Richard Goode’s Emergent Chopin

I    have a hard time with music I can’t hear and construe tonally. I suppose it’s a habit of ear.”
  —  Richard Goode, interview with Cheryl North, 2002.

R ichard Goode performed in Rockport today…

• Schumann: Kinderszenen, Op. 16
  
• Schumann: Kreisleriana, Op. 16
  
• Chopin: Nocturne in E-flat No. 2, Op. 55
  
• Chopin: Scherzo No. 3 in c-sharp minor, Op. 39
  
• Chopin: Waltz in A-flat No.3, Op. 64
  
• Chopin: Waltz in C-sharp minor No. 2, Op. 64
  
• Chopin: Waltz in F Major No. 3, Op. 34
  
• Chopin: Ballade No. 3 in A-flat Major, Op. 47

T he performance reminds me that the delicacy of Chopin involves not only the delicacy of touch but also delicateness of the mind. The Scherzo Op. 39, especially, illustrates this. The C# minor tonality is latent, deferred for a long time, 24 bars or so, depending on how you interpret some of the bars. This was composed during one of the periods when Chopin’s tuberculosis was exacerbated—a time when we naturally imagine his uncertainty about his health and what would come next was also exacerbated.

T   uberculosis was never confirmed, and the Chopin autopsy report has never been found. Both cystic fibrosis and alpha-1-antitrypsin deficiency are possible differential diagnoses that can explain his symptoms.”
  —  Ulf Kongsgaard, University Hospital, Oslo, 2011.

T he tension abates a bit when the original pattern is overcome by C# sonorities that are more persuasive both metrically/cadentially and tonally. The stable major harmonies that began the composition are transformed into contrapuntal chords, ones that evoke passing tones—naturals, flats, double-sharps—on the path toward a less-complex C#. The meaning of what’s gone before gradually emerges as the complexity recedes. The essayist’s/composer’s/performer’s ideas are not expounded so much as they’re ‘discovered’. (The Op. 39 Chopin descending D-flat major ‘sparkle’ figures in the upper register presage Ray Lynch’s celestial electronica by more than 100 years.)

I n other words, these ‘character pieces’ reveal the composer-as-discoverer or composer-as-kluger/tinkerer/experimenter, and stand in stark contrast to the usual notion of composer-as-omniscient-designer/architect.

G oode gazed out the windows at various moments during the Schumann, looking at the large waves crashing outside on the rocks. How could this scene not influence his next move? How could the liveliness of the waves not have an impact on the ‘Sehr lebhaft’! How could the excitement of the wheeling gulls not impart something extra to the ‘Sehr aufgeregt’!

O ne or two attendees asked whether the screen could be drawn, to darken the hall and “Could you please put a spotlight on Mr. Goode’s face?” David Deveau, MIT Senior Lecturer and founder and Artistic Director of Rockport Music, replied after the intermission that, no, no changes would be made: the lighting and the open view of the sea were precisely as Mr. Goode had requested. Goode finds the late afternoon light of the Atlantic stretching off to the northeast a fine and rewarding view to contemplate while performing these particular works.

I n summary, it was a performance that was intensely enjoyable, warmly recommended, with even more of the spontaneity and essayistic qualities for which Goode is so well known. Perfect for this complex, chilly, drizzly Sunday in October. The F-minor Chopin waltz and Bach’s Sarabande from the B-flat partita were Goode’s parting encore gifts to us all. We went away satisfied and grateful.

T he new Shalin Liu Performance Hall is very nice, by the way—acoustically as well as visually. The irregularities of the dry-laid stone walls on the main floor are enough to prevent any notable resonances or dead zones. And the multi-glazed windows and reception hall on the third floor provide excellent acoustic isolation. There was a 25-knot breeze blowing outside and 1-meter chop in Sandy Bay, none of which was audible inside the Shalin Liu hall. Delightful.

P .S.—Cystic fibrosis was only recognized as such in the 1930s [Andersen D. Cystic fibrosis. Am J Dis Child 1938;56:344-99] and alpha-1-antitrypsin deficiency was only discovered some 30 years after that. So the fact that Chopin’s death was attributed to “tuberculosis” is not surprising, given the minimal medical knowledge at the time.

I   have a photo of Richard Goode in my office. I have known Richard for 25, no, 30 years. When my son was small, he asked ‘Dad, is that picture Beethoven?’ And I laughed and replied, ‘No, but almost. As good as if it were Beethoven. He plays almost as if he were Beethoven.’ ”
  —  David Deveau, pre-concert remarks.

• Goode page at Frank Salomon Associates website
  
• Goode bio at Jay K. Hoffman Associates website
  
• Bedau M, Humphreys P, eds. Emergence: Contemporary Readings in Philosophy and Science. MIT, 2008.
  
• Blum D. Quintet: Five Journeys toward Musical Fulfillment. Cornell Univ, 1999. [Ch. 4 ‘Going to the Core’, pp. 112-151]
  
• Bunge M. Emergence and Convergence: Qualitative Novelty and the Unity of Knowledge. Univ Toronto, 2003.
  
• Corradini A, O’Connor T, eds. Emergence in Science and Philosophy. Routledge, 2010.
  
• Feltz B, et al., eds. Self-organization and Emergence in Life Sciences. Springer, 2006.
  
• Herer B. Tuberculosis and music: A case report and review of clinical, epidemiologic, and cultural factors. Med Prob Perf Artists 2005;20(3):131-8.
  
• Hoeckner B. Programming the Absolute: Nineteenth-Century German Music and the Hermeneutics of the Moment. Princeton Univ, 2002.
  
• Kongsgaard U. Frédéric Chopin and his suffering. Tidsskr Nor Laegeforen. 2011;131:707-10.
  
• Montecucco L, ed. Complexity and Emergence. World Scientific, 2003.
  
• Chopin Scherzo No. 3, Op. 39, score at IMSLP
  
• Rockport Chambermusic Festival website
  
• Society for Complexity in Acute Illness (SCAI)
  
• Performing Arts Medicine Association (PAMA)

Meta-complexity in Brahms’s Clarinet Quintet

A nthony Burton’s program notes for the London Phil’s ‘Chamber Contrasts’ series at Wigmore Hall emphasize how impressed Brahms was with the potential of clarinet, as a result of his hearing clarinettist Richard Mühlfeld perform in 1891. But Brahms composed this Op. 115 clarinet quintet within a few years of his death from cancer, a period when many of his friends and family died (his sister Elise, his brother Fritz, Elizabeth von Herzogenberg, Hermione Spies, Theodor Broth, Clara Schumann, etc.). This makes me think that the recursive, ‘re-considering’ structures in this quintet maybe derive more from the emotional impact of those events on Brahms—than from any scheme Brahms may have had, to create in Op. 115 a virtuosic clarinet showpiece for the great Mühlfeld.

L arge-scale variation comes from relationships between variations (the theme included) and how these relationships are united into a pervasive algorithm that encapsulates the entire set—that is, an operating system governing the entire set. In other words, these are not a mere series of independent objects and methods (scripts) that are expected derivatives of a parent object or class. They are a ‘network-based object-oriented OS’.

W hat I mean is, Brahms’s variations feel to me ‘network-based’, not ‘hierarchical’. It seems (to me) that Brahms was exposing larger-scale connections, and transforming his idea into a multi-domain network rather than a hierarchical structure with conventional ‘parent’ exposition classes and ‘child’ instantiations. The arrangement of variations involves pairs of diatonic pitch-class cells derived from the theme. But the textural differences that follow are like remote procedure-calls that cross-link the tension-producing structures within the variations’ designs. This gives the piece an attractive sort of ‘meta-complexity’.

I n other people’s analyses (links below), variation sets in Brahms’s multi-movement instrumental compositions are usually only moderately complex. Variation sets in interior movements often do not have full ‘closure’. In the variations in this Clarinet Quintet in B minor, Brahms suggests or ‘projects’ closure by recapitulating first-movement phrases. But the promised closure doesn’t come until the very end. It is as though there is a latent, suspended complexity that is irreducible until the very end.

T his gets me to thinking about how Brahms does this, and how we might devise similar structures and mechanics in new music. The ‘Kolmogorov complexity’ (links below) of a software program or script, or a piece of text or a musical composition, is a measure of the computational resources needed to specify the object. Kolmogorov complexity is also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity.

O ne of the appealing, intuitively plausible qualities of Kolmogorov complexity as a metric to characterize what I was hearing last night in the account of the Brahms clarinet quintet given by Robert Hill and his colleagues has to do with how the aggregate complexity goes, for large composite or ‘compound’ or ‘network’ or ‘cloud’ objects that are constituted from multiple smaller objects. For example, consider a compound object built up from objects X and Y. The Kolmogorov complexity of the two of them together K(X,Y) is:

K(X,Y) = K(X) + K(Y|X) + O(ln(K(X,Y)))

T his says that the shortest program that reproduces X and Y is no more than a logarithmic term larger than a program to reproduce X and a program to reproduce Y given X. This basically puts a quantitative ‘bound’ on the amount of mutual information there is between X and Y in terms of the Kolmogorov complexity.

T he amount of unresolved tension we feel in the inner movements in this Brahms quintet—and the intensity of the desire we feel for the eventual resolution of these tensions at the end—feels, to me, logarithmic. Maybe some future music theory PhD candidate will explore this notion properly and critically. For now, it’s happy enough for me to give you a few interesting links below and the glimmer of a potential reason why the complexities and proportions of this quintet seem so ‘right’ and so beautiful.

• Robert Hill page at Royal College of Music
  
• Robert Hill page at LPO
  
• Brahms clarinet quintet in B minor score (free download at IMSLP)
  
• Chain Rule for Kolmogorov complexity (page at Wikipedia)
  
• Wodowski clarinet mouthpieces (used by Robert Hill and others)
  
• Calude C. Information and Randomness: An Algorithmic Perspective. 2e. Springer, 2010.
  
• Dovern W. Polyphony & Complexity. Wolke, 2002.
  
• Downey R, Hirschfeldt D. Algorithmic Randomness and Complexity. Springer, 2010.
  
• Horne W. Review: The variations of Johannes Brahms. Music and Lett 2006;87;334-7
  
• Katz M. Templets and the Explanation of Complex Patterns. Cambridge Univ, 2009.
  
• Leister K. Brahms Clarinet Quintet. (Brilliant, 2007.)
  
• Li M, Vitanyi P. An Introduction to Kolmogorov Complexity and Its Applications. 2e. Springer, 1997.
  
• Littlewood J. The Variations of Johannes Brahms. Plumbago, 2004.
  
• Manno R. Brahms Clarinet Quintet. (Oehms, 2009.)
  
• Miller F, Vandome A, McBrewster J, eds. Chain Rule for Kolmogorov Complexity. AlphaScript, 2010.
  
• Narmour E. The Analysis and Cognition of Melodic Complexity: The Implication-Realization Model. Univ Chicago, 1992.
  
• Pacun D. Large-scale form in selected variation sets of Johannes Brahms. PhD Dissertation, Univ Chicago, 1998.
  
• Walton B. Brahms Clarinet Quintet. (Testament, 2007.)

Jeff Herriott: ‘Dissipation of a Thought’, Emergence of Another, Yet Another

I    ’m working now with some very high-pitched material... It’s seeming likely that I’ll end up with something for two soprano saxes, with some high multiphonics cascading on top of one another. Right now, the form is seeming like it will consist of some close intervals that slowly open up and out, with focus on some intricate tuning adjustments or quarter-tones. There will likely also be a few little ascending and descending lines as the piece progresses, and the whole thing will probably end up being close to 100 seconds. My plan is to take my thin electronics part and try to flesh out the ‘live’ part a bit more.”
  —  Jeff Herriott blog, 28-APR-2009.

T  he thing that troubles me about the analysis in Peter Kivy’s new book is that it seems to crystallize both music and text—holds them, for the sake of analysis, to be ‘static’ when in fact they are dynamic and ‘emergent’, particularly when the material is new to us. Implicitly, the analysis undervalues the processes of remembering or forgetting—of retrieval, of dissipation. In other words, the ‘ancient quarrel’ between literature and music seems to depend on our ignoring major aspects of neurobiology and how our cognitive processes handle qualitative complexity. Dependent, too, on our ignoring not just the emergent aspects of reading, playing, and hearing the piece, but the emergent aspects of the compositional process itself—embodied by remarks like the ones that composer Jeff Herriott makes in his blog (blockquote above).

T  his thought occurred to me as I listened to Jeff Herriott’s ‘dissipation of a thought’, right after finishing reading Peter Kivy’s book.

H  erriott’s compositions are often surprisingly textual—even the ones that are wordless, instrumental pieces. How can we know this? Well, text linguistics studies structural and formal variants of textuality, for which separate descriptive and ontological models are developed beyond surface-level syntax. A ‘text’ is defined as an utterance or communicative occurrence that meets [most of] seven criteria of text-ness (Beaugrande & Dressler, 1981):

• Expressive cohesion,
  
• Coherence,
  
• Intentionality,
  
• Acceptability/Consensuality,
  
• Informativity (conveying something or bringing about a change in [many of] the text’s readers/hearers),
  
• Situationality, and
  
• Intertextuality, including persistence and/or replication-publication.

[‘dissipation of a thought’, for flute, vibraphone, cymbals, crotales, voice and live electronics]


T  he structure of ‘dissipation of a thought’ meets most if not all of the seven criteria above. It is not only a ‘text’ in the sense of a persistent, published, replicable, intertextual document. It is coherent, cohesive, and localized to a situation or context. The intentions... may be ambiguous, but the evocative title is enough to focus our reception of the piece, beyond what the music itself does.

T  he hermeneutic ambiguity in the first section of ‘dissipation’ arises in its complex harmonies, paradoxically at odds with the piece’s ‘primrose path’ development. It also arises in Herriott’s ingenious manipulation and deviation from prevailing electroacoustic topoi. Examples include a deviation from deceptive cadences and voice-leading, as well as Herriott’s use of subtle, remote tonal relationships—between the tonal base of ‘dissipation’ and the modulation in later sections.

E  ven the ambiguity that we experience can be assessed from the perspective of the seven standards of textuality:

1. the musical text itself [‘dissipation’] as process and product, including harmonic relationships and voice-leading in cohesion and the relationships among underlying morphemes caused by the manipulated topoi in coherence (including novel, remote tonal relationships);
   
2. the participants’ intentionality (manipulation and deviation from topoi) and the recipients’ [listeners’, performers’] acceptability concerning various approaching interests rather than contextual understanding (the reasons for the perceived ambiguity);
   
3. the broader context of informativity (including the musical events based on the simulation of resolutions, the deception instead of fulfilling of expectations and the compensation for the deceptions as well as unexpected deviations from usual topoi), the situationality of the title ‘dissipation’ concerning its genre and intertextuality involving similarities to other mixed-ensemble electroacoustic compositions.

S  o how we interpret a piece while playing or listening should be decided not only by intuition but also by a contextual understanding of musical flow. We get clues from the application of rubato, for example; from the manipulation of expectation and deception in the management of rhythmic flows. Through the correlation of Herriott’s [explicit] ‘temporal management’ to his [implicit] ‘compositional plot’, the tension and relaxation of a composition become clear to us—become informative.

I    t may be crucial that some [sub-]systems stay constant or do not learn, whilst some must have ‘flexible-response’ characteristics, including learning and innovation and forgetting. Taken-for-granted movements of the hands and feet may be focused-on with uncustomary, acute consciousness in music, dance, visual art.”
  —  Jenks & Smith, p. 204.

T  o find a piece informative, we don’t need to posit a ‘persona’ or ‘personae’ who are engaged in a representational tableau. Nor do we need then to concede that a narrative piece that is not inhabited by personae is necessarily ‘program music’, a point that Kivy persuasively makes (Ch. 5). So here we have a case-in-point, this ‘dissipation of a thought’ by Jeff Herriott. Not that it doesn’t or couldn’t have personae represented by the parts; it could. My points are that we are not sure about this during our early engagements with it, and that our comprehension of the piece’s textuality ‘grows’ on us, emerges, is subject to ongoing revision as we absorb it.

P  eter Kivy is right in saying that there is nothing wrong with absolute music affording [empty] pleasure to the ear and mind—providing that and nothing more. Some music happily does precisely that. But it seems to me a mistake if we so narrowly define what a musical ‘text’ is in such a way as to rule out the possibility that it provides much, much more—define it so narrowly and statically as to rule out processes that routinely do happen to us… happen inside us as we perform or listen to absolute music, such as Jeff Herriott’s ‘dissipation of a thought’.

E  mergently, each thing leads to others.

O  ften [in a piece that is new to us, or that we have heard or played only a few times], we don’t appreciate what the meaning of a passage is until its successor is already upon us, or maybe not until much, much later. In some cases, our recognition of the meanings conveyed by a musical text takes a lifetime to emerge. How about you?

T   here is a kind of Gradgrindian mentality at work [when researchers report that listening to Mozart improves academic performance, etc], which must find a utility in every innocent pleasure, pleasure itself not being enough—perhaps a waste of time; worse still, harmful in some way or, at least the product of mere ‘amusement’, which Aristotle described as a form of rest, necessary ‘because we are not able to go on… and therefore not an end, since we take it as a means to further activity.”
  —  Peter Kivy.

• Jeff Herriott website
  
• Jeff Herriott at Sonict
  
• Jeff Herriott page at UW Whitewater
  
• Due East ensemble
  
• de Beaugrande R, Dressler W. Introduction to Text Linguistics. Longmans, 1981.
  
• Goldblatt R. Topoi: The Categorial Analysis of Logic. Dover, 2006.
  
• Jenks C, Smith J. Qualitative Complexity: Ecology, Cognitive Processes and the Re-Emergence of Structures in Post-Humanist Social Theory. Routledge, 2006.
  
• Kivy P. Antithetical Arts: The Ancient Quarrel between Literature and Music. Clarendon, 2009.
  
• Kramer R. Unfinished Music. Oxford Univ, 2008.
  
• Mazzola G. The Topos of Music. Birkhäuser Basel, 2003.
  
• Minati G, Abram M, Pessa E, eds. Processes of Emergence of Systems and Systemic Properties: Towards a General Theory of Emergence. World Scientific, 2007.
  
• Robinson J. Music & Meaning. Cornell Univ, 1997.
  
• Robinson J. Deeper than Reason: Emotion and its Role in Literature, Music, and Art. Oxford Univ, 2007.
  
• Schwarz D, Kassabian A, eds. Keeping Score: Music, Disciplinarity, Culture. Univ Virginia, 1997.
  
• Tarasti E, ed. Musical Signification: Essays in the Semiotic Theory and Analysis of Music. de Gruyter, 1995.
  

U    nfinished Music’ draws its inspiration from the riddling aphorism by Walter Benjamin: ‘The work is the death mask of its conception.’ The work in its finished, perfected state conceals the enlivening process engaged in its creation… We need to rescue the experience of absolute music from the clutches of that damning word ‘pleasure’.”
  —  Richard Kramer.

Relational Semantics: Lutosławski’s Beauty of Indeterminacy, Surprise of Proportion

A    fter 1961 Lutosławski worked largely independently of the fashions of the European avant-garde, refining and extending a compositional technique that produced, to use Bogusław Schäffer’s phrase, ‘stylistically the most independent works of modern European music’ ... Bohdan Pociej once described Lutosławski’s mature works in terms of four tendences: (1) the constant endeavour to achieve a ‘system’, to implement it, and to find one’s own personality [and social destiny] through it; (2) the harmonic, colouristic tendency—borne of a ‘Debussyan’ fascination with pure sound, grounded in a comprehensive [Cernerian] architecture of inter-related chords; (3) the poly-chronic tendency, reflected in a constant and intense inclination to organize ‘parallel plots’ and to split the composition into many interpenetrating levels and planes—to fill the musical space with multi-directional and multi-tiered motions; and (4) the dramatic tendency expressing itself in conflict, confrontation, struggle—in the various vicissitudes of form.”
  —  Steven Stucky, p. 107.

T he new recording of Lutosławski’s works for violin and piano, by Ariadne Daskalakis and Miri Yampolsky, has captured my imagination these past several days—and it may well capture yours as well.

• Recitative e arioso (1951)
  
• Partita (1984) [commissioned by Saint Paul Chamber Orchestra and premiered by Pinchas Zucherman and Marc Neikrug in January 1985 in Minnesota]
  
• Subito (1992) [his final completed composition, before his death in 1994 at age 81; written for the International Violin Competition in Indianapolis]

T hese are pieces of tremendous clarity, alignment, and focus. They are, in fact, astonishing for a sort of post-traumatic stress disorder (PTSD) sort of ‘urgent, combative hyperclarity’.


    [50-sec clip, Daskalakis & Yampolsky, Lutosławksi, ‘Recitative e arioso’, 1.6MB MP3]


    [50-sec clip, Daskalakis & Yampolsky, Lutosławksi, ‘Partita’, 1.6MB MP3]


    [50-sec clip, Daskalakis & Yampolsky, Lutosławksi, ‘Subito’, 1.6MB MP3]

L utosławski destabilizes the chromaticism in the violin part characteristic. Opposing this, the piano has vertically symmetrical chords and seems to offer respite and restore stability. Lutosławski’s early love of mathematics and the aesthetics of symmetrical are evident here—when the distances between adjacent tones in the chords are measured, one gets a numerical pattern of pitches that is invertible ... the same whether measured from the top to bottom or bottom to top.

T he developments and the transitions are beautiful, and their beauty and coherence leads us to imagine that there can be success and a happy conclusion, if only we can be sufficiently mindful and ‘good enough’. But the best and most diligent efforts can be for nought, and our grip on success can slip away. Passages that initially sound complete and self-contained turn out to be erodable or transitory ... stuff happens.

T he violin part struggles existentially. Life and its accumulated burdens take their toll, and the violin ends up (in ‘Subito’) chromatically down a half-step from where it started.

T he motoric chromaticism of the violin and the contrast provided by the piano are beautifully rendered in the Subito and the Partita.

H ear these three pieces together, one after the other on this disc. You will be impressed by Lutosławski’s skill in constructing relational algebraic expressions (Verhaltniss). Which part is the operator and which is the operand? Is the violin-piano matrix singular? Is the operation that they just played ‘commutative’?

T he size and prominence of a part are context-dependent and comparative qualities—you form an impression of them only in relation to other parts, or to the overall whole. Size and prominence are indeterminate—indefinite qualities that empower the performer/listener. They can increase or diminish without limit; there is interpretive latitude—so much latitude, in fact, that it may lead to PTSD-like anxiety, agoraphobia.

O ur judgment about the relation of parts arises both from the evidence that’s provided in a particular piece (or performance) and from custom. These make us used to specific proportions, such that wide deviations from them strike us as novel or exaggerated or contradictory. If we hear something that’s common or familiar, our expectations are already pre-conditioned and we tend to hear what we are expecting to hear. But if we hear something that’s unusual, or if a familiar pattern or relationship has a part that is relatively larger or smaller proportioned than what’s customary, then it awakens ideas about uncertainty and disparity.

A nd it’s not just the scope or extent or prominence of a part where we are awakened by relational contrasts. There can be semantic misrelations as well. Paradoxically little stimulation evokes impressions of despair, depression. Unexpectedly abundant stimulation evokes impressions of mania, agitation. The Recitative e arioso is dark, dark, dark. The year 1951 must have afforded Lutoslawski lots of dark moments to propel this piece—and Daskalakis plays as though she understands this from the inside-out. The bowing technic admits alternately of great energy [“This is how I was mistreated, and here is what I did to oppose them.”] and then of great vulnerability [“At last there was nothing more we could do, and we had to wait and see what the outcome would be.”]. The consonance of performance and writing is wonderful, an embodiment of good relations between the semantics of the composer and the gestures of the performers—Daskalakis and Yampolsky alike.

T he so-called ‘poly-agogics’ that Lutosławski uses are tastefully handled. Polyagogics are simultaneous accelerandos in one part and slight ritardandos in the other part. These microrhythms amount to a kind of polymeter—a transient complexity that confers extra tension on the piece. The Subito and the Partita have poly-agogic features, often associated with veiled or pensive, waiting, uncertain passages. I will need to get a copy of the score, to see how many of the poly-agogic rhythms are notated ones and how many of them are extemporized by Daskalakis and Yampolsky. Either way, their skill and faithfulness to what Lutosławski meant are to be commended—a fantastic Naxos CD.

A riadne is the new Dean of Strings for the Hochschule für Musik Cologne. She is also leader of the Berlin-based Ensemble Oriol and of the Manon Quartet.

• Ariadne Daskalakis website
  
• Daskalakis & Yampolsky. Lutoslawski: Complete Music for Violin and Piano. (Naxos, 2009.)
  
• Witold Lutosławski page at Wikipedia
  
• Witold Lutosławski page at Polish Music Center (USC)
  
• Attali J. Noise: The Political Economy of Music. Univ Minnesota, 1985.
  
• Cobussen M. Deconstruction in Music.
  
• Deleuze G. Difference and Repetition. Columbia Univ, 1995.
  
• Lerdahl F. Cognitive constraints on compositional systems. Contemp Mus Rev 1992; 6:97-121.
  
• Lewin D. Studies in Music with Text. Oxford Univ, 2006.
  
• Lewin D. Music, theory, phenomenology, and modes of perception. Music Perception 1986; 3:327-92.
  
• Rae C. The Music of Lutosławski. 3e. Faber & Faber 1999.
  
• Skowron Z. Lutosławski on Music. Scarecrow, 2007.
  
• Stucky S. Witold Lutosławski and His Music. Cambridge Univ, 2009 (reissue in paperback of 1981 biography).