombinant from spare parts. Despite jumping from one thematic idea to another, I maintained the general harmonic outline for the blues throughout the piece. The finer details of the harmonic progression, however, are much more fluid: I might stretch a single chord out of proportion, gloss over the motion between two or three chords, or repeat a two-chord progression simply because I had two different ways of working out the progression, and didn't want to decide between them. Nevertheless, the piece can be audibly divided into four choruses, according to the overall harmonic structure.
Although Recombinant is never lacking in energy, I do try to continually ramp up the intensity over the course of the four choruses, adding in textural, timbral, and registral constrast as the piece goes on. By the time the fourth chorus rolls around, the music is nearly spilling over with exuberance, and very nearly runs aground at the climax. Instead, the cello intervenes with a few low notes, and the trio safely winds down to a halt. Recombinant was originally composed for the Triple Helix piano trio, and the title, borrowed from genetics, alludes to both the method of composition and the origin of the group's name. After a reading by Triple Helix, I decided that portions of the piece needed to be reorchestrated. Nearly all of my own performing experience has been in wind ensembles and bands, so the combination of multiple string instruments is less familiar to my inner ear. Nevertheless, I feel that I succeeded at my primary goal in writing Recombinant, which was to make the violin and cello an equal partner to the piano in terms of percussive force.
According to John is my take on a Gospel piano ballad. I originally composed it for the able fingers of John McDonald, my mentor at Tufts University, and so you have Gospel, according to John. Try not to read any deep symbolism into this, for I assure you there is none.
Although this piece is firmly rooted in the jazz and Gospel traditions, its genesis was due to an entirely different tradition. I was sitting in a practice room at Tufts, pausing between exploratory improvisations, when I heard the pianist in the next room practicing something. It sounded like Chopin; maybe it was a waltz or a mazurka. I didn't recognize the piece, but I definitely recall that the opening notes were B#-C#-G#, and then the chords picked up in F# minor. This progression struck me much more than the piece itself, partly because the unseen pianist kept repeating the first few measures, over and over. Annoyed at hearing the same melody leading into the same chords over and over without closure, I decided to vent my frustrations by borrowing that same melodic figure, and taking it in a new direction. Right away my fingers picked out some juicy chords, outlining a basic ii-V-I progression in A major, but with added notes and substitutions and a subversion of the first cadence which, come to think of it, might have suited Chopin just fine.
Really, this music is all about the harmonies, not necessarily for their progressions, but for their sounds. Taking a nice, tall chord and adding in a couple of extra notes that might not even belong in the key. Letting the boundaries between harmonies blur, building up a sensuous wash of sound. Landing on a chord that sounds so good, I just have to stop time and slowly pick it apart. Don't get me wrong -- there's melody and rhythm too, and they're important. The melody shapes the harmonies, tells them where to go, and the rhythm makes both melody and harmony breathe, come alive. Add a pianist who can bring all this together, and you get According to John. Not a bad place for a decontextualized snippet from the practice room to end up.
The Four Little Preludes are among my earliest works; in fact, the first prelude, composed around 1999, is probably the oldest piece I still consider fit for public consumption. If nothing else, the Preludes are a reflection of my love of jazz, especially jazz harmony. I learned more about harmony from playing piano in a high school jazz band for three years than I did from all my semesters of college music theory. Of course, I'm still learning, with every piece I write. Years ago, not long after I finished the Preludes, I recorded them for my then-current portfolio. I stuck a couple of mics behind my dad's ancient Steinway upright, which for years spoiled me with its hazy tone (I swear it's not that tinny in real life) and soft action, and banged out my renditions. Since then, I've gotten better recordings of a better performance with a better pianist on a better piano, but when I encountered these gems on the hard drive of my digital recorder, I knew I had to share them with you. Enjoy!