Date Completed: May '12
Vafþrúðnismál is a poem from the Old Norse Poetic Edda, a collection of the most important extant stories of Norse mythology. It tells a weird little story about Oðinn (otherwise known as Odin or Wotan), the father of all gods, visiting a wise giant named Vafþrúðnir (Vafthrudnir) and challenging him to a battle of wits as depicted in this woodcut by Lorenz Frølich:
Apparently these sorts of battles were common—one person asks the other a series of questions (to which the questioner must know the answer) and the other must respond correctly in order, at least in this case, to keep their head. Oðinn goes to Vafþrúðnir's home disguised as a weary traveler named Gagnráðr and challenges him. Vafþrúðnir asks him several difficult questions about the origin of the universe which "Gagnraðr" answers correctly. Then it's Oðinn's turn to gain the knowledge he seeks. He asks the giant several questions about Ragnarøkkr (Ragnarok-the final destruction of the gods) that he doesn't actually know the answer to. Foolishly, the giant gives him the information in the heat of the battle, and is then destroyed when Oðinn asks him, "What spake Oðinn himself / in the ears of his son, Ere in the bale-fire he burned?" Of course, only the god knows this answer, and Vafþrúðnir has to concede defeat even as he realizes the identity of his opponent and discovers that he's given him forbidden information. Oðinn kills him and returns to Valhöll or Valhalla.
So, to summarize the summary: Oðinn is a dick.
(You can read what seems to be a decent translation of the whole poem here.)
This piece is a duet for scordatura violin (representing Oðinn or "Gagnraðr") and scordatura cello (representing Vafþrúðnir). After a loud introduction, the cello asks a four-note question and the violin answers with the remaining eight notes. The cello asks increasingly longer questions which leave ever smaller possible answers for the violin, until the cello asks an eleven-note question that has only one possible answer. Of course, the all-knowing violin provides this note with alacrity.
Then it's Oðinn's turn. The violin asks a similar set of questions, and initially the cello has no difficulty answering. But then the violin asks a question that uses all twelve notes and the cello can't do anything but sputter impotently. Vafþrúðnir explodes in a violent tirade in which he accidentally spills secrets about Ragnarøkkr, until the violin slices his head off with three sharp chords.
This piece was written specifically for a little mini-tour that, at the time of this writing in May 2012, is happening next week. Violinist Jeff Young invited me to be the guest artist in a series of three shows in Boston, New Haven and New York City called Beasts of Improvisation on Parade. Here's further info on the Boston show at Yes.Oui.Si, the New Haven show at InterCambio and the New York City show at Vaudeville Park. The piece was written specifically to use the same scordatura cello tuning as Fr.II.a-k, a recent unaccompanied piece that I'll also be playing in these shows.
I don't know if anyone's interested in this, but this piece was quite carefully built around set-class theory. The primary harmonic and melodic structure used throughout the piece is the set class (0167), which is a particularly symmetric set. The opening harmony (and open-string tuning of the cello) is an instance of this set, as is the first question asked by the cello. The violin's answer is the octachord complement to this set. The cello's second question is a hexachordal superset of (0167), namely (012678), and the violin's complementary answer is another member of the same set.
The third cello question is also the first indication that Vafþrúðnir isn't as clever as Oðinn. It uses the set class (01245689T), a nine-note set which does not have (0167) as a subset. Cleverly, the violin's answer begins with precisely the note needed to turn the last three notes of the cello question into an instance of (0167)—Oðinn is already turning the tables subliminally. Oh, and the three-note complementary answer to this question is a member of (048), the augmented triad set. This is important in relation to the third violin question discussed below. Then, the cello's final question uses only eleven notes, and the violin immediately responds with the twelfth.
I'm a little anal retentive, and so I wrote the questions in such a way that the first note of each of the four questions also form a member of (0167). The same is almost true of the last note of each question, but if you take the sneaky violin answer to the final question as the real last note, then it truly is a member of the same tetrachord. Sneaky, sneaky, dickish Oðinn.
The violin's question are in a very similar pattern. The first question is an (0167), the second question is a different hexachordal superset of that tetrachord, as is the cello's answer. Things shift in significant ways for the third violin question. Instead of a nine-note set as in the cello's question, Oðinn opts for an eight-note set—(0134679T)—which does have (0167) as a subset. The cello is forced to respond with the tetrachordal complement (0369), which is the fully-diminished seventh chord set. This is an indirect relationship to the augmented triad that formed the violin's third answer earlier. The diminished seventh chord has the same kind of tritone components as (0167), but they are spread out in a very different fashion. The violin is forcing Vafþrúðnir away from the true path.
The violin's final question is very similar to the cello's, but it has all twelve notes, and there is thus no possible answer to the question. The cello is enraged, but powerless. The final four-note chord in the violin is a last, triumphant statement of (0167). Oh, and this just made me realize something about the introductory measures. Not only is the primary four-note harmony shared by the two instruments  a member of that set class, but the opening four-note rolled chord in each instrument— in the cello and  in the violin—are as well. But notice that Oðinn has been in control since the very beginning; both instruments begin with a four-note chord but only reiterate their top two notes. The resulting four-note harmony is the same as the violin's initial and final chords, but different from the cello's. I don't recall doing that on purpose, but it's kind of cool if you're into that sort of thing.