jwilzewske: mathematics

Showing posts with label mathematics. Show all posts

Thursday, December 13, 2012

Beiser/Harrison/YPC: Joyous Time Loops, Just Intonation

T his is the basic premise of the Transient Glory® project: that a child’s voice is a unique instrument during that fleeting time between childhood and after-childhood... and that this instrument can tackle the most challenging and uncompromising music written for them. Children leave something behind [as they grow up and leave childhood]. I don’t know what it is, but children are able to communicate in a way we adults have forgotten how to do.”
— Francisco Núñez, YPC, 09-MAY-2011.

T he entirety of ‘Time Loops’ is performed using ‘just intonation’ tuning, based on whole number proportions. With ‘Time Loops’ I am demonstrating the simpler and more harmonious aspects of just intonation. As a result the tunings on the CD don’t push boundaries per se, but rather they sound clearer and more direct than the normal equal-tempered scale that is used in most Western music.”
— Michael Harrison, 23-AUG-2012.

T he new recording ‘Time Loops’ is a superb stimulus to joy and reflection. Meditation to bring peace at this or any time of year.

I n concert performances, cellist Maya Beiser plays the lead part live accompanied by pre-recorded, digitally-processed tracks forming an auto-ensemble of many sonic layers. Multi-media artist Bill Morrison created a film for ‘Time Loops’ that incorporates archival footage and CGI images that illustrate the movement of the planets, celestial mechanics mathematically conforming to the integer ratios of the music’s just intonation. Composer Michael Harrison performs the piano part with sensitivity and feeling. Even amidst the complexity and conflict of everyday life, we rediscover here the beauty and solace that are immanent in the natural world—the patterns and harmonics of a clockwork Universe whose physics was first formalized mathematically by Kepler, Galileo, Newton, and others—and rediscover that our own homo sapiens processes are as real and natural and immutable as those.

T he last and largest-scale work on the CD, ‘Hijaz,’ was composed by Harrison for Beiser and the Young People’s Chorus of New York City under the direction of Francisco Nuñez, as well as composer and percussionist Payton MacDonald on tabla and shaker. The text combines a prayer written by Harrison with spoken South Indian rhythmic syllables, which merge with the choral textures to evoke a sense of joy and unity and transcendence—deeply fitting for this holiday season.

E specially vivid and poignant are the perspectives of the school-age voices in the choir (see blockquote above). Wise beyond their years; empowered and uplifted by the music. To me, joy is mainly what music is for, and people should, through writing and performing music, feel joyous and acquire a better ability to create more joy. This CD—the compositions and performances—is first-class evidence supporting this idea. Evidence, too, of how crucially important opportunities are for kids to learn and perform music—before adulthood overtakes them as it does us all. Not a nostalgia for a childlike simplicity, but instead a meditation on clarity, on earnestness, on wonder, on the youthful drive to penetrate the truth of things, on receptiveness to joy.

[50-sec clip, Beiser/Harrison/YPC, ‘Hijaz’; (track 8), 2012, 1.4MB MP3]

M y intention was to invoke a sense of pilgrimage, either to a wondrous or holy place, or, metaphorically, to a sacred place within each of us. The chorus is the soul of the journeyer... The pulsing rhythms trace our footsteps, and those of our camels, as we make our way on the path of self-discovery.”
— Michael Harrison, 23-AUG-2012.

T he recent release of ‘Time Loops’ coincided with the first productions of Maya Beiser’s ‘ELSEWHERE: A CelloOpera,’ created by Maya with director Robert Woodruff, composers Missy Mazzoli and Eve Beglarian and writer Erin Cressida Wilson. For more information, visit www.elsewherecelloopera.com.

Saturday, November 10, 2012

Xenakis Matters

Xenakis, photo (c)1999 Ulf Andersen/Getty Images

T he Demiurge (1) creates from an intuition of Good; (2) takes disorder and friction and waste and makes it orderly and efficient, so far as is possible to do; (3) places Reason within the soul, and the cosmic soul within the cosmic body; (4) models the cosmos on the form of a generalized sentient lifeform, i.e., an animal with moral standing; (5) creates the cosmic body on principles of geometric proportionality; (6) creates the world soul out of population-level sameness and difference; (7) blends these into a durable alloy; and (8) divides the alloy into useful, value-generating harmonic intervals.”
— Plato’s ‘Timaeus’, quoted by Eric Lewis in Kanach, p. 81.

U nlike Schoenberg, who controls and organizes his music at the level of the individual note, Xenakis works at the level of the whole population [of all notes, taken together, as a sound-mass].”
— Brian Kane, in Kanach, p. 97.

T he new book, ‘Xenakis Matters’, the latest in the multi-author, multi-volume series edited by Sharon Kanach and published by Pendragon, provides a superb and many-faceted view of the enduring impacts of composer-artist-architect-engineer Iannis Xenakis, who died in 2001. Sharon Kanach is Vice-President of Centre Iannis Xenakis in France and Founder and President of the Xenakis Project of the Americas of the Brook Center at CUNY. She served as Xenakis’s assistant for two decades prior to his death in 2001.

X enakis was an iconic, formative influence on me, even though I encountered him and his teaching only for a short while in 1972. Xenakis was then still on the faculty at Indiana University at Bloomington in 1972... IU with its beautiful-and-powerful-and-then-new Control Data 6600 computer, sylvan wooded paths of the campus, and its quiet, clear-flowing limestone creek so incongruous with the intensity of the University and the minds gathered there.

S pringtime 1972 was, I suppose, before many of us recognized that the Sixties were over. It was when students at the University of Minnesota were protesting the War and barricading Washington Avenue with piles of lumber set on fire, an incendiary deconstructionist action undertaken not far from the School of Architecture where I attended Xenakis’s lectures.

S pring 1972 was when my life still straddled music and engineering equally—and when Xenakis, his music, his cross-disciplinary, fusion-avid compositional methods and materials, and his talks and writings were the epitome of innovation—his compelling, unifying vision a convergence of nature, science, engineering, and art.

H is mathematical models as automatic generating functions—not only for making music but for representing it—where equations accomplished this in a manner so much more compact than mere notes on paper could ever do: so crystalline, the beauty of this.

T he idea becomes the machine that makes the art .”
— Sol Lewitt.

H is programmatic transformations of acoustic forms and found-sounds—embodying a mode of creativity beyond pitch and rhythm and traditional music pedagogy—a random and happenstantial process can nonetheless have statistical self-similar or fractal properties across the ensemble of parts/voices and across time, and can manifest and evoke specific, real meanings.

C an order be established from noise? Well, your music was the first to discover this.”
— philosopher Michel Serres, remark during Xenakis’s PhD thesis defense.

H is physicality and love of ‘immersive’ media and sonic productions—in which the raw and elemental and cranked-up challenged us to (re-)discover the boundaries between Nature and the human.

H is famous book, ‘Formalized Music’, wherein he referred to some of his work as the musical equivalent of the “phenomena of a political crowd... protesters forming a human ‘river’, and their shouted messages propagating from front to back, comprehensible to an observer situated at a distance from the crowd but often not coherent, as such, to individuals within the crowd”.

I ’ve spent the 40 years since then in very different ways than I would have imagined, most of them doing software engineering. But the maieutic* debt that I owe to Iannis Xenakis as an important teacher in my life is great. [*uncovering through analysis; eliciting knowledge by provoking or questioning; assisting-in-coming-into-being; midwifing]

I suppose only as we get older do we really begin to appreciate/apprehend the entire cycle of Life. There is a sense of totality to life and its review, a summing-up. The emphasis is on the ‘examined life’, on how we assess our life and how we have lived it, and assess what truth we have synthesized from the events that have accumulated, from our own efforts and decisions, and from the acts of others and how they have filled and inhabited our lives.

A powerful mixture of emotions—happy memories; regret; guilt; 40 years’ longing and loss—is part of what this book caused to well-up in me—part of what will lead me to read and re-read this volume in years to come. The poignancy of what is remembered so vividly across the decades is staggering. I become reattached to my past as it is reanimated by these authors on these pages.

S ignificant for many readers besides me, though, is how this book works as historiography—revealing how life crystallizes itself in the artifacts that remain in us, emblems of the impact that others have had on us.

I n hindsight, it’s impossible to exaggerate Iannis’s importance to my development, as a person and as an engineer. While insisting on holding students to high standards, he also took an active, personal interest in each one’s well-being. Puckish and provocative, but always seeming to accurately gauge the limits of each. Xenakis’s legendary generosity/hospitality/charity is part of his legacy and, no doubt, a major reason why he is remembered so vividly by so many people, even ones like me who only encountered him briefly.

R emembering now Iannis Xenakis’s smiling face, remembering his exuberance and enthusiasm—how he confided his uncertainties about what some of his music meant, while he simultaneously professed that each motive and pattern did have meaning(s), however ineffable those meanings may be; how he excitedly expressed his ideas and showed his students how to make them work, or, at a minimum, how to believe sufficiently in the possibility so that they fearlessly strived to make it happen—redeems me a bit from my long history of sinning by transience and forgetting.

G enuine problems are... both necessary and impossible. Possibility arrives right when you no longer expect it. That is what an ‘event’ really is.”
— Alain Badiou, quoted by Olga Touloumi in Kanach, p. 101.

I n summary, reminiscence can be dynamic and creative—it can be productive of new discoveries; reminiscence does not have to be reductionistic or static—and I thank Sharon Kanach and her co-authors for this gift.

A ll of the essays in ‘Xenakis Matters’ are engaging and a joy to read. Each essay advances the scholarship regarding the composer’s ideas and influence. And each conveys the kindness, humanity, and something of the humor and kindly nature that are what I remember of him. Robert Wannamaker’s chapter (pp. 127-141), especially, on math exhorts composers to emulate Xenakis’s use of ‘discretion’ in humanizing the combination of mechanical/programmatic musical elements with human ones, to achieve a synthesis that can touch the heart and move us in valuable or even life-changing ways.

M usic is a mathematical exercise, disguised in such a way that the mind does not realize it is counting.”
— Gottfried Wilhelm Leibniz.

I love this book—for reasons noted above, universal as well as personal. Whether or not you have personal memories of Xenakis as an excellent human being, you will, I’m confident, love the book too.

Recording of Pianist Yuji Takahasi performance of Xenakis’s ‘Herma’

I n 1963 I became [Xenakis’s] composition student. When I showed him my piano piece, he pointed to two sections in the piece and offered me a big eraser... I can still feel the notes of ‘Herma’ at my fingertips. Performing ‘Herma’, I discovered the gravity-free state of sound. It was the feeling of lightness, rather than the violent movement other people surmise from the pianistic virtuosity of the work... I hear through those hundreds of notes—and I sense from them at unexpected moments—something like a voice of the inexplicable.”
— pianist Yuji Takahashi, quoted by Roger & Karen Reynolds in Kanach, p. 13.

Sunday, May 20, 2012

Terry Riley’s Aleph (א): Music to Code By

A leph in Jewish mysticism represents the oneness of the Divine. The letter can been seen as being composed of an upper yud, a lower yud, and a vav leaning on a diagonal. The upper yud represents the hidden and ineffible aspects of God while the lower yud represents God’s revelation and presence in the world. The vav connects the two realms.”
— Wikipedia.

T he 1-hour 53-min recording of Terry Riley’s solo synth performance of his composition, ‘א’, is beautiful—and precisely the sort of experience you would expect from Riley.

B ut, apart from whatever else it may be and apart from its merits as a composition and as a performance, I have found it to be especially conducive to my own productivity when working on complex math problems and coding software to solve them. For me, silence works only up to a point, after which I need minimalist music.

B ut not just any minimalist music. For example, Michael Nyman’s music interferes with concentration. La Monte Young’s music contains, for me, too many distractions. I do find Ellen Fullman’s recent work conducive, though, in the same way that Terry Riley’s ‘Aleph’ is conducive.

T he timbre of the Korg Triton Studio 88 Synth is bright like a Chinese single-reed or double-reed, but with a lot of spectral flux like a car horn... or a choir of Chinese tenor and bass suonas. Spectral flux and spectral irregularity are distinguishing features in car horns (see Lemaitre 2003, link below).

T he two-hour performance is filled with dense, organic, continually-changing textures—nimble car horns, if car horns can ever be nimble, and these are supernaturally nimble. The automaticity of preschool kids’ trying out their fingers on a keyboard, enjoying the raw pleasure of making notes and reproducing patterns and sequences... reflexive movements of their fingers and arms, yielding arpeggiation that involves just those notes that are within easy reach without stretching.

T he effect, some minutes into listening to it, evokes a freedom from intention and planning that is unknown to sober adults, and this is what facilitates my problem-solving and coding mind. The uncertain continuation of woodwind-like fingering patterns without aim, as long as they last, until superceded by some new motif... the stochastic, aleatoric innovations... Riley discounts the creative value of mind and deliberation and discounts it again, and again... the dollar-store of intellect... until the passion of meat is all that’s left, and animal instinct is restored...

O nly connect the prose and the passion, and both will be exalted, and human love will be seen at its height. Live in fragments no longer. Only connect...”
— E.M. Forster, ‘Howard’s End’, Ch. 22, 1910.

H ere’s a short MP3 clip.

T here is a ceremonial, magisterial, quasi-liturgical quality of ‘Aleph’ that reminds me of requiem forms. Or of chant, which can be heard as both archaic and contemporary. It is a mystical piece that unfolds at an implacable, glacial pace. The tone is largely meditative and serene, which provides space for contemplation and veneration. There are dozens-of-voices atmospheric Ligeti-like sound-fogs... fields of dissonance that convey an inhuman, infinite, primeval power—this surely is part of the Hebrew significance of Aleph; as is true also of the meaning of ‘א’ in mathematics—fitting as well in the context of requiem-writing.

I t has been said that my ‘Requiem’ does not express the fear of death and someone has called it a lullaby of death. But it is thus that I see death: as a happy deliverance, an aspiration towards happiness above, rather than as a painful experience. The music of Gounod has been criticized for its over-inclination towards human tenderness. But his nature predisposed him to feel this way: religious emotion took this form inside him. Is it not necessary to accept the artist’s nature? As to my ‘Requiem’, perhaps I have also instinctively sought to escape from what is thought right and proper...”
— Gabriel Fauré, 1902.

T hroughout, the piece is prodigiously inventive, with prolific layers upon layers of rhythmic and harmonic complexity, yet all presented with what appears on the surface to be minimalistic... it embodies the best of what minimalism can be: full of latent variety that captures and nourishes the listener’s awareness. (Which is why I find it helpful to listen to when I am tackling a hard problem, and why I am writing this blogpost you are reading. If you are interested in reading more about quantitative evidence concerning music listening and work productivity, have a look at the links below, esp. the book by Vikram Kiran.)

T he seamless, cluster-like blends fan out like a spilled liquid on a flat surface—part of the organic quality of just intonation, providing a support structure for the synth suona-like parts, a Toop-style “rawness” of intonation that sustains the emotional intensity of the piece.

M ost a cappella ensembles naturally gravitate to just intonation because its ‘stability’ or ‘target-pitch predictability’ is comfortable. In that regard, maybe the spectral flux and on-again-off-again frisson of this Terry Riley recording will be of special interest to people of a vocal bent, both amateur and professional singers alike.

T his sound of synth suonas keening, synth voices keening, choir of synth car horns keening... bears some resemblance to the György Ligeti piece in ‘2001 A Space Odyssey’, ‘Lux aeterna’... A friend who was overhearing my repeated playing of the 2 Riley ‘Aleph’ CDs wondered aloud “How can you stand that!? It’s driving me nuts!” So, to be truthful I should say that this is an acquired taste, or reveals a patience borne of equanimity. It is like being transported by William Kraft’s music in the walkway between terminals underneath Chicago’s O’Hare airport. It is like listening to a choir of chainsaws in the forest at a great and comfortable distance. Or like the persistent-but-beautiful bleating and tintinnabulation of sheep in a high alpine meadow in the Swiss alps, below the Jung Frau Joch in the late mornings of mid-summer. In other words, the bleating and tintinnabulation signify tolerant, salutary, and humane qualities that are implicit in our planet’s troubled story. Children of the Universe, you (every living creature) are here, hurray. Have a good life.

I n short, these are qualities which make humans, the sum of which could be seen in love (esp. agape, which in turn can be seen as an embodiment of the ‘idea of One’). The musical gaze cast from this sphere upon the story world is distanced, more or less withdrawn, non-judgemental, calm, quiet, and slightly melancholic, yet non-sentimental. As film music, tintinnabuli music often qualifies as an ‘against all odds’ score capable of making the complicated plot-level matters more poignant.”
— Kaire Maimets-Volt, p. 172.

I f you were in a foreign country and experiencing the local people performing on their native instruments, a long raga, for example—you would exhibit a tolerance toward such bleatings and tintinnabulations. But if instead, like my friend, you regard it as a choir of annoying car horns—multiple car alarms being set off repeatedly by marauding kids on a street a couple of blocks away—you just want it to stop.

I n summary, playing these 2 CDs consecutively without a break induces an awareness that can facilitate productive concentration at work and lift you into a realm beyond human understanding or hearing. The music requires an audience who must be willing to accept the spirit of the work and suspend their disbelief in order to receive its many rewards.

Sunday, March 18, 2012

Morgenstern Trio: Ravel, the Amateur Mathematician

P antoum poetical form—where each subsequent line changes function to become an antecedent line in the next stanza. Ravel’s music shows a love of the musical equivalent of this, playing on in-built ambiguities between antecedent and consequent to build up large-scale forms and at the same time hold our attention by letting the ambiguities surprise us.”
— Roy Howat, 1993.

T he Morgenstern Trio (Catherine Klipfel, piano; Stefan Hempel, violin; Emanuel Wehse, cello) have a uniquely intense, incisive style, as was abundantly demonstrated in their performance of Debussy, Mozart, and Brahms in a Music Alliance Series program Friday evening.

T he trio also have a characteristic, wry sense of humor, as befits the eponymous Christian Morgenstern, a German poet who was born in 1871 and died of TB in 1914.

T he Trio’s whole performance was superb—fresh; exciting; technically flawless—no surprise, given the many prizes they have received in competitions.

B ut even their encore—the second movement of Ravel’s piano trio, entitled ‘Pantoum’—delivered more, more than one routinely expects from an ‘encore’. The piano opens with the edgy, intense first theme, and the strings respond in double octaves. The short scherzo and trio ‘A-B-A’ structure makes for a perfect encore-length morsel. But there are ironies and meta-meanings in this piece. The repetitions and surface-level structures of the piece are not as straight-forward as they seem. The structure is like a ‘spell’ cast by a witch in a folktale. The rhetoric is one not of declamation but enchantment.

R avel wrote the trio theme in a completely different metre (4/2) from the scherzo (3/4), and the two time signatures co-exist—a kind of metrical dissonance that adds a lot of drama to an otherwise ‘dèpouiller’ (‘pared-down’, to the level of a children’s fairytale) narrative.

T he ‘piano-against-strings’, ‘4/2 vs. 3/4’ meter switches with the 4/2 that is initially in the piano part later swapped as the strings go from 3/4 to 4/2 and the piano returns to 3/4. The “competing meters” metrical dissonance persists for a long, long stretch: 168 quarter notes at 192 bpm, almost a whole minute’s worth.

T he ornaments are ‘reflexive’, as if they are compulsory, happenstantial features of how the music lays under the physical hand for each instrument, and as contrasted with a fully-deliberated, polished, composerly gesture.

T he reflexive, organic sounds wash over us, and we develop a suspicion of ambient, non-human order; a sense of diabolical, out-of-control natural forces at-work; a mix of awe and wonder and foreboding.

T he tension between the different meters—the different time percepts—inducing us to switch between an ‘ensemble algorithmic level’ and an ‘individual voice level’ depending on what is more significant or more commanding of our attention—is the primary reason why this ‘Pantoum’ movement is so exciting, I believe. In the languid section between numbers 11 and 15 in the score, the trio “sound grains” are large, and the listener attends to the ensemble sound and its algorithmic metrical structure.

B ut in the emphatic pizzicato passages, our attention is absorbed in the motion of the individual string parts, and we suspend attending to the algorithmic interactions associated with the metrical dissonance.

T he metrical dissonance persists and “lurks”, though. It is still within our awareness—and we feel apprehensive about the finiteness of our attention and the risks that might come true on account of shifting our attention away from the metrical dissonance “ensemble” features and onto the individual parts, much as a child hearing a fairytale experiences apprehension as her attention is absorbed by some new story development but the wolf is without doubt still in those woods and nightfall is not long off.

O ne may say that the number of functions is extremely small whereas the number of characters is extremely large. This explains the two-fold quality of a folktale—its amazing multiformity, picturesqueness, and color... and, on the other hand, its no-less-striking uniformity—its repetition.”
— Vladimir Propp, Morphology of the Folktale, p. 20.

I t captivates us—it fully absorbs us, this fairytale-like pantun of Ravel’s—all the way to its ending flourish. We are spell-bound, returned to a primitive state of wonder, feeling much like we felt as children listening to thrilling stories—ones we had never heard before—told to us by belovèd grandparent or parent. You don’t get this entrancing music experience from recordings—not really. You need to attend a “live” performance, like the especially fine one given by Morgenstern Trio Friday night!

L ass die Moleküle rasen,
was sie auch zusammenknobeln!
lass das Tüfteln, lass das Hobeln,
heilig halte die Ekstasen.

[Let race the molecules,
tossing together what compounds they may!
Let the random tinkering continue; let the atoms’ planes and dihedral angles,
Keep holy the ecstasy.]”
— Christian Morgenstern, Lass die Moleküle rasen.

[Lehmer Sieve, 1932, solving Diophantine equations]

D iophantine Pantoum where A=7, B=3

¹Lehmer sieve’s ribbon o’er Diophantine field;
²White paper slides to the tune of rods’ switches.
³Sieve sings congruences, linear aria concealed,
⁴Seeks solutions to be found in theory which, as

²White paper slides to the tune of rods’ switches,
⁵Ribbon infers nineteen B minus eight A equals one.
⁴Seeks solutions to be found in theory which, as
⁶A father’s age AB is one less than twice BA the son,

⁵Ribbon infers nineteen B minus eight A equals one.
⁷Polynomial conjecture, in Fermat’s margin centuries’ toil!
⁶A father’s age AB is one less than twice BA the son
⁸Yields seventy-three and thirty-seven, algebraically closed foil.

⁷Polynomial conjecture, in Fermat’s margin centuries’ toil!
³Sieve sings congruences, linear aria concealed,
⁸Yields seventy-three and thirty-seven, algebraically closed foil—
¹Lehmer sieve’s ribbon o’er Diophantine field.”

— DSM.

Thursday, March 15, 2012

Higher-Order Geometry: Murray Perahia and Chopin’s Polonaises

M usically, the most important consequence of the geometry is the following: since a nearly-even N-note chord occupies the same cross-section of the [metric] space as its transposition by 12/N semitones, such chords can be linked by particularly efficient voice-leading. Thus, nearly-even two-note chords are very close to their six-semitone transpositions; nearly-even three-note chords are very close to their 4- and 8-semitone transpositions; nearly-even 4-note chords are very close to their 3-, 6-, and 9-semitone transpositions and so on.”
— Dmitri Tymoczko, Geometry of Music, p. 97.

M y enjoyment of last night’s excellent concert by Murray Perahia was enhanced by paying special attention to the intervals and root-motions of the chords—especially in the Chopin pieces on the program.

A nd, while Dmitri Tymoczko’s ‘Geometry of Music’ has in the year since the book was published reaped some objections and a certain notoriety (David Headlam and Rob Schneiderman (AMS), among other commenters), I do feel that considering the quantitative and statistical properties of a musical work can help some of us to understand the work better, be moved more deeply by it, and, possibly, learn how we ourselves might compose music more successfully, or measure and figure out how something we have composed compares, for better or worse, to other beautiful and effective compositions.

F rom the score of the Polonaise Op. 26 No. 1 in C-sharp minor that Perahia performed last night, I transcribed a number of the intervals contained in the 138-bar, 414-beat-long piece. Like Tymoczko and others, I used a root-motion log-frequency representation of intervals in my array, so that distances of notes N-semitones apart are uniform in any octave. I then utilized the ‘phom’ package in the R system to examine the distribution of those intervals in topological S³ space. This relies on theory set forth by Gunnar Carlsson and coworkers at Stanford, on persistent homology. I had occasion to collaborate with Gunnar about 5 years ago on analysis of critical-care ICU timeseries data. Persistent homology computes topological invariants of filtered sequences of simplicial complexes, constructed from my transcribed Chopin Polonaise interval dataset. The relevance of this to music theoretic analysis is that conventional topological invariants are unsuitable for characterizing the geometry of music since they are simultaneously too sensitive, and too weak. They are too “weak” because of their homotopy invariance, such that the underlying harmonic/intervallic structure can be stretched in any way (as long as it is not ripped) without changing its homology groups.

L ots of additional empirical work would be needed, to accurately and adequately characterize just this one Chopin Polonaise, so beautiful and evocative as performed by Perahia. I leave that to the card-carrying music theorists. But, unlike Professor Headlam and others, I do think that such effort would be rewarded. As an amateur musician, I have no academic career in music theory to advance, no tenure review to worry about, no political axes to grind in my analysis and writing—posting this tiny, speculative blogpost as I am here, and pointing interested readers to a new open-source R package that might aid others’ endeavors.

I n summary, it is simply a deeply pleasurable thing for me, to roll up my own sleeves and bring novel empirical tools and concepts to bear and see what I can learn. And, having corresponded in years past with Dmitri Tymoczko several times by email, I truly believe that his aims and aspirations are as wholesome as this as well, not so cynical or bombastic as Schneiderman and others allege. For some of us, loving something magical like this Chopin music [or, alternatively, loving someone] means, among other things, persistently and deeply wanting and striving to comprehend it [or them], by numerical quantitative means as well as by subjective, qualitative means, that’s all.

B y the way, Gunnar Carlsson’s papers are very readable, if you care to visit the links to them below...

Saturday, December 24, 2011

Hans Zimmer & Co. save Holmes, entropically

I t’s the furiously melodic likes of Gladiator, The Lion King, Inception, Batman Begins, Dark Knight Rises, Pirates of the Caribbean, Kung Fu Panda, and Sherlock Holmes that’s elevated film music to a thing of rocking beauty, as Zimmer and his team have employed every oddball instrument and influence from Gustav Holst, Lebo M. and the sound of bat wings into percussively thematic adrenalin.”
— Daniel Schweiger, 2011.

I f you ask me, Zimmer’s score rescues Sherlock Holmes (and Guy Ritchie et al.) in the new ‘A Game of Shadows’ film.

Z immer and his composer-orchestrator colleagues at Remote Control Productions created a beautiful and varied score that augments the color and vista of the film, lending atmosphere, scope, and interest to what otherwise could seem predictable. Never gets in the way of what the script and imagery are doing, but never merely reinforces or sonically reiterates what’s been said or shown.

B ut more than this, I am really thrilled with the tempi and the rhythmic architecture of this score. I got the soundtrack and listened to it several times, measured the tempi bar-by-bar in each of the cues, and created a spreadsheet of the values (see jpeg above). I also put an EKG on myself and digitized my heartrate during each listening. Not only did my heartrate adapt to each of the tempo changes, but the heart rate variability (HRV, using the simple RMSSD metric) also synced with Zimmer’s music. Empirically, I suspect that that “N-of-1” experiment is indicative of why this music “works”—physiologic response “pulls” cognition, rather than the other way around.

S ee the book by Bacci and Melcher (link below) for more on phase-locking and rhythmic ‘entrainment’ of breathing, heartbeat, and other physiologic rhythms, syncing with music.

S ince I’d captured the tempo timeseries, I decided to do some other calculations on it, too. I used the open-source R system’s package ‘entropy’ (link below) to calculate the Miller-Madow, James-Stein, Tsallis, Chao-Shen, and Shannon/Jeffreys entropy values. The entropy of the timeseries of tempi for these 18 cues is H = 2.72... pretty high... indicating a substantial amount of variability/unpredictability/interestingness. If you do entropy calcs for “bad” or ineffective film scores (as I happened to do several times last summer), you get much lower values, H between about 1.10 and 1.90.

M ost film schools don't even mention music, much less compare examples of good and bad scoring.”
— Richard Bellis, 2006, p. 8.

T he cues’ titles (track-names) collect words and phrases from the screenplay that are cadential—perfect rhythmic-harmonic demarcations of the narrative arc and plotting. It’s clear that Zimmer applied an admirable amount of objectivity in the spotting session, to inject material that adds considerable depth to the character or the story without the material asserting itself as a vehicle for his own ego.

T he score (Die Forelle; The Red Book; Moral Insanity) makes Robert Downey Jr’s Holmes more alert and angry when he is facing Jared Harris’ Moriarty. The score (He’s All ‘Me! Me! Me!’) makes Jude Law’s Dr. Watson all the more hapless as he gets unwillingly caught up in the plot.

T he producers and Guy [Ritchie, the director] and Jude [Law, co-star] and I got together and tried to have it feel like an extension of what we think brotherhood is—the bickering and miscommunications are part of something that aspires to something higher.”
— Robert Downey Jr., Scotland BigIssues Magazine 05-DEC-2011.

A Game of Shadows’ stands as a valentine to the public-school buccaneer. It provides Ritchie with a licence to run wild with Gypsies, trade punches with cossacks, or just generally arse about in expensive hotels. It gives us anarchy as panto and global espionage in the guise of a homoerotic stag weekend.”
— Xan Brooks, The Guardian.

I n other words, Zimmer’s score truly ‘services’ the film’s narrative, neither over-writing nor under-writing. Naturally, given the big-action subject matter in this film, there are lots of huge orchestral cues. But there are more than half of the cues that are intimate, chamber-like pieces.

M any think that what we do is ‘Art’. I disagree. Music is an art form. Film music is a craft with its roots in art. Art is a form of self-expression, and the last thing a director wants is some composer coming in and expressing him/herself all over the director’s film.”
— Richard Bellis, 2006, p. 69.

F olk idioms in the Romani melodies (doina repeated-note gesture of lament), pentatonicism, Phrygian scale with the second and third scale degrees raised when ascending, and fraigish harmonic minor, flying-staccato, alla zingarese poco a poco accelerandos “hallgató/lassú-közép gyors-friss" (e.g., Kesergö or or verbunkos or csárdás style in ‘It’s So Overt, It’s Covert’; ‘Romanian Wind’) to breakneck speeds, acrobatic violin with pitches bending and glissing, and the tone growling and crying ... great colla parte tempo-leading.

T he Hungarian hallgató of the ‘Did You Kill My Wife?’ brass band is superb.

G ee, this soundtrack is an admirable thing! The tremolos begin slowly, and the accelerandi melt into the flourishes so that they sound like one gesture—far bigger ones than you imagined when they began. The playing and conducting are excellent throughout. Precisely nailing the tempo variations, yet sounding totally organic while remaining faithful to meter. Very, very nice!

Saturday, June 18, 2011

Nicholas Kitchen: Are Bach’s Sonatas and Partitas for Solo Violin Scale-Invariant ‘Fractal’ Works?

Nicholas Kitchen, NE Historic Genealogical Soc, 18-JUN-2011

W hen I was, I think, 8 years old, I first heard Bach’s Ciaccona, from the Partita No. 2 in D minor, BWV 1004. I could not stop listening to it. I wore out the record. Afterward, looking at that vinyl record across the room, you could see that that band on the record’s surface… could see that the grooves were completely gone.”
— Nicholas Kitchen, remarks at BEMF recital, New England Historic Genealogical Society, 18-JUN-2011.

T his page in the manuscript [of the Sonatas and Partitas], where the end of the Ciaccona is followed immediately by the beginning of the next Sonata, one right after the other, on the same page—this is what revealed to me that there is a ‘glue’ that Bach had devised that is holding these pieces all together. The multiple pairs and powers-of-2 in these pieces, the recurrences of palindromes and the inversions in these pieces—these are not [conveniences; mere expediencies]. All of these pairs form a great monumental ‘architecture’ upon which emotions can be expressed and better understood.”
— Nicholas Kitchen, remarks at BEMF recital, New England Historic Genealogical Society, 18-JUN-2011.

A lways when you listen to Nicholas Kitchen perform and/or speak, you will learn things that you would never have expected.

N icholas’s performance today of major portions of Bach’s solo violin works [Partita No. 1 BWV 1002; Partita No. 2 BWV 1004; Sonata No. 3 BWV 1005; Partita No. 3 BWV 1006] was a complete joy for us. And, amazingly, the acoustics were not bothered at all by the Stanley Cup-winning Boston Bruins and their more than 1 million boisterous fans jamming the streets just outside the recital hall.

K itchen vividly accounted for the correspondences among these works, noting the various plausible motivations for Bach’s G minor-B minor-A minor-D minor-C major-E major affective and intervallic progressions.

M ore than this, though, Kitchen discussed the ingenious sequences of meters and tempi, which constitute a Daubechies-like ‘wavelet’ Z-shape over the course of these pieces, performed in this order. Nicholas’s expressions were phrased in terms of geometric series (powers-of-2, and powers-of-3) in a way that is understandable for general audiences of all ages. And his explanations emphasized the sequences—the succession of structures that govern the architecture of these pieces—that is, he described things in a linear, narrative way that is the natural and preferred idiom when teaching or explaining things to people.

B ut it was clear from his gestures, and from the way that he plays these Bach works for solo violin, that Nicholas is also thinking of how these multi-scale structures look when the metric and harmonic time-domain patterns are transformed into frequency-domain by Fourier Transforms or Wavelet Transforms.

T he textural parallels—the sacred posture of the sonatas, juxtaposed with the equal/noninferior profane dance-tune posture of the partitas—occur on various scales, from ‘micro’ scales within a single measure, to ‘macro’ scales involving power-of-2 multiples of measures, to ‘hyper’ scales involving all 6 of these works. The works contain structures that are reminiscent of fractal scale-invariant symmetries where the smallest structure embodies features of the largest and all scales in between.

A perfect way to spend a Saturday afternoon! Bravo!

[James Nicolson and Board of Directors present Nicholas Kitchen with the 2011 CSEM Arion prize]

Friday, December 11, 2009

Tallis Scholars, Notes on Remembrances, Riding

T he oxymoron ‘aural image’ highlights the special nature of musical ‘exemplarity’ and notational representation. Notated music examples are doubly distant from the aural phenomena that they represent: the notation stands for sound, but, excised and framed as example, points back to a presumed whole that it represents (synechdoche) and also forward from the new discourse of which it becomes a part... In moving from an analogical mode to an iconic one, the example itself becomes exemplar—inducing an imitative realization on the part of the audience.”
— Cristle Collins Judd, Reading Renaissance Music Theory, p. 5.

C oncerts like the one that Tallis Scholars presented in Kansas City last night reconstitute iconic ‘things’ in their own likeness, by encompassing them as examples.

A s Cristle Collins Judd (Dean for Academic Affairs & Prof of Music Theory at Bowdoin) has written, examples are inherently ‘dependent texts’: they occur in the context of other/larger texts or discourses, which provide the framework by which we understand them and systematize them and recognize them and remember them.

T he holiday season and concerts that are performed during the holiday season are meta-exemplary? They abound in the recognizable. They leverage both tradition and memory to work their magic. As ‘exemplary’, they bring what’s ‘outside’ into the ‘inside’—inside the texts/discourses that they enlarge and annotate and illuminate as we listen and participate in the spell that’s being cast...

T here are, of course, discontinuities and rhetorical processes that aren’t discursive. The music; the program notes for the Tallis performance; the snippets of rendered music notation that we are able to review, etc.—are extreme in their ability to simultaneously provide streams of visual imagery and sonic stimuli along with the unfolding ‘text’.

W e delight in Josquin’s 6 usual Marian tropes—the delight made juicier by our knowledge that the Missa de beata virgine was later piously excised in the 22nd session of the Council of Trent, in 1562-1563.

I s my reveling at papal pique and Counter-Reformation vanity so wrong?

O h, the final cadences, enriched with thirds that Josquin did not put there. The mensuration of transitions resolved to clean, clear ‘sesquialtera’ completions that were not Josquin’s. The final notes’ durations lengthened or more notes added to tidy it up. Bare spots filled-in. ‘Tis a thing now of even greater beauty than it were in Josquin’s day...

I need to go to library and check out a copy of Sherr’s wonderful book (link below).

T his Tallis Josquin has got to be the most beautiful version of the Kyrie and Sanctus I have ever heard! Tallis’s Missa de beata virgine is a scholarly version, not a vehement or sentimental or valedictory one. I find the Tallis Scholars’ approach brings a new freshness to the piece that I can’t help but prefer. In particular, the soprano, countertenor, and alto parts have a lovely tone and some soul-stirring melodies above the lower voices. The friendly acoustics of the Cathedral of the Immaculate Conception lends extra warmth to the endeavor.

P hillips’s conducting—and the responsiveness of the ensemble to his direction—are the causes of the vibrancy and freshness. And just watch! The ‘vibrancy’ is explicit, demanded by Phillips’s hand gestures on many downbeats and on fermatas. So besides the notation and the ‘aural image’, we have the visual image of the conductor and the choir...

P hillips’s hands extend outward from his waist, oscillating in a diminuendo—the amplitude of the hand vibrations decays from 2 centimeters, peak-to-peak, to zero centimeters over a period of a second or so. The waveshape of the gestural decay is approximately exponential each time, with a time constant 1/λ equal to about 200 milliseconds. He does this throughout the performance; it is clearly a core idiom of Phillips’s personal conducting language.

A(t) = A₀exp(-λt)

T his is not a ‘bouncy’ gesture. Instead, it suggests exquisite ‘tautness’, controlled impulsion—an equine sort of ‘puissance’ being brought gracefully to rest. It reminds me specifically of a manner of applying ‘leg aids’ to the flanks of your horse when you are bringing your horse to an elegant halt in the dressage ring.

W hat I mean to say is, this choral ensemble ‘animal’ loves its work, and it aims to utterly please. And the choral ‘rider’ [Phillips] loves the suppleness and compliance he finds in the animal, and his subsequent hand ‘aids’ generously adapt to the eager suppleness that’s displayed by the animal.

W hat we see and hear, then, is this sublime unity of the joy of conducting and the joy of singing, the joys of riding and of being ridden. Spirituality through innocent, virtuosic carnality. Maybe that’s what the Council of Trent was worried about.

A usterity, logic, and Josquin’s complete command of compositional form and contrapuntal symmetry permeate [Missa de beata virgine], suggesting a purity of conception meant to please God in its perfection—not excite the passions of men and women.”
— Peter Phillips, Tallis Scholars Programme Notes, 10-DEC-2009.