Paradoxes
Michael Wittgraf
About this work:
Paradoxes
Three Songs for Soprano, Flute, and Percussion
by Michael Wittgraf
2006
Program Notes
Paradoxes is a three-song cycle composed in 2006 for Trio Lorca. The texts, by
the composer, are stylized adaptations of three well-known mathematical paradoxes,
written in the first person to add a personal quality to a potentially dry subject. The first
song, Zeno of Elea, is an adaptation of Zeno’s dichotomy paradox, which asserts the non-
existence of motion. The second, Thompson’s Lamp, refers to the paradox of the same
name. The third song, Complement, tells a story of space travel where speed doubles at
an increasing rate, and is a complement to the paradox in the first song. The texts of each
song, as well as musical descriptions, appear below.
The primary musical element that informs each song comes from the extensive
list of musical modulation examples in Max Reger’s On the Theory of Modulation. In
particular, it is the modulation from C major to B-sharp major. Musicians recognize the
paradox here because B-sharp major and C-major are enharmonically equivalent keys,
making them indistinguishable from each other to the ear when played on a keyboard
instrument. Modulation is generally agreed upon to mean a change of key.
Zeno of Elea
I wish to run from here to there (point A to point B; from here to there).
However, in order to accomplish that, I first must reach the point midway between here
and there (midway between point A and B, perhaps a place I call “point C”). Following
that, I must reach first the point midway between point C and the end (midway between C
and B, C and B, perhaps “point D”). In fact, after continuing in this manner for some
time (midway, midway, midway, midway, midway), it will become clear that I must pass
an infinite (infinite! infinite!) number of midpoints in order to achieve my goal, a task
that is certainly impossible. I tire merely thinking of the prospect. Merely thinking.
Thinking. I think that I will not even try.
The music in Zeno of Elea exploits musical patterns that approximate the
mathematics of the paradox, including rhythmic patterns that double an halve their
speeds, and intervallic patterns that double and halve in size. The augmented triad
saturates much of the song due to the fact that pitch patterns whose semitone intervals
grow from 1 to 2 to 4 to 8 and so on degenerate into a repeated pattern of two notes.
Those two notes combined with the last note before the degeneration form an augmented
triad. At other times important pitches serve as centers around which the music revolves
and converges. The Reger modulation appears over the long term here.
Thompson’s Lamp
I have a magic lamp! I have a magic lamp! I have a magic lamp! No, it is not,
nor does it remotely resemble Aladdin’s famous wish-granting genie-containing lamp.
Rather, it is James F. Thomson’s famous (or no-so-famous) electric lamp. With a simple
flick of the switch, I can turn it on. No, that is not the magic part. In thirty seconds, it
switches itself off. No, that is not the magic part, either. In fifteen more seconds, which
is half of thirty, of course, it switches itself back on. Still not magic. In half of fifteen
seconds past that, seven-and-one-half, I believe, it switches itself off again. The lamp
continues in this manner for one minute. On. Off. On. Off. On. Off. On. Off. Magic!
Tell me, is the light on or off after that time? On? Off? Can you tell me why I was so
excited about a magic lamp that in no way resembles Aladdin’s?
Thompson’s Lamp comprises three parts: a central section surrounded by related
outer sections. The central section is the primary element, and features a rhythmic
pattern that repeats, sometimes exactly and sometimes varied, over and over. Constant
repetition serves to imitate the repetitive motion of turning a lamp on and off an infinite
number of times, as suggested in the text. The Reger modulation is embedded into the
repeated pattern as it progresses.
Complement
Once upon a time, I was in a spaceship traveling through outer space, with no
destination in mind. Space travel, in fact, is so fantastic that one needs no destination in
mind. The journey itself is the thing that matters. Never mind whose spaceship it was,
nor how I came to board her in the first place. I will say, however, that it was glorious. I
shall describe the voyage. After 30 minutes of flight the ship doubled its speed, which
was already wondrously fast. 15 minutes later it doubled speed again, and again after
seven and one half minutes more (double, double, double, double, double, double,
double). I was exhausted after only one hour, because the voyage already had been quite
distant. My head was spinning. The stars flew by in a blur. I wonder how far I had gone
in that fantastic hour?
Complement returns to the motivic material of the first song, but in a much
different context. Formally, the music accelerates to frantic speeds several times,
mimicking the ship in the paradox. At the end, the narrator asks a question, which is set
in hymn-like fashion to the Reger progression.
Year composed: 2006
Duration: 00:11:00
Ensemble type: Voice, Solo or With Chamber or Jazz Ensemble:Voice with Chamber/Jazz Ensemble, 2-5 Players
Instrumentation: 1 Flute, 1 Percussion (General), 1 Soprano
Instrumentation notes: percussion includes extensive marimba writing