The Musical Matrix Reloaded

Contemporary Perspectives and Alternative Worlds in the Music of Beethoven and Schubert

by Barbara Barry (Author)
©2020 Monographs 372 Pages


The Musical Matrix Reloaded proposes a striking new scenario for the music of Beethoven and Schubert in the contemporary world. It draws on the theory of Multiple Worlds in physics, and on sci-fi and movies, as powerful contemporary models of alternative realities to explain radical features of interpolation, dislocation, and ultimately of return.
Confronting familiar assumptions about Beethoven’s and Schubert’s music as long-range consonance, the book proposes instead that musical action is predicated on an underlying disruptive energy, Nietzsche’s Dionysian disruptive background re-interpreted in the contemporary world. When it breaks through the musical surface, it dislocates continuity and re-routes tonal narrative into new, unforeseen directions. These unforeseen paths enable us to glimpse in Beethoven’s and Schubert’s music the beautiful, and often haunting, reality of another world.

Table Of Contents

  • Cover
  • Title
  • Copyright
  • About the author
  • About the book
  • This eBook can be cited
  • Foreword
  • About the Essays
  • Contents
  • Worlds
  • 1. ‘Many Worlds’ and Black Swans: Contemporary Models in Music, the Arts and Ideas
  • Contemporary Cosmologies
  • 2. Out of This World: Modeling Beethoven’s ‘Grosse Fuge’ in the “Bubble Wrap” Universe
  • 3. Is Anybody There? Texting in Schubert’s Musical Stratosphere
  • Imagination
  • 4. Invisible Cities and Imaginary Landscapes: Timely Meditations on Beethoven’s Quartet in C Sharp Minor, ‘Quasi una Fantasia’
  • 5. ‘The Matrix’ Revisited: A Reconsideration of Schubert’s Sonata Form Movements
  • Confrontation
  • 6. Utopia and Dystopia Revisited: Contrasted Domains in Beethoven’s Middle-Period F Major and F Minor Works
  • 7. Schubert’s ‘Quartettsatz’: A Case Study in Confrontation
  • Time
  • 8. Classicism in Retrospect: Op. 135 as Beethoven’s ‘Haydn’ Quartet
  • 9. Reflections on Schubert’s ‘Die Winterreise’: In Search of ‘Temps Perdu’ and the ‘Interpretation of Dreams’
  • Investigations
  • 10. In Search of the Enigma Code: Beethoven’s A Minor Quartet, Op. 132, and the Double Helix
  • 11. A Shouting Silence: Further Thoughts about Schubert’s ‘Unfinished’
  • Worlds Revisited
  • 12. Multiple ‘Personas’ in Parallel Worlds: Shakespeare’s Ghosts and the Return of Schubert’s ‘Doppelgänger’
  • Bibliography
  • Index

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1. ‘Many Worlds’ and Black Swans: Contemporary Models in Music, the Arts and Ideas

We have seen that the brain is a creativity machine. It searches for patterns amid chaos and ambiguity and it constructs models of the complex reality around us. This search for order and pattern is at the heart of the artistic and scientific enterprise alike. Eric Kandel1

In ‘The Road to Reality,’ Roger Penrose raised the need for scientific theory to forge powerful directions for the 21st century if it was going to reveal significant new discoveries of comparable import to those of the 20th century.2 Since contemporary ideas differ substantially from those of the past, they need innovative approaches to develop new theories. Such new approaches in turn provoke different questions, and in the attempt to answer them, reveal striking perspectives on events and existential contexts.

The value of new theories is not that they make truth claims, although after a time they tend to become ingrained in the intellectual landscape. Rather, they offer challenging ways to rethink existing premises of how the world works. David Passig writes that while convincing scientific theory most closely corresponds to facts, theory is not in itself truth but rather an explanatory scenario. In this context, he notes: “We need to remember, however, that scientific paradigms are useful in offering us mental patterns, not eternal truths.”3

Those mental patterns are subject to both external influences involving changing social and cultural paradigms, and an internal evaluation of problem-solving. Adopting new theoretical and philosophical approaches from a different intellectual sphere may yield surprising insights. Isaiah Berlin, reflecting on the agenda of ←17 | 18→philosophy, sees modeling as a central method of defining identity by providing a framework for explanatory criteria and proposing new intellectual constructs.4

One aspect of the contemporary intellectual landscape is the coexistence of theories that propose descriptions of reality from radically contrasted points of view. In physics, for example, concurrent with classical descriptions of time and space providing identifiable co-ordinates in the physical world, competing narratives in quantum theory describe highly unpredictable behavior at the micro level of existence in the indeterminate behavior of sub-atomic particles. As the prevailing conceptual model, a seemingly random substructure underpins patterns of existence.

There are some surprising, albeit logical consequences of quantum theory for contemporary existence, and by extension, for musical works. One is the parallel between the unpredictable “underworld” of quantum existence and the unstable “overland” climate of the postmodernist world, dislocated by terror attacks, economic collapse and natural disasters.

With unpredictability and chaos prevalent in so many areas of life and perception blurred by advertising images and computer graphics in a hologram of unstable identities, it is not surprising that perception of contemporary reality is often closer to the random quantum world than to any set of known co-ordinates. In times of personal anxiety or social disruption, even when forefronted by what Philip Roth has called “the unstable illusion of stability,”5 the randomness of underlying existence becomes effectively the model for lived experience. As part of the multiplicity of contemporary identities, artworks, past and present, nevertheless propose modes of experience different from everyday reality, even when they are in part referential to existential human dilemmas. Through innate structure and dramatic designs, they can be construed as alternative worlds, self-standing entities with their own rules of engagement.

Penrose proposed that reality can be described as conceptual worlds from three perspectives: mathematical, physical and mental. While each approach is autonomous in material and perceptual modality, it may nevertheless have connections to the others in terms of imagery and/or conceptual values. At a further level of connection, though, a construct in one of these conceptual perspectives may provide a model for another, so that imagery in one world becomes the basis for a reconfigured metaphor in another area of discourse. As instance, Gluck and Calzabigi crafted their classicizing agenda for opera in the 1760s and ‘70s by ←18 | 19→adopting the terminology of “moving architecture” to musico-dramatic realizations of the noble and statuesque. Plasticity of ideally represented human forms in classical sculpture and harmonious proportions of architecture are reinterpreted in the opening instrumental music in Act 2 Scene 2 of ‘Orfeo ed Euridice,’ which conveys the serenity of the Elysian Fields through rounded melodic contour and symmetrical phrasing. But an alternative agenda to idealized human beauty also impacted Greek sculpture. Heroic human forms could be equally contorted by rage and vengeance, as in the intense twisting movement of ‘Laocoön and his Sons’ in the Vatican Museum. The father and his two sons are strangled by writhing snakes in retribution by Poseidon for revealing the trick of the Trojan horse.


Fig. 1: Laocoön and his Sons by Rhodes sculptors Agesander, Athenodoros and Polydorus

This dark underbelly of violence in the ancient world, with its blood feuds and vengeance, has its counterpart in the preceding scene of the opera which takes Orfeo to the gates of hell and confrontation with the aggressive Eumenides, the vengeful Furies from the ‘Oresteia’.

In ‘The Birth of Tragedy from the Spirit of Music’ Friedrich Nietzsche identifies incipient violence that threatens to derail human action in his modeling à l’antique.6 Reinterpreting the opposed imagery of Apollo, the god of reason, and ←19 | 20→Dionysos, the god of inebriation and unbounded sexuality, Nietzsche depicts drama as polarized emotional conflict, locked between the intense striving for love and the downward pull towards death – in Freud’s terms, between Eros and Thanatos. Nietzsche envisages this experiential conflict as the powerful tension between the background’s Will-driven surging energy field that threatens to engulf “left-brain” activity like logical action and decision-making, and the Apollonian constraint of foreground structure through words and motifs that make drama – and music drama – possible.

At the interface of Penrose’s mathematical and mental worlds, the present musical model, in reinterpreting musical structures and journeys, draws on two aspects from theoretical physics. The first of these construes musical background as predicated on the quantum world, with its apparently random behavior of sub-atomic particles – a background of indeterminate behavior and random actions that nevertheless underlies the foreground of physical existence. While such highly digressive background that underpins ordered foreground structures appears counter-intuitive, on further reflection it may help explain complex areas of human and musical behavior. In many respects, the contemporary musical world – discontinuous, multifaceted and simultaneous – is a quantum world, characterized by unpredictable courses of action. The model of primal background energy, continually striving to push through and dislocate foreground order, reverses Schenker’s normative description for tonal repertory as a law-like underlying harmonic / linear Ur-structure that supports digressive foreground events ‘composed out’ at the musical surface. In Nietzsche’s terms, Schenker’s background structure is Apollonian, whereas the random background energy field in the present model is Dionysian. Its disruptive potential is held in check by foreground structure, but at stress points those constraints can, and do, rupture.

If Penrose is right that a referential framework can be identified in different disciplines as a shared climate of discourse, then the idea of a potentially unstable equilibrium between disruptive background forces and foreground constraint is present in, but not limited to, mathematical and musical worlds. It is the modus vivendi in conflicted societies struggling against oppressive political extremism, and can also be discerned in unpredictable economic forces where seemingly irrational movements cause both the rise and fall of market sectors in the globally linked world.

As well as these external manifestations of background Dionysian force-fields which have the potential to disrupt normal enterprise, the model has striking parallels with the structure of the mind. Beneath the neo-cortex’s rational faculties of order, reflection and decision-making are the disruptive drives of the old ←20 | 21→crocodile brain. In everyday social relationships, the conscious mind imposes essential constraints on the primitive brain’s libidinous desires; but, unfulfilled and often unvoiced, those repressed desires seek outlets in fantasy, dreams and art.

Despite the mind’s distinctive arenas of action, these mental ‘dramatis personae’ are not completely immured from one another. At the interface of consciousness, which Freud, in ‘The Interpretation of Dreams’ compares the portal of the mind to the archeology of a buried city, suppressed emotions from the subconscious cross those fuzzy boundaries, allowing the psychic substratum to emerge into conscious existence.7

The second aspect of modeling from quantum physics is another kind of intersection, the tunnel-like connectors between space-time zones known as “wormholes.” In particle physics they are infinitely brief links between domains, and on account of the extremely difficult conditions needed to create and, even more, sustain them, they primarily inhabit the realm of theoretical calculations. Rather than limited to largely hypothetical possibilities in the actual world, “wormholes” have become actual connectors in hypothetical worlds – in pop culture’s fantasy fiction and sci-fi movies, where “wormholes” are effective short-cuts between remote cosmic zones, like the jump into hyperspace to avoid enemy pursuit in the ‘Star Wars’ movies or that ultimate inter-terrestrial hiphop ‘The Hitchhiker’s Guide to the Galaxy’. In this lighter vein, physicist Alex Vilenkin calls “wormholes” “shortcut tunnels though space-time for intergalactic travel.”8

While “wormholes” are passageways between otherwise discrete realms of time, space and the imagination that have become permeable, they are not just connectors in the external world, real or fantasy, to the remote past or distant space. They are equally the means of recourse to other worlds of inner experience, in the seamless crossover to the past in dreams and memories, interspersed with fragmentary consciousness of the present. Proust’s recreation of internal imagery, as part of the multiple existences of individual human existence and the porous boundaries between them, stems from the evocation of such shifting layers of consciousness.

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The famous description of the madeleine, the cake moistened by lime-tea, is precisely such a connector between the present and the past. It opens up a whole inner world buried under years of oblivion which now springs to the surface of consciousness with vivid immediacy.

And suddenly the memory revealed itself. The taste was that of the little piece of madeleine which on Sunday mornings at Combray (because on those mornings I did not go out before mass), when I went to say good morning to her in her bedroom, my aunt Léonie used to give me, dipping it first in her own cup of tea or tisane….And as soon as I had recognized the taste of the piece of madeleine soaked in her decoction of lime-blossom which my aunt used to give me, immediately the old grey house upon the street, where her room was, rose up like a stage set to attach itself to the little pavilion opening onto the garden…10

The madeleine is the technique that opens the whole novel by connecting the weight and disillusion of present time to the richly textured past. Juxtaposing a dark present to images of love and longing beneath the surface, ‘A la Recherche du Temps Perdu’ is very much a ‘Winterreise’ world. Instead of a physical image that springs open memory, in many of the ‘Winterreise’ songs, slippage between the physical present of the frozen landscape and the inner world of memory is effected by the switch of tonal domains between tonic major and minor. In ‘Frühlingstraum,’ no. 11, the opening dream of colorful flowers in May is brusquely torn aside by the incursion of the dark, cold present with ravens screeching from the rooftops. Ending this abrasive intrusion is a fierce ascending A minor broken triad, ‘ff’. Across the ensuing silence, the pitch A is the connector to A major, ‘pp,’ as the dream world resumes, as longing for a spring that never comes.

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Ex. 1: Schubert, ‘Die Winterreise,’ no. 11. ‘Frühlingstraum’

A similar pitch connector between tonic minor and major occurs in ‘Der Wegweiser,’ no. 20, in the second part of the cycle, where the narrator has reached a decisive point in the journey through the revelation, near the end of the song, of where the journey is taking him. In the first verse in G minor, the narrator looks out at the rocky landscape ahead of him with dread, where there is, literally and metaphorically, no path, tonal direction slips from G minor to F minor and back.

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Ex. 2: Schubert, ‘Die Winterreise,’ no. 20. ‘Der Wegweiser,’ bars 10–9

At the end of the first verse, the repeated pitch G in the right hand of the piano changes the tonal direction into G major. Experiential questioning turns inward as he asks himself why he feels compulsively driven out into the wilderness. It is on this same repeated G that he finally sees the signpost of his final destination.

Such connectors between zones, remote not just in time but even more in expressive character, are not limited to vocal music but are just as powerful in instrumental music, often positioned at salient points of structural articulation. In the 1st movement of Schubert’s C major string quintet, D. 956, the second subject in G major, prepared by rhythmic forward momentum and ending on an emphatic G (bar 58) in cellos 1 and 2, is deflected in one of Schubert’s most magical moves. While cello 1 sustains the pitch G, cello 2 moves down chromatically to E flat for the second subject, in a connected but remote imaginary landscape.

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Ex. 3: Schubert, String Quintet in C major, D. 956, 1st movement, exposition

The E flat major section ends in G, using the Eb triad with F# as a German 6th in G major. After the E flat section repeats, with the cello parts now rescored in violins 1 and 2, the second resolution then remains in G, leading to the modified version of the second subject in G major. The whole E flat major episode can accordingly be seen as both “time out” in the movement’s expressive delineation and part of the contour of its tonal planning.

“Wormholes” as pitch connectors between “time out” temporal zones also occur in Beethoven’s instrumental writing. In the 1st movement of his Fourth Piano Concerto, Op. 58, the piano’s second entry, elaborating the first theme, opens out into confident triplet passagework that counterpoints the first theme presented by the winds, with forward rhythmic momentum impelled by ‘sforzandi’ on the second half of the beat.

Unforeseen from the point of view of logical process, this rhythmic momentum and sweep across tessituras is arrested by an unexpected interpolation in B flat major (bar 105 in Ex. 4). Poised ‘pianissimo,’ the B flat major section, belonging neither to what has preceded nor what will follow it, holds in suspension the movement’s time and action, its very stillness like music reflecting on itself from a remote distance. These planes of momentum and reflection are linked by a slender funnel of two pitches, D and F in flute and oboe, as the switch point into the stillness of the B flat major section. The interpolation lasts only six bars – four for the B flat reflection itself and two as transition back to the main action of the movement. Reinterpreting the pitch Bb as a chromatic 6th like the Schubert quintet example, this is followed by a bass G#, enhancing A as the dominant of D major in preparation for the second subject.

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Ex. 4: Beethoven, Piano Concerto in G major, Op. 58, 1st movement, exposition, bars 104–11

A similar procedure of pitch and temporal connection between contrasted material and expressive domains occurs in the slow movement of Beethoven’s 9th symphony, where the keys of its double variation form, alternating B flat major, ‘Adagio molto e cantabile’ in 4/4 and the¾ ‘Andante moderato’ in D major, are connected by a re-contextualized link. Towards the end of the first B flat major section, the outer pitches of the strings, F and A, (bar 23), frame the dominant 7th of B flat major with its implicit expectation of resolution. On the last beat of the bar, though, the bass line F rises to F#, bypassing expected closure, and switches onto the sharp side of the tonal spectrum. The bass F# realigns with the 2nd violins and violas, which unfold the beautiful D major theme, as seen in Ex. 5.

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Ex. 5: Beethoven, Symphony no. 9 in D minor, Op. 125, slow movement, bars 20–8

←27 |

Connecting disparate expressive domains through key, dynamic plane, contour and instrumental sonority, pitch-hinges may be seen as “wormholes” in musical structures that provide access to a remote domain by pitch linkage and/ or enharmonic reinterpretation.


ISBN (Hardcover)
Publication date
2021 (January)
Berlin, Bern, Bruxelles, New York, Oxford, Warszawa, Wien, 2020. 372 pp., 11 fig. col., 148 fig. b/w.

Biographical notes

Barbara Barry (Author)

Barbara R. Barry holds two degrees in piano from Trinity College of Music, London, and three in musicology and theory from the University of London, with PhD ‘magna cum laude’. She was on the music faculty at the University of London Goldsmiths’ College and the Radcliffe Seminars at Harvard, and was Chair of Music History at the Guildhall School of Music and Drama. Barbara Barry is the author of five previous books and many articles.


Title: The Musical Matrix Reloaded
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