jwilzewske

Wednesday, November 5, 2008

Change We Can Believe In: Sofia Gubaidulina’s Mathematics of Physical and Religious Time

Co•na•tiv•i•ty (kō-nā-tiv'-ə-tee)
n. The aspect of mental processes or behavior directed toward change, including impulse, desire, volition, and striving.”

To-date, the analytical attention that’s been paid to Fibonacci series and other mathematical constructs in the compositions of Sofia Gubaidulina (София Асгатовна Губайдулина) has mainly concerned the role of mathematics in devising her melodies and harmonies and in guiding her voice-leading. Actually, it’s unclear whether Sofia actually uses the words ‘numerology’ or ‘gematria’ in discussing her own compositional methods. Her methods are in any case deeply associated with her Russian Orthodox religious beliefs and spiritual practices.

But besides the mathematical origins of her choices of pitches, she also creates ‘ambient’ fields of multi-rate polyrhythms that are based on the recursive Fibonacci and other mathematically derived series. Becomingness. ‘Change we can believe in,’ to borrow a phrase from the just-completed political election process in the U.S. I’ve recently been exploring recordings of Gubaidulina’s compositions, to discover Fibonacci-accelerando and Fibonacci-ritardando patterns—rhythmic counterparts to her number-theory-based polyphony. This CMT post is meant to tell you a little about what I am finding so far.

T hree hippocampal rhythms: theta rhythms (4-10 Hz), gamma rhythms (30-80 Hz), and a fast oscillation (140-200 Hz). These rhythms are independently generated; we have observed that gamma oscillations persist without theta and compete with fast oscillation... There is a definable relationship among all brain oscillators: a geometric progression from band to band with a roughly constant ratio of e— the natural (Naperian) logarithm. Since e is an irrational number, the phases of coupled oscillators of the various frequency bands will vary on each cycle forever, resulting in nonrepeating, quasi-periodic, or weakly chaotic pattern: this is the main characteristic of the EEG. [But] why are there so many oscillators [in the brain]? Why can the brain not use a single, fixed-frequency clock for all of its computing functions? There are multiple answers to these questions... Once a slow oscillator appeared in simple animals, faster ones could be added as needed in subsequent evolutionary stages [for controlling functions on faster timescales]. We observe the continued coexistence of all of those independent clocks in the neurophysiology and neuroanatomy of brains today. The brain is not like a single, precise, fast clock and time-division [to produce a series of slower clock rates from the fast master clock] as is seen in digital computers. [‘Intelligent Design’ zealots notwithstanding,] the human brain did not appear de novo. The myriad independent clocks are the residue of evolution of the brain over many millennia. There is extra resilience and survival fitness that comes from the multiplicity of biological clocks, from the N-fold redundancy”
— Gyorgy Buzsaki, Rhythms of the Brain, p. 113.

O nce the hippocampus has been primed by stimuli that come down the perforant pathway, its own subsequent responses are greatly enhanced. Three seconds after granule cells in the hippocampus receive their first priming burst from above, they open up the ‘gates’. They transmit impulses much more efficiently across their synapses. This enhancing effect rises to its peak 15 to 20 seconds later. What is the most effective rate at which to deliver these brief trains of potentiating stimuli? Stimulating at the natural theta frequency: 5-7 Hz. Why is the result called ‘long-term potentiation’? Because transmission remains increased for as long as three weeks after the stimulation. Where does the theta rhythm come from? Chiefly from the medial septal region. Medial septal cells are ‘pacemaker’ cells. Their temporal pattern of acetylcholine release drives theta rhythms throughout the hippocampal formation.”
— James Austin, Zen and the Brain, p. 181.

Since the 1980s Gubaidulina’s work has been deeply informed by her Orthodox faith and her ‘zahlenmystik’, or the use of gematria, numerology, mystical mathematical formulae such as the Fibonacci series and the Golden Ratio. Sofia began to use the Fibonacci sequence as a way of structuring the form of the work. The sequence was especially appealing because it provides a basis for composition while still allowing the form to ‘breathe’—the naturalism referred to above. It plays a prominent role in such pieces as ‘Perception’, ‘Im Anfang war der Rhythmus’, ‘Quasi hoketus’ and the symphony ‘Stimmen... Verstummen...’ ). Later the Lucas series and Evangelist series, sequences derived from that of Fibonacci, were added to her repertoire. These compositional devices and effects are easiest to study in Gubaidulina’s chamber works.

There’s a naturalness ... an innate and almost inevitable quality to Gubaidulina’s rhythmic structures. The proportions of the durations and the statistical distributions of the durations of notes feel like ratios and distributions that we are deeply familiar with from phenomena that occur in Nature. When things ‘wind-up’ toward a climax in a Gubaidulina composition, they wind-up in the manner that we see when gravity accelerates a falling object. When things ‘wind-down’, they wind-down in a progressively diminishing pace that we see in dissipative processes in Nature. The music of Sofia Gubaidulina imparts a distinct impression that it complies with the Laws of Thermodynamics and other physical principles. Mass and Energy are conserved, neither created nor destroyed in the course of performing the music. Entropy increases slightly from the beginning to the end of each piece. It can be measured, if you are inclined to do so. But even if you don’t measure it, you feel it. The Universe is proceeding as it should.

Apart from the Orthodox spirituality that Gubaidulina intended to confer on her compositions, all listeners can at least apprehend the ‘organic’ cosmology that her compositional designs embody—the internal consistency and balanced energy and entropy budgets.

Okay. Measure it? Sure. Take one of her simpler pieces, like ‘Serenade’—the Swedish guitarist Mats Bergström (jpeg above) has a nice recording of this piece. It’s clear and the polyphony and rhythmic complexity are not too daunting. The Gibbs-Shannon entropy of a random variable that takes on values i with probability p_i is defined as:

If the rhythmic lines’ clock-rates are arranged so as to be Poisson-distributed, then the entropy of the Poisson distribution is given in terms of an infinite sum:

where λ is the time-constant of the distribution. For long values of λ, the asymptotic form of this expression is:

Or, in a slightly different formulation, the Renyi entropy of order α where α varies between 0 and 1 is defined as:

Obviously, if a composer sticks scrupulously to a mathematical construct in devising rhythms and orchestration, the result may be too complex to be playable. So there are compromises and simplifying decisions to make—collapsing the complexity into something that retains the feel of the programmatically-generated structure but omits things that inject too much variability or impose cognitive demands that are excessive. There’s a need to write forms that support ‘mutual entrainment’ of the disparate rhythms, re-syncing them on some regular basis. I try computing statistical copulas, to do multivariate measurement of synchronization/association between clocks...

Sofia Gubaidulina, Serenade, Fibonacci-beamed 10:3, 11:3, 12:3

C ommunities of Clocks... ‘Mutual entrainment’ is a theme that recurs again and again throughout the physiology of coupled rhythmic systems... [The systems’] ‘phase-scatter’ is altered in proportion to the derivatives of new clock-phase with the old phase and the magnitude of the perturbing stimulus, as characterized by the following differential equation:
— Arthur Winfree, The Geometry of Biological Time, p. 119.

Winfree, Clock-phase ‘mutual entrainment’ of two coupled biological clocks

Based on my measurements thus far, it looks like Gubaidulina’s ‘Fibonacci N-tuplets’ (? Fib-tuplets) and other rhythmic figures are hard for humans to play in a perfectly Fibonacci-timed way. With the note-durations normalized to the duration in milliseconds of each N-tuplet, the 10:3, 11:3, and 12:3 Fib-tuplets in ‘Serenade’ have as-written theoretical Shannon entropies of -2.06, -1.78, and -1.58, respectively.

As performed by Bergström, we get average values of -2.11, -1.85, and -1.72——entropy values slightly lower (more ‘ordered’) than the theoretical as-written values, owing to the [neurophysiology of entrainment that gives the--] plateauing of durations in the middle. (N-tuplets comprised of notes of perfectly identical durations would have Shannon entropies of -2.30, -2.18, and -2.07, for the 10:3, 11:3, and 12:3, respectively.) Interesting...

The ‘clocks’ in our brain that control our muscle function evidently tend to rush the accelerando beginning and ritardando ending just a little, and have a rate ‘plateau’ in the middle where the durations of the notes do not change as much from note-to-note as they should if they were strict, perfect Fibonacci.

It’s just how we're ‘built’, part of our innate physiology—beyond our interpretive control, really. What Gubaidulina reveals in these Fib-tuplets is a boundary between our humanity and our animality; between our conscious, sapient nature and our unconscious, instinctual nature; between things under our control and things that are beyond the possibility of human mastery. It is a fine and beautiful thing she does, reminding us performers and listeners of these things—we are stewards, not owners, of our mortal, animal bodies; we should be mindful of other animals with whom we share the planet; and so on. The Fib-tuplets induce a rhythmic meditation on humility, a spiritual posture that is receptive to grace... Have a listen to the MP3 clip below and you will see what I mean.

MetanoiaMind.com ‘EEG rhythms and states of consciousness’

And the spiritual effect of these naturalistic, physiologically propelled rhythmic structures is what I would say is this: ‘instantaneous epiphanies’ during neural pulse-entrainment. Maybe not on the first performance or the first casual listening. But if you do these pieces with intensely focused repetition, as part of a meditative practice? Wow! How long does an epiphany take to reach? And, once arrived, how long does the moment last? Try it and see!

So Gubaidulina’s music can induce dramatically altered perceptions of time, and transport the listener or performer to ecstatic, mystical, sufi-like states. Try it when you’re alone with your ‘significant other’. Maybe you will get to some exotic tantric, transfigurational, mutual-entrainment place you’ve never been to before. Change you can believe in! The tantric, ecstatic quality of Gubaidulina’s writing is maybe related to ‘theosis’ or the ‘Doctrine of Deification’ and ‘participatory union’ with God in the orthodox patristic tradition (see Russell, Tatakis, and Zizioulas links below).

Mats Bergström is a graduate of the Royal University College of Music (RCM) in Stockholm and Juilliard in New York. He made his recital debut at the Wigmore Hall in London in 1983 and has since pursued a career as soloist, accompanist and ensemble player in various genres. In 2006, he was elected member of the Royal Swedish Academy of Music. He performs solo recitals as well as the standard works for guitar and orchestra, and collaborates with artists such as singers Malena Ernman, Annika Skoglund, Olle Persson and Mikael Samuelson, flautist Anders Johnhäll and violinist Joakim Svenheden. He stretches the concept of chamber music in much of his work. Beautiful, fascinating. Mats currently lives with his wife and 3 kids in an old schoolhouse 30 km northeast of Uppsala.

[50-sec clip, Mats Bergström; Sofia Gubaidulina, ‘Serenade’, mm. 22-35 1.2MB MP3]

Here is a little spreadsheet I put together, which shows the Fibonacci-prescribed accelerando and ritardando timings for Gubaidulina Fib-tuplets that appear in ‘Serenade’ and other of her compositions. You can click on the screenshot to explore or download a copy to play with. Enjoy!

A student doing a practicum in a nursing home reported to me an incident. She was walking with a resident along the hall where there were pictures of various bucolic, relaxing, unobtrusive scenes. One was a painting of a blacksmith shoeing a horse while a small boy looked on. The patient stopped at this picture and told the student, ‘This is a picture of me and Dad.’ The student asked me if, in fact, the picture was of the resident and his father. I told her that the patient's father had indeed been a farrier and that when he was young the son had often helped his father, but this was merely coincidental. The mid-19^th Century Currier & Ives ‘Village Blacksmith’ picture was certainly not a depiction of this particular man and his father in 1925.”
— Allen Edwards, A Psychology of Orientation: Time Awareness Across the Life Stages and in Dementia, p. 208.

[This moment was for the elderly man ‘epiphanic’. And his fugue-like behaviors and experiences were these days continuously filled with small epiphanies. How brutal it would be to dispute his statement. How utterly awful to try forcibly to ‘correct’ the patient’s ‘mistake’ by compelling him to acknowledge it is Currier & Ives’s picture of some generic blacksmith, as a part of a cruel regime of medicalizing and treating the patient’s ‘confusion’ or ‘disorientation’. The old man’s variant, epiphanic reality must be permitted to stand——must be allowed anyhow if one cares a jot about his psychological condition and spiritual future.
—— dsm.]

Sunday, November 2, 2008

Weilerstein & Barnatan: Prepared Cello, Unexpected Microtonality

W eilerstein showed that she certainly has the technique to emerge as one of the leading cellists of the next generation. She produced a consistently lavish tone and demonstrated remarkably assured technical facility... With nearly flawless passagework and intonation, the cellist provided some pretty thrilling playing.”
— Chicago Tribune.

B arnatan … has an instinctive understanding of Schubert’s fragile, deep world... he obtained a hypnotic tone from the piano... he made sounds that might have won the approval of Schnabel himself.”
— The New Yorker.

Cellist Alisa Weilerstein and pianist Inon Barnatan performed a program of Kodály, Golijov, Chopin, and Beethoven on Saturday evening in Kansas City in a Friends of Chamber Music concert at the Folly Theater. The program allowed the audience a wonderful opportunity to experience each of the artists as soloists, as well as their special chemistry together. Each is a tremendously passionate, emotional interpreter; together, their responsiveness to each other was magical.

Beethoven: Sonata No. 5 in D Major, Op. 102, No. 2
Kodály: Sonata for solo cello, Op. 8
Chopin: Barcarolle in F-Sharp Major, Op. 60
Golijov: Omaramor
Chopin: Sonata for cello and piano, Op. 65

Alisa Weilerstein is the daughter of Donald Weilerstein, the founding first violinist of the Cleveland String Quartet. At 26, she has performed with top U.S. and European orchestras and has given recitals throughout the U.S. and Europe. Her festival performances (Spoleto, Aspen, Caramoor, Schleswig-Holstein,Verbier) have been well-received. Alisa is the recipient of an Avery Fisher Career Grant. (She is also a 2004 graduate in Russian History (Columbia University). This is something of a unique path for an artist of her caliber, one made accessible for her by the stature and acclaim that her parents have as musicians, in addition to her own performance ability from an early age. How many people have the option to pursue studies in another field—liberal arts, engineering, whatever—and not have the door to a career in music shut on them? Not many. It is wonderful to see Alisa make this dream happen!)

Inon Barnatan is an artist of the Chamber Music Society of Lincoln Center. He has performed with the San Francisco Symphony, the Aspen Music Festival, the Mostly Mozart Festival at Lincoln Center, Carnegie Hall, the Concertgebouw, Salla Verdi in Milan, the Royal Festival, and Wigmore Hall in London. In past seasons Barnatan has made his debut with the Israel Philharmonic, Netherlands Chamber Orchestra, Orchestre de las Suisse Romande, Jerusalem Symphony, and numerous other ensembles. He trained with Maria Curcio with additional coaching from Leon Fleisher, Radu Lupu, Richard Goode, Murray Perahia, Claude Frank, Menahem Pressler, and Christoph Eschenbach.

The performance last night was engaging throughout. But the Kodály sonata especially intrigued me. Not the ubiquitous Kodály Eastern-European folk music elements, nor the fact that this sonata is imbued with the milieu of 1915, composed as it was in the early days of WWI. Yes, it’s a very passionate piece, and is therefore a perfect vehicle to illustrate the range of Ms. Weilerstein’s extraordinary expressiveness. Alisa’s use of rubato and rhythmic flexibility renders the improvisatory character of Hungarian elements with style, energy, and elegance. Yes. But those are not the aspects that really intrigued me.

What intrigued me—Alisa revealing this piece to us as though we were hearing it for the first time—was to grasp Kodály’s use of classical sonata form here and—oh, what does it amount to?—to figure out whether our own expectations have any force or moral standing? whether we’re fated to struggle and struggle and eventually lose? What I mean is, sonata form is conventionally an epitome of Enlightenment rationality. But, in this piece, our expectations keep getting dashed. Struggle and lose. How does this happen? Why? I think it’s not enough to think in terms of Epstein’s concept of ‘structural downbeat’ or ‘structural accent’, or, say, E. T. Cone’s concept of ‘frame’. I think the ‘How’ goes well beyond the notes on the page and the nominal structural features that are there. Our anticipation—and how it gets dashed repeatedly—is bound up with the timbral changes and the scordatura and the metrical displacements that keep happening.

Op. 8 requires scordatura tuning, borrowing an instrumental practice of the 16^th and 17^th centuries. The timbral characteristics of the cello are altered by the detuning of strings, and the cello’s resonance takes on a mysterious, hollow, melancholy quality. The scordatura is indicated at the beginning of the movement, above the first bar. The notes are performed ‘as-written’, as if the instrument were tuned normally.

The other characteristic element of this sonata is what I referred to as ‘metric displacements’, through which the repositioning of the beat continually generates a sensation of ever-present alternatives. Although written in 3/4, the beginning of the first movement up to m. 31 is marked by metric ambiguity caused by variable positioning of accents in each measure, so that our anxiety is heightened. The emphatic 4-note chords are a major source of the metric ambiguity—quasi-boundaries or pseudo downbeats. The metric slippage and preemption—the displacements—create a sense of pulse in a different part of the successive measures. It’s like structural accents, as discussed by Epstein (1995, p. 23-6). Even when we achieve a ‘stable’ measure, whose downbeat is strong enough to be believed, it cannot be trusted for long. The ‘exceptionalism’ is recurrent, pernicious … so emphatic that it’s inescapable. The exceptions become the rule rather than the exception. The metric ambiguity is one of the main elements lending (or permitting the performer to give—) an improvisatory feel to this sonata.

The first movement begins with two chords that are repeated emphatically as a feature of the first theme. Things progress in mm. 21-25 (the bars pictured above), but, dashing our expectations, a transition surprisingly drives instead in measure 31, to the beginning of a new thematic group. Once we get here, we naturally feel things should move toward some new harmonic center of this new (second) thematic group. But, again, our expectations are thwarted.

The slow, lamenting phrases have these rich ornamentations—offering some emotional solace, I suppose. But instead of solace, these make us feel still more ‘on-edge’.

The metric displacements can preoccupy a performer, but not Alisa. She preserves a ‘speaking’ style in each phrase—to which the paroxysmal rhythmic gestures are incidental, not dominant. I imagine Kodaly’s rhythms and phrasing are somehow descended from the inflections of the Hungarian language. Weilerstein ably contours her phrasing, through agogic and rubato embellishments—in the lamenting sections especially. While Alisa may not be Hungarian, her sense of these inflections is admirable.

Beyond the interesting metric displacements, the scordatura intrigued me even more—how it sounds in the rapid technical passage work; and how it sounds in the context of the impressive Weilersteinian ardor.

It feels weird to place your fingers when the string(s) is (are) de-tuned, the scordatura does. This wasn’t written in C minor—in which case Kodaly could’ve either (a) left the lower two strings normally tuned and the fingerings on the upper two strings would’ve been higher by a half-step or (b) called for raised-tenor scordatura up-tuning of the D string and the A string, to E-flat and B-flat. No, he wrote it in B minor. And the open strings have a dramatically different timbre compared to stopped strings. The sound the bow produces at a given pressure and bowstick velocity is different from normal. (The hollow, scary quality of scordatura is why Saint-Saëns scored it in ‘Danse Macabre’—the discordant double, unstopped bowing in the scordatura-detuned first violins evokes a far-gone, unstoppable, decomposing, pell-mell ride to oblivion. Also, the departure from conventional tuning suggests some sort of irrevocable departure from the community of the living.)

Scordatura’s an aggressively soloistic thing—it cannot help but draw attention to the otherness of the scordatura-detuned instrument, in much the way that prepared piano draws extraordinary attention to the pianist. This is noticeable even in a solo piece like the Kodály sonata Op. 8…

Oh, the scordatura changes things—easy to say, but what does it mean really? Well, when you tune the string(s) down to lower pitch, the upper partials of the lower-pitched strings now become significantly lower in amplitude than the neighboring partials of the normally-tuned strings. And, if you do Fourier Transform analysis of a digital recording of it you see that, since the acoustic spectral energy tends to decrease with successive partials, the higher-pitched tones now tend to ‘mask’ the partials of the lower-pitched tones more than the reverse. So the lower-pitched strings now sound … long-dead. Cool effect, directly related to the acoustic physics of the harmonics/partials—and how (and anatomically where, in millimeters from the cochlear apex!) these superimposed sounds register in the nerve cells of the inner ear.

Have a look at the graph below, showing the frequencies of the harmonic spectrum for a bowed cello’s top string, A220 (solid lines), and as detuned to G196 (dashed lines)—and showing too the anatomical positions within the inner ear where those frequencies are sensed. A relatively large change in millimeters on the x-axis, this—especially for the higher partials. Look how much those shift downward (to the left in the plot), compared to the big spike, the fundamental frequency of the note, off to the far left. It doesn’t shift nearly so far when it’s detuned down to G196. We could do a similar graph for the cello’s detuned C and G strings, as called-for in the first movement of this sonata…

Scordatura changes which haircells in cochlea of ear are affected by sound

And it’s not just the string by itself. It’s the change in the Chladni-plate resonances of the body—the radiation of the sound of the instrument. It’s the change in what the fingers are doing—the scordatura stopped string sounds muted (in general) compared to what the conventionally-tuned stopped string would sound like at the same pitch, because of the altered finger placement, the altered fingerboard coupling and the altered resonance acoustics. And it’s what the strings do in reaction to the bowhair, under the lesser tension after the strings have been scordatura-detuned. More weight of bow against the detuned string digs deeper than normal, starts up bigger amplitude vibrations quicker than normal. Bow speed that you are accustomed to now microtonally ‘pitch-bends’ on the detuned string many cents different than you expect. The note on the page, that’s not the half of it!

The scordatura-perturbed fine motor control of the hand muscles—and the disruption of the mind-body imaging of the fingerboard and its relation to the pitches—add yet another dimension (for the performer; not for a listener). The note on the page and the placement of your fingers no longer produce the note that your mind expects to hear. It’s tremendously disturbing to people with perfect pitch. But it’s disorienting to almost every performer. In fact, a friend of mine in Minnesota once said she couldn’t possibly play scordatura—it was too ‘painful’.

Conventional wisdom has it that the Kodály sonata in B-minor has the cellist de-tune the two lower strings by a half-step from C to B and G to F#, respectively, to enable open-string sonority for the recurring 4-note B-minor chords (bottom three notes are then open strings, with the scordatura arranged this way; only one finger down on top A-string) and to put the hand in first-position and make some of the passages easier to play. This ‘lowered-bass’ tuning, B-F#-D-A, down a half-step on each of the two lower strings is very different from the ‘raised-base’ tuning (up whole-step) that’s occasionally used with violin.

To hear Alisa Weilerstein play this is to realize that there are other timbral and gestural reasons to do the scordatura. The breadth of the 4-note chords forces you to attack the detuned low (B) string and quickly roll to the F# and D string together. The bowstick speed over that bottom string gives a forlorn, microtonally-bending B. This effect would be there, had Kodaly written it in C minor, but the effect would not be as pronounced as it is with the low B.

And besides that, with the open F#, etc., the string players among us just sense the different double-stops that are available, even if the composition turns out not to call for them. Sense where vibrato will not be. You don’t have to be up there performing it; you sense these things just sitting in your seat in the audience listening. It’s this pervasive, latent intuition of ‘possibilities’ now opened, of possibilities foreclosed—of unhingedness, of all bets now being ‘off’. And it seems implausible that Kodály would not have found all of those effects and rationales interesting and supportive—not just the nominal ‘detune the lower two strings, to enable open-string, tonic B-minor’ one. On the eve of WWI, all bets were definitely off…

Scordatura does appear in Bach’s ‘Six Suites’ for solo cello; many other Baroque pieces, too. In the Bach Suite No. 5, the discant string is tuned down one whole tone, from A to G. The cello in George Crumb’s ‘Vox Balaenae’ (for electric flute, electric cello, and electric piano) calls for detuning from C-G-D-A to B-F#-D#-A, which makes the B major last movement that much more sonorous, much like the Kodály.

Probably the weirdest and most symbolically over-the-top is Biber’s Sonata XI (The Resurrection of Christ), calling for detuning the G-D-A-E violin strings to G-G-D-D octaves and switching the two inner strings between the bridge and tailpiece, to make the sign of the cross. The D string moves into the position of the A string and vice versa! I don’t know of anything quite this strange in the cello literature, though.

The ‘other-worldly’ impact of scordatura on the performer is both visual as well as registral/timbral/aural. As mentioned above, the ‘normal’ sight-sound intuitions are thrown out-of-kilter by detuning the string(s). Since the notated music you see now bears only a tenuous relationship to what you hear, you experience a profound loss—a sense of alienation. I try it on my violin, and the psychological effect can be hypnotic … if you take it further, do we get a detachment from the self; a sort of ‘dissociation’ experience? Very weird anyhow, the visual disorientation and eyes and ears ‘lying’ to each other. I wonder whether scordatura matters to folk fiddlers who don’t read music…

Curiously, out of the detuning and disrupted sight-sound relationships come these beautiful pitch-bent microtonal pitch anomalies. The fingers go where they’re told, but not quite. We get circumstantial microtonal pitch shifts, not just the different timbre associated with the detuned strings. And we get big differences from performer to performer, owing to underlying neurophysiologic differences between individuals maybe?

[50-sec clip, Janoš Starker, Kodály Op. 8, ‘Allegro maestoso ma appassionato’, 1.2MB MP3]

[50-sec clip, Xavier Phillips, Kodály Op. 8, ‘Allegro maestoso ma appassionato’, 1.2MB MP3]

[50-sec clip, Roel Dieltiens, Kodály Op. 8, ‘Allegro maestoso ma appassionato’, 1.2MB MP3]

How did I get on this peculiar path—microtonality via scordatura—with Weilerstein and cello and Kodály? Well, Ted Mook’s concert of microtonal cello compositions by Ezra Sims and Daniel Rothman occurred a couple of weeks ago (16-OCT-2008) at Roulette in New York. ‘Sensitized’ to microtonality in this way, it’s not much of a ‘stretch’ to start hearing interesting microtonal features in cello pieces that are not, on the face of them, overtly microtonal—like Weilerstein’s Kodály. Not actively looking for microtonal features, but nonetheless finding some. Thanks for your interest in this topic. Please feel free to comment or email me about microtonality caused by circumstantial or biomechanical/technic pragmatics that you happen to notice in compositions that are not explicitly scored as ‘microtonal’ pieces per se. And please go and attend Alisa’s and Inon’s concerts whenever you get a chance.

T he notes and groups you ornament ... are, I think, best always performed with a glissando or portamento. This applies even when some notes will be detached clearly from the group.”
— Kodály Zoltán, Pentatonicism 1970, p. 239.

Alisa Weilerstein and Inon Barnatan at Friends of Chamber Music, Kansas City, 01-NOV-2008.
Alisa Weilerstein website
Inon Barnatan website
Weilerstein A, et al. Jennifer Higdon: Piano Trio; Voices; Impressions. (Naxos, 2006.)
Weilerstein A. Debut. (EMI, 2000.)
Barnatan I. Schubert Recital (Improptus D.935; Sonata in B-flat Major D.960). (Bridge, 3006.)
Osvaldo Golijov website
International Kodály Society website
CelloGeek.com blog
Cellos2Go.com
DSM. Unplugged Folias & Romanescas. CMT blog, 12-MAY-2007.
Pierre Lewis page on temperaments
JustIntonation.net
Stingting Huygens-Fokker website
American Festival of Microtonal Music website
AFMM Ensemble. Microtonal J.S. Bach, J.M. Bach, and A. Werckmeister. (AFMM, 2005.)
Boston Microtonal Society website
Ezra Sims website
Braun M, Chaloupka V. Carbamazepine induced pitch shift and octave space representation. Hearing Res. 2005; 210:85-92. [anatomico-physiologically hard-wired octaves]
DSM. Welcome to My Pitch Universe: Carbamazepine, Aripiprazole, and Pharmacological Pitch-Bending. CMT blog, 26-JAN-2008.
Dieltiens R. Kodaly Op. 8. (Harmonia Mundi, 1995.)
Epstein D. Shaping Time: Music, the Brain, and Performance. Schirmer, 1995.
Kodály Z. Pentatonicism in Hungarian Folk Music. J Soc for Ethnomusicology 1970; 14:228-42.
Phillips X. Kodaly Op. 8. (Harmonia Mundi, 2006.)
Starker J. Kodaly Op. 8. (Delos, 1992.)

Y ou have to figure out what string players can do. It’s interesting when the instrumentality has been radically shifted. I love collisions. I hate cross-over, multi-culti—I prefer a colossal smash, where you get sparks that actually deliver something else, something surprising that the players could never have premeditated. The notion of musical possibilities defined by the instrument and by the playing—scordatura, for example—that’s of interest. But when the instrumentalist tells the composer what’s possible and what’s not, you usually don’t get the best results. An improviser is going to actually deliver that stuff all the time they play. That’s in the nature of music practice.”
— Jon Rose, The Relative Violins, ‘Johannes Rosenberg: Violin Music in the Age of Shopping’.

Saturday, November 1, 2008

Amuses Bouche, Amuses Oreilles: Williamson and One-Minute Wonders

T his concept, of one-minute piano compositions, arose as] a component of the first-year piano test in which all students are required to learn a short piece without assistance in seven days [at University of Surrey School of Music]. Though the students find this demanding, it is actually a very good test of their musicianship. The ‘Spectrum’ series deserves mention too: compiled by Thalia Myers and published by the Associated Board, it is a collection of short piano pieces by distinguished composers presented for students at a variety of levels of ability. I was also aware of the component of the composition course to write a piece of one minute for one instrument: it is a challenge for a composer to be able to communicate a sense of personal style within this time-frame. For me as a performer with a great deal of experience of working in new music as well as with student composers in workshops, there was clearly something personal which I felt able to contribute.”
— Clive Williamson, Professor of Keyboard, School of Music, University of Surrey.

Their small size belies the big challenges that ‘miniatures’ present, both to the composer and to the performer. ... And, come to think of it, to the listener.

Subsequent to the University of Surrey program referred to in the blockquote above, Clive Williamson recorded 36 of these on a disk released on Cadenza Records two years ago. His performance of each one is meticulous and empathetic, brilliant.

Clive has been a soloist at the Barbican, Queen Elizabeth Hall, Wigmore Hall, and many other venues throughout Europe and America. He has performed on BBC2 (‘Music in Camera’) and Channel 4 (‘Scipio’s Dream’). Additionally, he has been a guest artist with the London Sinfonietta, the Composers’ Ensemble, Sinfonia 21, and Sound Intermedia. He records for BBC Radio 3, West German Radio, and Netherlands Radio, and on the Col Legno, Wergo, Hyperion, and Cadenza labels. He trained at York University and the Royal Academy of Music with Ruth Harte, among others.

The technical and emotional palettes represented in the ‘One-Minute Wonders’ collection are tremendously diverse. Some of the pieces are ‘novelties’—humorous responses to the one-minute compositional challenge, performed in a jesting manner. But other of the pieces are serious, just as some so-called ‘microfiction’ (ultra-short stories, generally less than 250 words long; 2 min) or ‘nanofiction’ (complete stories in 55 words; 30 sec) is serious. [cf. ‘flash fiction’ (500 to 1,500 words; 4 to 10 min) and ‘sudden fiction’ (1,500 to 4,500 words; 10 to 30 min).]

Harold Edgerton, MIT, high-speed photo, apple and bullet

For the composer just as for the microfiction author, it’s a huge challenge to say something worthwhile in so small a space. The ‘density’ of expression entails big risks, of turning out contrived or forced or trite. Assuming that the composer succeeds in creating something that’s emotionally genuine and aesthetically interesting, for the performer it’s then a monumental challenge to enter into the piece and effectively deliver authenticity in so short a time. For the audience members, it’s a huge challenge to quickly apprehend what’s being set before them.

The beginning sentence is difficult. Who are you? Somebody! Do you want your piece to open with notes evoking a character doing something or thinking about something? You haven’t the luxury of putting a theme forward and letting it register with the listener/performer for a goodly number of measures; you have to figure out crystal-clear cues, ones that orient the listener/performer quickly.

What’s more, you have to have some sense for the neurophysiology of context-switching and memory, how fast the listener/performer can adapt to new ideas you introduce, or to transitions between ideas. You have to consider the diversity of your listeners/performers, in terms of their attentiveness and receptiveness to the ideas you are laying down. When people become charcters, they’re no longer fully ‘human’; they're symbols to be ‘pointed out’. Indicial/referential icons, nothing more.

Begin your one-minute wonder:

With a generalization or pastiche of something that's familiar (like Michael Finnissy does with his send-up of Chopin’s Op. 64 No. 1);
With a narrative summary that sketches and encapsulates the whole piece;
With a syntactical curiosity, a palindrome, or a chiasmus that begs the question as to whether we fully understand things that are conventional wisdom or second-nature—or that intrigues the listener by way of inviting consideration of a seeming absurdity;
With a dramatic morsel of dialogue;
With several characters already in-action but no dialogue;
With a vivid setting and a solitary character;
With a performer/narrator reminiscing or establishing a point of view in first person;
With the performer/narrator describing something in third person.

Are ‘arch’ shapes the way to go, to create bomb-proof coherence and continuity? Is instead a sense of fragmentation a good way to induce a strong desire for continuation? Or, yet another angle, is a vegetative repetition (for example, Skempton’s ‘Stroking the Keys’) a good way to induce a curiosity about the psychological state of the main character?

B revity and Conciseness are the parents of Correction.”
— Hosea Ballou.

The coincidence of the registral and (experienced) dynamic shapes of the music in the first few bars almost have to generate a strong cadential feeling, or the piece will fall apart before our eyes (ears). But how far should we go in terms of ‘tessitura’?

And how about the dynamics? What to do to insure that we capture the aural attention of the listeners, and yet not devolve into clichés and cheap theatrics?

The resolution/ending is just as challenging as all the rest. Actually, G. Thomas has some wonderful suggestions that are as useful for composers as they are for authors.

Here are some example 30-sec MP3 clips from his ‘One-Minute Wonders’ CD. The accompanying books containing sheetmusic for these compositions are inexpensive (£10) and nicely laid-out and printed. You may find miniatures like the ones represented on Williamson’s disk are useful in your repertoire. Some, like the Benjamin Hooper one, have virtuosic qualities that are well-disposed to serving as encore material. Other ones are coloristic and bonbon-like but are more contemplative or enigmatic than is usually suitable for an encore.

Composers may likewise find these instructive, emblematic as they are of a variety of gestures and tropes and architectures in miniature.