Panharmonicon

… but on a smaller scale… this time recounting compositional thinking over the past two weeks.

The series of parabolic arcs seemed less and less promising as a central organizing structure, because it threatened to be too symmetrical, and thus too predictable in the second half of the piece. So, upon returning to arbitrary shuffling of various textural combinations, I found myself drifting toward a modified (as in, simpler) version of the enneagram form I used to structure my orchestral work In search of the miraculous (2002). The same principle of a circular path is applied, but now with only six focal events instead of nine… and given the smaller performing forces, I’ll almost certainly need to devise less literal, more abstract interpretations of the cross-fading from one focus to another.

Funny thing is, once I settled on that exceedingly symmetrical structure, I realized that it could be fun to superimpose the asymmetrical series of parabolic arcs. To be more specific: with the circular scheme governing the succession of musical textures, the parabolic arcs promise to provide a useful Urlinie. As of this writing, I’m wondering whether to multiply this idea, such that each arc comprises not merely a single (chromatically ascending and then descending) line, but rather a set of four such lines, that begin as a convergent pitch (point of impact) and “bounce” upward, diverging to arrive at a four-note chord that “floats” at the top of the arc (i.e., that accrues the longest durations).

I find the notion highly attractive, but it could be problematic in terms of sheer speed of work… that is, it means generating four times as many columns of numbers in a spreadsheet, which I’ll then need to convert to a more friendly format on music manuscript paper. Perhaps worth the time investment… I suppose I’ll just have to make a test set, to determine whether this particular investment of time pays sufficient voice-leading dividends to propel the piece forward, even through its more sparse, fragmented, fragile expanses.

It’s as though a selection were teed up, ready for some other stimulus to swing away…

A few days ago, I was checking a transcription of Luis Bonfá’s “Manha de Carnaval,” from the Black Orpheus soundtrack, for a friend. (It turns out that he was really just asking me to check the Portuguese text underlay… but a few months ago, harmonic discrepancies among different printed versions had come to light, so I misread his request as checking the harmonies. That’s a whole ’nother brain-research topic, though.)

I listened to the song several times in rapid succession. Did the tune stick in my head? No.

Now comes the punchline: Last night, while washing a sinkful of dishes, I was listening to Stockhausen’s Mantra. About twenty minutes in, there’s a recurring motive of an ascending minor sixth, just as at the start of “Manha” (for the record, it’s a half-step higher: F to Db, rather than E to C). Stockhausen keeps bringing it back, and it reminded me of the Bonfá… but didn’t immediately trigger a worm.

So this morning, I awaken… and from the moment my eyes opened, the Bonfá has been on perpetual loop.

Earlier this week, an inquiry on the Theremin World website sparked a flurry of responses from me. Afterward, it dawned on me that my crazed natterings might be of interest to the hypothetical student whom I imagine as my blog-audience… especially if said student has ever worried about not having Absolute Pitch.

(That’s right: I’m taking my own writings on the Internet, and lifting them wholesale. It’s OK, though… none of this material is taken from the Associated Press!)

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6/21/2008 5:47:20 PM

About absolute pitch: No, of course you don’t strictly need it, any more than singers need it. Absolute pitch is only an advantage, insofar as it keeps you from drifting off-pitch while you play.

I should point out right away that I also do not have AP; rather, I have good relative pitch. BUT, I have found that there are pieces–especially highly chromatic ones–which I can sing from start to finish and stay on pitch, but tend to drift a bit when playing on the theremin.

What’s going on here? Well, there are two forms of memory involved: cerebral (remembering pitches with your “ear”), and muscular (remembering what the vocal folds are supposed to do, or where the hand is supposed to go in space).

It is much, MUCH easier for the muscles that control the vocal folds to remember where they were a few seconds ago, than it is for the muscles of the hand and arm to remember exactly where they were a few seconds ago. So, theremin players are constantly making small corrections.

If you have AP, then you’re always making the proper correction. If you don’t, then small errors of intonation can gradually accumulate, until you’ve wandered up or down a semitone from where you started.

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6/21/2008 7:15:38 PM

[following a couple of posts about improvisation with the theremin]

And, oh yes, about AP:

When I was [a teenager], I was sure that I don’t have AP, and that I never would.

However, when I was in graduate school, I discovered that I can get closer than I thought. That is, if you listen to the same piece of music day after day (preferably, day after day after day after day after day), it will begin to burn into your mind at that exact pitch level, and you’ll be able to recall it.

(I think it’s Daniel J. Levitin, author of This is your brain on music, who led research that found that people in the general population, with no formal training in music whatsoever, can recall familiar pop songs with astonishing accuracy of pitch level and tempo.)

I believe (but can’t prove) that this is a matter of short-term vs. long-term memory… and most importantly, that it’s not a cut-and-dried, black-and-white, either/or situation. Rather, there’s a continuum (shortest term, short term, long term, longer term…) of abilities. At the godlike upper extreme are the folk whom you can awaken in the middle of the night, ask for an F#, and get one dead-on. At the bottom end are people who can’t stay on pitch from beginning to end of a phrase. Most of us fall somewhere in between… and yes, you can improve with time and practice.

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6/22/2008 9:15:46 AM

[in response to a post about the amazin, mad-skillz thereminist Pamelia Kurstin—a self-confessed non-possessor of AP—and a clip of her performing the Pachelbel Canon in D, which she performs at the proper pitch]

About Pamelia and the Pachelbel: Again, I strongly recommend thinking in terms of a continuum, rather than either/or.

Obviously, Pamelia had been working on the piece, and probably practiced it by using a reference “D” to start. So, I wouldn’t be surprised if she could start it dead-on, even without a reference pitch before that particular performance… especially if her frame of reference were already “set.” (For example, if I’ve been playing guitar or piano for an hour or more before theremin practice… or listening to music for which I know the key… then I can often find any given note, in a way that I can’t if you just stop me on the street, or wake me up in the middle of the night.)

Mind you, it’s Sunday morning, I haven’t had breakfast yet, I’m not fully awake. Upon reading your post, I tried to find a “D,” and then checked myself with a pitch pipe. I was about a quarter-tone sharp (maybe 3/4-tone). Does this mean I have AP?

(Ideally, I would’ve been a full semitone flat… and then I could’ve congratulated myself on an historically appropriate lower pitch… oh, well… maybe next time.)

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6/22/2008 9:40:52 AM

[in response to someone jokingly calling my sense of pitch “absolute not-yet-perfect”

Nearly-perfect… or nearing perfect…

Incidentally, I had always believed that Pamelia does have AP, so I’m highly encouraged to learn that she doesn’t (at least, not in the ultimate, disabling sense that she writes about in her blog entry).

What she does have is astonishing intonational accuracy, to kill for. Speaking of Baroque music, she’s done a marvelous recording of Dido’s lament (“When I am laid in earth,” from Henry Purcell’s Dido and Aeneas. (You can hear it on her mySpace page; it’s the item labeled simply as “Purcell”.) The only flaw is that the piece incorporates (on paper) a literal repetition of the vocal line for each half… but in Purcell’s day, no one would’ve dreamed of literally repeating the vocal line. Instead, one would’ve taken the repetition as an opportunity to show off one’s ability to improvise ornaments, runs, mordents, suspensions, etc.

Yes, I feel churlish for pointing this out… but I would argue that this performance-practice shortcoming is far outweighed by the fact that she recorded all five string parts with a theremin… and her intonation is so phenomenally precise that I was 3/4 of the way through listening for the first time before it hit me that l’orchestre, c’est elle.

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6/22/2008 1:19:15 PM

Okay, some more unscientifically collected information (“anecdata”?), and then I should do useful things:

As noted above, when I tried to recall a piece of music that I haven’t heard or played in months, if not a year or two, I was off by a quarter-tone (or slightly more).

However, just now, I tested myself with two pieces that I have been working with in the past week: the Queen of the Night’s “Der Hölle Rache” (from Mozart’s The magic flute, and “Isolde’s transfiguration” (from Wagner’s Tristan and Isolde). Recalling the former’s altissimo arpeggios in F major, I was able to find an F exactly! Likewise, recalling the latter’s opening fourth, I was able to find Eb and Ab exactly. (At first, I thought I was way off, because I was thinking that it starts with F# to B natural… then I remembered the correct starting pitches, and realized that my aural memory was dead-on.)

Lastly: I first realized that I could retain pitches from day to day when I was taking voice lessons about 15 years ago. One of the selections became my standby for finding B to C (Tom Rakewell’s recitative “Here I stand,” from Stravinsky’s opera The rake’s progress.) Even five years after those lessons, my memory was still reliable for this. After the Mozart and the Wagner, I decided to stretch by finding Tom’s opening notes… but I was off by several semitones.

The moral of the story: My memory for pitch is most reliable over a span of hours, or days. Months and years, not so much.

P.S. Just to clarify the experimental conditions: I wasn’t practicing or listening to music between posts (au contraire, I was avoiding work by playing poker on FaceBook).

I’ve spent the past few days trying to figure out the overall form of the piece. The image in my head is of a slow bounce across the lunar surface, so I’ve been doodling various arrangements of parabolic arcs.

My musical intuition tells me that a proper, physically plausible trajectory would lead to dull stretches in the music. Instead, I’ve been toying with arcs that start low and flat, succeeded by increasingly higher and narrower ones, and then returning to the previous profile. The resulting patterns are scientifically implausiblem, and visually not as pleasing, but they seem more musically promising.

All of this is mentioned with great heaping grains of salt, because I don’t yet have a clear sense of what these parabolic arcs will govern (register? voice-leading? rhythmic accelerations and decelerations?). I hope to arrive at more crisply defined ideas by next week, so that I can move on to determining the gory musical details of various sections of the piece. Pragmatically, I need to get this piece out the door on or around August 1st.

At last: after another week haunted by those jumelles, the Legrand tune was finally displaced by “I know that my Redeemer liveth,” from Handel’s Messiah (one of my new theremin victims).

That’s now the reigning tune in the back of my mind, interrupted only briefly by a bit of Adam Ant’s “Goody Two Shoes” (which I haven’t heard in years), thanks solely to the lines:

We don’t follow fashion

That would be a joke

Don’t you know we’re going to set them, set them

So everyone can take note, take note

…which crossed my mind as an uncharacteristically danceable, albeit hyperbolic, summation of my attitude toward my artistic career.

One cliché of bossa nova arrangements that I’m morally obliged to exploit (through multiplication, recombination, and general mutation) is a legato descending chromatic line. In classic arrangements, it’s typically assigned to the strings, arco, but it can also be seen as part of a characteristic voice-leading maneuver (especially in Jobim’s work, as influenced by Chopin: see “Insensatez” and “Aguas de março,” to name just two prominent examples), irrespective of instrumentation.

Yesterday, I was having tremendous fun investigating isolated harmonies, and then finding ways to connect them. For some reason, the same project held no interest for me today, so instead I started looking into simple tenor chords that the clarinet, theremin, and ’cello might play, moving in simple parallel motion.

…oh, right, as if. This bored me, so I de-coupled the rhythms (keep in mind that the players will be scattered to the four corners of the stage; ergo, in this piece, precise synchronization will be a special case, rather than the norm), and the move to fourth-species (yes, I am powerless to resist the allure of dissonant suspensions) naturally led to an all-out polyrhythmic wedge, with seven descending lines, moving at different speeds (because they’re covering different distances).

In doing so, I stumbled upon something very cool (that is, narrowly “cool” in an unspeakably geeky, music-theoretic way), which I suppose someone with better numeric intuition would’ve seen coming:

1) To make sure that changes of pitch don’t coincide, I assigned each line a different prime number as its cardinality. Given the seven voices, I chose the series <5, 7, 11, 13, 17, 19, 23>.

2) To enrich the sound of the chords as the series proceeds, I chose to make a converging wedge: i.e., the chords start with larger intervals, and then gradually grow closer together, culminating in a chromatic cluster.

3) To avoid a sudden lurch at the end (with all seven voices moving together), each line counts from “1” rather than from “0” (so, f’rinstance, a line of 13 winds up covering precisely an octave, rather than a minor ninth).

Okay, here comes the cool part: If you use seven voices to make a chromatic cluster, it fills a tritone… and if you arrive at that tritone from the series above (where the lowest voice moves covers 5 pitches, the next-lowest covers 7, etc.), the first chord is no random assortment of pitches, but rather a complete hexatonic collection, in a clear, internally consistent voicing.

That is, the differences among <5, 7, 11, 13, 17, 19, 23> are < 2, 4, 2, 4, 2, 4 >… but because each voice begins 1 semitone from the next, this interval pattern becomes < 3, 5, 3, 5, 3, 5 >.

Or, if that’s too abstract for you: The goal cluster of {A2, Bb, B, C3, C#, D, Eb} represents the culmination of multiple chromatic descents from { C#3, E, A, C4, F, Ab, Db5 } (a.k.a. the hexatonic “East” collection from Rick Cohn’s hyper-hexatonic system).

Yes, that really did make my day… though it gets even better now, as I’m heading home to pack up gear for a free-improvisation gig in downtown Middlebury. I’ll be playing theremin and keyboard synthesizer, running both through nifty little delay/filter/feedback device, the JoMoX T-Resonator; the results ought to be anything but ordinary.

…or, more specifically, from abstract harmonic ideas to concrete implementations with the instruments at hand.

This afternoon, I found some beautiful high harmonies for theremin, marimba, and clarinet, with ample room for a ’cello melody below. If anything, the chords sound a bit too beautiful on the piano—that is, they’re shown off to tremendous advantage by the bell-like ringing of a piano’s high notes, especially when I exploit the damper pedal to hear all the notes together (they’re eight-note chords… not the most convenient to roll with finger-legato). I have half a mind to save them for a context with harp, vibraphone, and glockenspiel.

I’ll do a test run in Sibelius’s playback, though it might not help much, given the atrocious sound of marimba rolls assembled from non-roll samples. (Each chord comprises a four-note harmony rolled on the marimba, with the theremin alternating between two pitches above, and the clarinet alternating two pitches below… both at speeds slower than the marimba’s.) Perhaps a slow-motion approximation of the roll will provide a sufficient hint of what the chord would really sound like when I hear it for the first time in September.

The experiments below (“Yikes”) suggested that the phrase “a sort of low-gravity, slow-motion samba,” while poetically evocative, isn’tgoing to help me write the piece. More specifically, the bossa nova style is already a slow-motion samba (typically 72 beats per minute, as opposed to 120 for samba)… but I don’t want Dança to sound like just another Jobim song, so to the extent that I try to create a surface-of-the-moon bossa, the Verfremdung will come from fragmentation, rather than slowing it any further… or to the extent that even slower bossa patterns happen, they’ll represent brief flashes, rather than the spine unifying the entire piece.

[oops… was distracted… forgot to finish before posting]

So, creative energies are currently focused on adapting a standard bossa nova guitar chordal pattern to non-chordal instruments (e.g., clarinet)… and investigating pitch tableaux that could be articulated by this particular foursome (given that the marimba will be a model that stops at A2… so only the ’cello can cover the range [C2, Ab2]… or I should say, only the ’cello can cover that range precisely, as the theremin can certainly swoop through it. Perhaps as a sort of lion’s roar, to mirror/foreshadow/echo its turn as the cuíca electronica in another part of the piece?

As a natural step in trying to figure out what, exactly, “a sort of low-gravity, slow-motion samba” would sound like, I’ve started taking various canções and slowing them down… drastically… demais.

Or tried to, but suddenly Audacity has become tremendously finicky about which .wav files it deigns to read. Ergo, the only desecration so far has been Marisa Monte’s 1994 recording of Paulinho da Viola’s 1972 song “Dança da Solidão.” The results were positively grotesque, and, depending on whether the original pitch is preserved, either dully so (at pitch, it’s just slow, without any other redeeming transformations), or all too interestingly (when the pitch is dropped an octave, Monte becomes a psychedelic alien baritone). Better yet is the quarter-speed version in which pitch is dropped two octaves, wherein the guitar becomes a strangely percussive bass, Monte’s voice devolves into whale song, the percussion becomes dragging footsteps (or faltering industrial machinery?) and the bass clarinet licks become series of drones.

I doubt that I can use any of this, but it’s food for thought. In particular, the quarter-speed version lacks any detectable balanço… but its druggy dragging dirge could provide the foundation for some other future composition.

[Update: Oh, wow. Even more bizarre—and even more wrong for this piece—is the quarter-speed version in which all material occurs simultaneously two octaves below and two octaves above its original pitch. You would never guess that a human voice was ever involved in its making.]

I’m not a fan of Scott Adams; given my childhood career in the visual arts, I strongly prefer the work of cartoonists who can actually, you know, draw. (Also, I think the Dilbert strip jumped the shark when Adams left Pacific Bell.)

Nonetheless, he hit the nail on the head with this line, reportedly from his book The Dilbert principle:

“Creativity is allowing oneself to make mistakes. Art is knowing which ones to keep.”