jwilzewske: cosmology

Showing posts with label cosmology. Show all posts

Thursday, October 29, 2009

Anonymous 4: Aural Ambitions of Medieval Worship, Modal Fictionalism

T he performance by Anonymous 4 last Saturday evening in the Friends of Chamber Music’s Early Music series was beautiful, without doubt.

Marsha Genensky
Susan Hellauer
Jacqueline Horner-Kwiatek
Ruth Cunningham

T he program ‘Secret Voices: Music from Las Huelgas, ca. 1300 CE’ of pieces from the Codex Las Huelgas embodies both traditional and emerging aspects of the musical and religious practice of its time. There are motets that manifest secular or para-liturgical aspirations, but the music is also inherently liturgical and devotional.

A s I listened, entranced by the singing, I began to imagine medieval religious thought—the pious thought and feeling that motivated the creation and preservation of the Codex—as a kind of improvisation and ‘modal fictionalism’ that aimed to make the tenets of belief that the text expresses come true or be true. More than an expression of belief or mere devotional act, the words and music seem intent on establishing the possible world in which what the words say really happens. In other words, the impression that struck me was that the Las Huelgas nuns’ practice was far more radical than any ordinary kind of piety.

S ome links to recent books on modal fictionalism are at the bottom of this blog post, for your interest.

Motet Claustrum pudicicie Virgo viget, Triplum
Claustrum pudicicie, virginis triclinium,	Cloister of modesty, seat of virginity,
spes tocius leticie...	hope of all happiness...
virgo filium fac nobis propicium...	Virgin, make your Son merciful to us...

Discant
Fa fa mi fa mi re mi,	Fa fa mi fa mi re mi,
Ut mi sol re mi ut fa fa,	Ut mi sol re mi ut fa fa,
Fa re fa fa re ut re mi ut re mi.	Fa re fa fa re ut re mi ut re mi.
Est fatuum spernere	It is foolish to despise these
quia musicalia...	because they are the elements of music...

Alleluya: Que est ista?
Alleluya!	Alleluia!
Que est ista tam formosa,	Who is she, so lovely,
pulcra ut luna,	beautiful as the moon,
electa ut sol,	noble as the sun,
terribilis ut castrorum acies ordinata?	awesome as an army arrayed for battle?

B oth the Codex las Huelgas and the Codex Calixtinus (the subject of previous Anonymous 4 recordings and concerts) are noted for their importance in understanding the development of 12th and 13th Century polyphony. They are important on account of their scope, fine condition, and readability. There are oddities of alignment between the voices (see the reproduction manuscripts, links below). In the note-against-note style, it was fairly clear which notes went together, since they pair off nicely with few exceptions. On the other hand, when the upper voice is allowed to have more than one note for every note in the lower voice, it’s hard to determine on which notes the two voices coincide. Karp’s book is a good place to begin understanding the intervalic alignments and dissonances, especially the note-against-note portions.

R hythmic and metrical ambiguities in the notation also reveal how much improvisational latitude there is (was). These ambiguities and the performance decisions and interactions between the ensemble members last Saturday night were the cause of my meditations on modal fictionalism. The ambiguities are obliterated in modern transcriptions (like these), so you really need to look at [facsimiles of] the original Codices. Is the meter duple or triple?

P ossible-worlds semantics for modality says that an expression is possibly true if it is true in some possible world. In classical propositional logic, one can show that every logically-consistent set of propositions can be embedded in a ‘maximal consistent set’. A ‘maximal consistent set’ is an abstraction of a ‘possible world’—for the nuns of the Codex, a possible world where Mary is really Queen and all members of the Order really are virtuous. But the abstraction depends on the fact that modal logics are ‘finitary’, and it seems false that an infinite collection of sets of sentences—each finite subset of which is intuitively ‘possible’ in natural language—has the property that the whole set is possible.

S o questions about necessity (or what ‘has to be’, or what ‘must be true’, or what cannot be otherwise) and possibility (or what can be, or what could be otherwise) are questions about modality—and such questions are what the works that comprised the Anonymous 4’s ‘Secrets of las Huelgas’ program so strongly evoked.

F ictionalism is a philosophical approach which treats the claims or assertions as analogous to fictional claims: claims that are not asserted literally, but which are put forward to serve a specific useful function of deliberation. There is even a modal fictionalism in theoretical mathematics (link below).

B ut, despite the name ‘modal fictionalism’, it’s not primarily fictionalism about claims of necessity and possibility, but rather a fictionalist approach to claims about possible worlds. (For instance, modal fictionalism is not normally fictionalist about the claim that “it is possible that there be a species of tail-less kangaroo”, but rather about the claim that “there is a possible world in which there is a species of tail-less kangaroo”.)

T heories employing possible-worlds constructs have been found to be very useful in philosophy—‘thought experiments’, basically, to discover the implications and meanings of constellations of propositions. The ‘modal fictionalism’ approach has been extensively applied over the past 30 years in ethics and in areas other than philosophy, like linguistics, logic, and probability theory.

I sn’t it extravagant to believe that just because a situation or constellation of facts is possible, it must in some sense exist? ‘Weak modal fictionalists’ say ‘yes’ to this; they take commitments to the existence of possible worlds that are constructed in the mind—merely hypothetical situations, non-actual but possible situations—to be strictly or possibly false, and so they avoid the problems of believing in possible worlds. Nevertheless, they claim, they derive the epistemological benefits of using these seemingly problematic theories.

I think that the the nuns of Las Huelgas ca. 1300 may have been what we would today call ‘strong’ modal fictionalists—who say it is not extravagant at all.

A wonderful performance, with much food for thought...

S ince the late 12th Century, the Cathedral of Santiago in Compostela has possessed a manuscript entitled ‘Jacobus’ (Codex Calixtinus). How it found its way to Compostela is unknown, but it is undoubtedly a French product, probably compiled or writtin in Cluny around 1150. Although they represent a mere 10% of the music in Jacobus, the polyphonic works have received attention from scholars because they are among the earliest such pieces to have been written down. But the notation in Jacobus is ambiguous as to rhythm and meter, as well as to alignment of the pitches between the voice parts in the polyphony...”
— Susan Hellauer, Anonymous4 CD liner notes.

Thursday, July 19, 2007

Shadows Over Grandeur: Bach’s Partita No. 2 in D Minor, Chaconne

O n one stave, for a small instrument, the man writes a whole world of the deepest thoughts and most powerful feelings. If I imagined that I could have created, even conceived the piece, I am quite certain that the excess of excitement and earth-shattering experience would have driven me out of my mind.”
— Johannes Brahms, letter to Clara Schumann.

DSM: Christian Tetzlaff’s new CD is phenomenal! And the Partita No. 2—the Chaconne—is gorgeous. Many virtuoso violinists’ gestures aim to arouse the eye as well as the ear. The use of slight detuning of the strings or oddly difficult bow techniques can draw attention to their skill. But Bach’s sonatas and partitas are not conducive to (or tolerant of) such showiness–which tends to support the argument that Bach wrote them for his own use. Tetzlaff’s interpretation of Partita No. 2 is deeply true to the spirit of this composition—this four-bar harmonic progression with sixty-four variations.

CMT: The length of the Chaconne—about 15 minutes—is interesting in itself. Profundity requires time. The artist has to have enough space to capture the audience's attention, plant some seeds, and let them grow. Tetzlaff handles this nicely. Nothing is exaggerated or played merely for ‘effect.’ It is personal and absorbing, poetical yet natural and unadorned. Tetzlaff captures all the tireless circumnavigations around this single idea, making you wonder at Bach’s rhetoric. In Partita No. 2, Tetzlaff evokes the melancholy beneath the Bach’s tribute to his first wife, Maria Barbara. There is pliancy, grandeur, musical freedom. Tetzlaff’s playing displays no desire for ‘show’ but only the desire to engage with the musical core of this piece.

DSM: Bach’s Partita No. 2 in D minor follows a ‘da chiesa’ “church sonata” pattern, in which the slow and fast movements alternate with each other. And the Chaconne is not a short story or a novella; it is a full-blown novel! A novel has enough space to support introducing and developing a number of characters. This famous Chaconne is positively monumental in its scope and scale.

CMT: The arrival of every four-bar phrase on D is a striking aspect of the Chaconne’s beauty and poignance. It’s an emphatic eternal return, as though it were a physical “law.” The impression is one of inescapability, of inevitability. There’s also the ‘monumentality’ of the sheer variety that emanates from the solo violin as the performer progresses through the 64 variations that comprise the Chaconne. The music and the soloist become an omnipotent force. The piece evokes a transcendent ‘Other’—the Divine, if you wish.

DSM: The sheer diversity of the 64 variations compels us to acknowledge the Other. The diversity is so enormous as to boggle the listener’s mind and cause the jaw to drop. Boggling not in awe at a virtuosic human performer, but in awe at the mysteries of Life, of the Universe.

CMT: All of Bach’s compositions are, in some way or other, variations on a thoroughbass. With the first statement of the four-bar theme, the harmonies first move in halves and quarters. Then they accelerate to quarters at the cadence. Then they speed up to sixteenths.

DSM: Many of the variations occur in pairs—the second, for example, is similar to the first, but intensified. The opening eight bars comprise the theme and its first repetition, where the first three bars of the second statement are identical to the first. Then it broadens in register and introduces thirty-second-note rhythms. In terms of our cognition, Bach's 'haptic update rate' and the hypermeter of the variations’ cycling are what impart this transcendent quality to the Chaconne. Have a look at Choi and Tan paper in this month’s issue of the virtual-reality journal, Presence.

CMT: This presages the predominant dotted rhythm of the next four variations. The dotted-rhythm variations occur in pairs. The first pair is diatonic; the second pair introduces chromaticism—the descending tetrachord goes from tonic to dominant. And now this! And now this! Layer upon layer! World without end!

DSM: The texture perpetually evolves throughtout the Chaconne as well. As the velocity increases, the texture diminishes from the three- and four-voiced chords at the beginning, to single-line writing later in the piece.

CMT: As the texture becomes thinner, the chromaticism increases—the introduction of F-sharp and E-flat in the eighth statement, for example—and the registral ‘span’ increases, from the tenths in the first two statements, to about two octaves in the eighth statement and beyond.

DSM: This process—where some elements diminish while others grow—adds to the sense that the meaning intended or the theme that Bach is referencing is a commentary on life itself, on Nature, on the Cosmos.

CMT: When the next few variations featuring sixteenths evolve into an ever-expanding array of bowing patterns, wider and wider articulations, my impression is one of galaxies, of a universe that is expanding, of a supernova.

DSM: When runs of thirty-seconds first appear they are slurred (mm. 65-72), then they are separately bowed (mm. 73-76). More and more intensity. More and more and more.

CMT: The changes of mode—to the grand D major and back to D minor—are accompanied by returns to the slower rhythms that we had at the opening of the Chaconne. There is a renewal, another aspect of the eternal return.

DSM: But with each rebirth we have the beginnings again of the growing speed and chromaticism and intensity. Inescapable. Inevitable. Changes of changes. Wheels within wheels.

CMT: There’s a tension—for the performer especially, but also for the listener—between the elements of articulation, tempo, affect, bowing, fingering, and other aspects of technque. The variations call upon these in different ways—increasing the importance of one or another of them and diminishing the importance of the others. This is part of the ‘novel-esque’ character of the piece. Obviously, it's also part of why the Chaconne is such a showcase for virtuosic playing.

DSM: But it would be a mistake to dwell on technique. A technically brilliant performance of the Chaconne may be emotionally empty. Instead, the tension between these demands is the source of a cast of ‘characters’ in the composition.

CMT: These are different voices, I think—not the soliloquy of a single voice. The textures of the four strings, how Bach uses the violin's four strings, are, to me, at least four different voices in this Partita.

DSM: The developments in the Chaconne are logical and yet suprising. Its inordinate novelty—novelty begetting yet more novelty—is the source of much of the piece's profundity.

CMT: There’s an inherent urgency to the Chaconne as well. Something like the remark J. Tillman made upon hearing Josh Bell play the Chaconne in the Washington D.C. subway station last January – ‘the kind of music the ship’s band was playing on the Titanic, before the iceberg.’

DSM: In other words, the Chaconne “knows” that it must end. It is anticipating the end of the universe. In the beginning there was the Big Bang. The Chaconne is showing us the approach of the Big Crunch.

CMT: Yes, this Chaconne is not sticking to the script of Church dogma in the way that Bach’s sacred music does. This Chaconne is agnostic, or even atheist in its view. We feel the finiteness of our existence on Earth and are not exhorted to believe in any life hereafter.

T o prepare for a friend’s funeral service, I had been practicing the Chaconne every day—fussing over individual phrases, searching for better ways to string them together, and wondering about the very nature of the piece—at its core an old dance form that had been around for centuries. After the many times I had heard and played the Chaconne, I had hoped it would fall relatively easily into place by now, but it appeared to be taunting me. The more I worked, the more I saw; the more I saw, the further away it drifted from my grasp. Perhaps that is in the nature of every masterpiece. But more than that, the Chaconne seemed to exude shadows over its grandeur and artful design. Exactly what was hidden there I could not say, but I would lose myself for long stretches of time exploring the work’s repeating four-bar phrases, which rose and fell and marched solemnly forward in ever-changing patterns.”
— Arnold Steinhardt, Violin Dreams.

F rom the grave majesty of the beginning to the thirty-second notes which rush up and down like the very demons; from the tremulous arpeggios that hang almost motionless, like veiling clouds above a dark ravine ... to the devotional beauty of the D-major section, where the evening sun sets in a peaceful valley: the spirit of the master urges the instrument to incredible utterances. At the end of the D-major section it sounds like an organ, and sometimes a whole band of violins seems to be playing. This Chaconne is a triumph of spirit over matter such as even Bach never repeated in a more brilliant manner.”
— Phillip Spitta.

Christian Tetzlaff, represented by Harrison Parrott Assoc.
Big Crunch wikipedia page
Josh Bell in D.C. Metro, L'Enfant station, JAN-2007. Washington Post article
Video of Josh Bell in D.C. Metro, L'Enfant station, JAN-2007.
Beach D. Aspects of Unity in J. S. Bach's Partitas and Suites: An Analytical Study. Univ Rochester, 2005.
Choi S, Tan H. Perceived instability of virtual haptic texture: III. Effect of update rate. Presence 2007; 16:263-78.
Efrati R. Bach: Interpretation of the Sonatas and Partitas for Solo Violin. Schott, 1993.
Mastroianni J. Chaconne. Damian, 2005.
Schröder J. Bach's Solo Violin Works: A Performer's Guide. Yale Univ, 2007.
Schwenger P. The Tears of Things: Melancholy and Physical Objects. Univ Minnesota, 2006.
Tetzlaff C. Sonatas and Partitas for Violin. (Hanssler, 2007.)

Thursday, November 16, 2006

Biss: Little Pieces in Cosmic Context

“Schoenberg … leads us into a realm where musical experience is a matter not of the ear but of the soul alone—and from this point of view begins the music of the future.”
— Wassily Kandinsky (1911)

CMT: Biss’ playing ( Kansas City and New York ) is phenomenal. Spacious. Expansive in his ideas and references to other works and other ideas. His pre-concert remarks were also very good (Biss Interview with Cynthia Siebert. 15-NOV-2006. )—indicative of the way his mind works; how he reacts to musical and social stimuli across space and time. So what? Where does Biss lead me? Working from Heidegger’s and Adorno’s and Wittgenstein’s “Philosophy of Language” concepts, I would say that a piece of music is only meaningful by way of that work’s relations to other works within a larger group, by way of the person’s relations to other persons, and in relation to the “game” that’s unfolding in the society that the composer, performer, and listener are members of.

DSM: When I experience a piece of music, I experience it in the context of this community of other related works and events and motifs—which include other cultural and political motifs, not just musical ones. Even if you consider only the characteristic features of a single work, the exceptional features of the specific piece inevitably arise in proximity vs. remoteness to other pieces that are somehow related to it. Even if the composer and the players scrupulously avoid listening to or studying or performing other works, they inevitably manifest aspects of their native culture. They can’t escape that—even if their work doesn’t overtly aim to express it; even if their work deliberately strives to hold itself at a distance from the prevailing culture or avant garde-ishly, consciously avoids reference to it.

CMT: This is, I think, basically right. We never experience a piece of music as self-contained in isolation. Nor is it possible to create one in total isolation. Each piece is like a star within a constellation of other pieces in our gaze. Musical understanding happens when we situate a particular piece within such a musical galaxy. Thought of like this, a work isn’t so much an isolated point as much as it is a location of gathering together. A condensation of matter and energy.

DSM: Well, yes. And the sustained appeal of Schenker’s theory and method of musical analysis is due to their ability to situate tonal pieces in the galactic realm of the proverbial masterwork, a musical equivalent of a Grand Theory of Everything in physics, the desire for a universal Gesamtkunstwerk.

CMT: So if we privilege the concept of historical backward-and-forward continuity—if we make that the “card” that “trumps” all others—then atonality just serves to extend and continue the tonal tradition. Seen in this way, atonality isn’t “really” atonal, but is instead just a more complicated kind of tonality. The disruptive effect of “atonality” is an optical-acoustical-cognitive illusion.

DSM: An example from Schoenberg’s Six Little Pieces, Op. 19 (1911), shows what I mean. The second little piece contains this G-B dyad that’s repeated throughout the nine measures. In m. 7-9, a progression of major thirds descends against the ostinato dyad—producing a sequence that goes F-A, E-flat-G, D-flat-F, C-E. A tonal analysis of this might take these thirds as a stepwise descent from G to C interpreted under a rubric of the key of C. But it’s ambiguous. It could be interpreted in the key of G, or no key at all.

CMT: Mitsuko Uchida’s account of Schoenberg’s Klavierstücke covers emotional light-years in the few bars that comprise each piece. Different from Jonathan Biss’ treatment but also deep and beautiful. Lots of dark matter in the interstellar space she spins out. The pieces in Op. 19 are so short that it’s impossible to say that there are clear expository sections—they’re a study in compactness. They’re a gauntlet to test your expressive artistry—they are not a crucible for virtuosic stellar playing.

DSM: Yes, they’re so compact conceptually as to be unexpectedly daunting to the performer. You can easily turn in an uninspiring incarnation of these Sechs Kleine Klavierstücke—but it's surprisingly difficult to materialize an inspiring one. Maybe this is a consequence of how compact the process of composing them was. Nos. 1 through 5 of Op. 19 were, you know, composed in a single day, 19-FEB-1911. And No. 6 was composed on 17-JUN-1911 in one go.

CMT: The longest, No. 1, encompasses just 18 bars, while the shortest ones, Nos. 2 and 3, only nine bars each. Some melodic repetition and manipulation occurs in No. 3, Sehr langsam Viertel, but it too is really compact, like astronomy’s M39, a globular cluster. Because of its tempo, Rasch, aber leicht (No. 4) is the shortest of the Klavierstücke.

DSM: In No. 2, the repeated third (G-B dyad), played ostinato, contrasts with the legato melody at a higher dynamic level. The pauses create galactic cadences—sparse structure, spacious. The most dramatic of the pauses occurs just after the vertical build-up of the thirds.

CMT: And a pitch-class set analysis of this might explain the various collections that result from combining other pitch classes with the central G-B dyad. The piece seems to center on the important trichords (0 1 4) and (0 4 8) and culminate with the statement of the (0 1 4 5 8 9) hexachord at the end. At least that’s where my own telescope focuses!

DSM: So what are we doing here on this blog? I notice, by the way, that sometimes you bring out your microscope instead of your telescope! And your mirrors! Always your mirrors! Like Beethoven’s “Diabelli Variations”—looking backward and forward at the same time.

CMT: Well, to quote Jonathan Biss from his interview with Cynthia Siebert: [The responsible person] “… must nurture discourse. He/she must make music part of the public conversation.” Because we lack voices in other spheres of life—and also because you and I live 2800 kilometers apart [ 91 picoparsecs or 1.6 megasmoots ], in Boston and Kansas City—we meet here in this bloggy part of the galaxy. We add more music conversation to the public commons. We’re discharging what Biss says is a social moral duty. Cogito ergo obtineo! Velicamus ergo crearāmus! DiggIt ergo sum!