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Back from Bach

The Sound Barrier : Blog

31st March this year marked the 333rd anniversary of the birth of Johann Sebastian Bach. There has always been a good deal of debate about how much symbolism there is in Bach's music – there is undoubtedly at least some, like in descending passages that describe death and upwards passages that describe resurrection – but whether that extends to intricate uses of numbers and hidden messages coded within the music's structures, intervals, and proportions is a little more contentious. But, however that question might be answered, we at least know that Bach, as a deeply religious composer, often sought to represent aspects of the Christian notion of trinity in his music and so it seems at least a bit apt to give him a little more attention on this, his triple-three birthday, which just happens to fall this year in the middle of the Western Easter weekend – the Christian festival for which Bach wrote some of his most magnificent music.

Bach's place in music is widely recognised now, but it was not always like that and, after his death in 1750 and until Felix Mendelssohn began to revive his music in third and fourth decades of the 19th century, hardly anyone knew of him or listened to his work. That Mendelssohn-led revival sparked a new interest in Bach's music, but it is perhaps in the music of the 20th century that the real import and impact of his compositional style began to reap its fruits. It was in the 20th century that musicians began to discover that Bach not only composed wonderful music that deserved to be listened to forever, but also that there was still so much to be found in his very approach to composition, in the way he constructed his pieces, the way he ordered musical elements, and that there was still much to be created from the ideas he had planted.

That potential lay in the notion of music as something that, as well as sounding beautiful, can be beautifully organised. Its notes can be constructed in patterns and proportions that contain an integration of what one of the 20th century's greatest Bach admirers and re-inventors, Karlheinz Stockhausen, was to describe an essential kernel in his own music: the bringing together of mathematics and magic. It was music in which relationships within musical themes was as important as the relationships between them. The vertical and the horizontal in music were equally important, dynamic, as musical phrases formed exquisite harmonies and staggering counterpoints. A melody could be turned upside down, or played in reverse, and combinations of each could be imposed on top of one another in endlessly creative ways, full of mathematical complexity and yet sounding like the heavens and stars had composed it, wondrous, enchanted. At times the music could be mind-bogglingly complex and yet sparkling with pristine clarity at the same time. Music like a huge and intricate, yet delicate, spider's web, with its patterns within patterns, every thread miraculous.

Throughout much of the 18th and 19th centuries, and continuing for many composers throughout the 20th and 21st as well, this structural complexity and fertility tended to give way to more thematic approaches – compositions where two or three themes, usually contrasting, were developed more or less as complete units, and only occasionally would the structures within those themes, like the pitch intervals between the notes, become relevant in shaping the music. Music became more about the sentences and paragraphs than about the phonetics and words, whereas in Bach there was a greater equity amongst the little bits and the big bits, and amongst the relationships between them all. It created a rich and vibrant language with endless possibilities for construction and reconstruction. It was a language full of poetic richness, where words could be ordered and reordered, like building blocks that have been finely crafted to allow different combinations that can form countless perfect, balanced, complete shapes. For Bach, music was a language with fecund grammar, a mathematical formula with so many variables and values to shift and mix in different ways, always offering something new to say. It was pure science and pure art, like the physics of a jaw-droppingly beautiful clear night sky.

Anton Webern: Ricercata a 6 voci from Musikalisches Opfer (1934-1935)
Undoubtedly one of the 20th century's first and greatest champions of Bach's musical language and its respect for the intrinsic value of musical proportion and structure, is Anton Webern, who, of the three composers of the so-called Second Viennese School – Arnold Schoenberg, Alban Berg, and himself – was surely the most adventurous in his use of the serial technique with which they are all so intimately associated.

Webern took the twelve-tone technique of his colleagues beyond a system that organised music into an entirely pitch-based series of notes, to one that also integrated other musical elements into the serial structure: the durations and dynamics of the notes, for example. It was an approach that would be developed in much more complex ways in the early 1950s by the composers who congregated at the Darmstadt Summer Music Courses, led by visionaries such as Karlheinz Stockhausen, Pierre Boulez, Bruno Maderna and Karel Goeyvaerts, but the seeds for it were planted by Anton Webern in works that were typically very short, very economical in their use of complex musical ideas.

But Anton Webern himself owed his debt as much to Bach as to his Viennese friends, Schoenberg and Berg, not only through his admiration of the mathematical precision of Bach's music, reflected in serialism, but also of its extreme ingenuity of economy and clarity, even in pieces with the most complex interplay of musical material. This was part of what Webern too mastered so well, and his own debt to Bach was acknowledged most overtly in his 1935 arrangement of the six-voice contrapuntal work, the Ricercar, from Bach's Musical Offering. It is a beautiful and inventive resetting of Bach's original, which itself never specified any particular instrumentation. Webern takes fragments of the melodies, distributing them amongst different instruments, giving the work a continually changing, vibrant sense of colour that demonstrated not only a respect for what Bach had created, but also an ingenuity in timbrel structure that foreshadowed the serialist uses of timbre that would be employed by some of the composers who followed on from Webern, particularly Messiaen and Stockhausen.

Sofia Gubaidulina: Offertorium (1980-1986)
Russian composer Sofia Gubaidulina showed her own intense admiration for both Bach and Webern in taking this approach a step further in her violin concerto, Offertorium (1980 – 1986). In this piece, Gubaidulina takes the same theme from Bach's Musical Offering (which was itself composed not by Bach but by Frederick the Great, who presented it to Bach as part gift, part challenge, for Bach to weave his musical magic on), and opens her Offertorium with a distribution of the theme, at first almost note by note, throughout the orchestra, where the theme is heard in full except for its final note. Slowly the Bach theme falls apart as it is varied and truncated, with one of its notes removed from the beginning and the end each time. It becomes scarcely recognisable anymore until it returns again at the end, reconstructed note by note just as it had been deconstructed earlier, but now built backwards against the soft sounds of a Russian liturgical chorale as the solo violin soars in incandescent beauty into the sky, radiant.

The Offertorium is a work in which Gubaidulina pays her respects both to these composers who had inspired her so much as well as to the spiritual and religious themes that were, and still are, so important to her. It tributes Bach and Webern not only because of its use of the theme from the Musical Offering, but also because it draws on the invention of both composers in growing new music from a single musical seed, and, in her case, allowing it to blossom freely and beautifully from the barest of material. It is a piece filled with her characteristic individuality of instrumentation and orchestral colour – a work that is both sombre and shimmering, like colour reflecting off a dark lake. The recording I played on the show featured the violin of Gidon Kremer, from whom Gubaidulina composed the piece.

Cornelius Cardew: Mountains (1977)
Cornelius Cardew's Mountains was composed in 1977, quite late in his very short life and at a time when he had moved away from a lot of the experimental graphic scores and indeterminacy of the 1960s, of which his huge compositions Treatise and The Great Learning are the most famous. By the 1970s he had become almost totally committed to writing revolutionary songs, generally in support of the Maoist cause in which he had become so deeply involved. But his Mountains for bass clarinet is one of his few departures from this and reverts back to some of his earlier experimentalism as well as taking on board some overt nods to music's more classical and baroque traditions – the work is essentially a set of variations on the Gigue from Bach's 6th keyboard Partita. The variations adopt techniques that owe more than a little to Bach himself, as the theme is inverted or extended or shortened, creating a heap of opportunities for multiple themes to interact with one another played out in different registers of the bass clarinet, like horizontal counterpoint. But there is some vintage Cardew in there too, like pages of graphic notation that are used to guide different aspects of musical development of notated, re-ordered, pitches from the original Bach theme. The music is ultimately reshaped using a kind of combination of graphic indeterminacy and serial order, and the only reference to Cardew's Maoism is to be found in a quote from a poem by Mao, about mountains, at the beginning of the score.

Some excerpts from the score, along with some commentary about the piece, can be found on the website of Chris Cundy, whose live performance of Mountains I played on tonight's show.

It is, of course, not just through direct quotes from Bach that Bach's influence emerges in music. All of these pieces, even Webern's direct arrangement with its distribution of a theme into fragments from which unique colours and timbres emerge, owe to Bach for the concepts of musical structure that they adopt. It is the notion that music can be built from the structural codes within its core themes – proportions and relationships that can then act as a blueprint for the rest of the piece, or organisational systems, mathematically precise and yet creatively fertile, that guide music's architecture. It is the mathematics of Bach that so often makes his work unique and enables it to generate so many possibilities. It is this aspect, much more than the themes themselves, that was so exciting to 20th-century composers who were looking for new ways of organising music that departed from the old and now somewhat exhausted thematically-driven forms of the classical and romantic periods.

It is this interest in structure and form, and in building whole pieces from relationships within, rather than just between, musical themes that grew from Bach and flourished in such different ways in the final two pieces that I played on tonight's show.

Dick Raaijmakers: Vijf Canons (1964-1967)
Other than being called canons, there is nothing that sounds very Bach-like in the Vijf Canons (Five Canons) of Dutch electronic music composer Dick Raaijmakers. The pieces are, however, very Bach-like in their focus on musical structure where a small amount of material becomes the basis for layers of sound, superimposed upon one another, according to formal organisational rules. In these pieces the sounds are tiny clicks and impulses of electronic noise that are then assembled according to detailed and quite complex plans, patterns and matrixes. These matrixes are formed by the impulses being combined or divided in different patterns, and the combinations and divisions are then ordered in different ways to create each of these five short pieces which the composer calls 'mouse music' because they 'produce the same sort of "music" that mice make as the nibble and gnaw their way around: dry cracking sounds, no audible pitch, at best a strangled squeak, never too loud, more often too soft, never knowing what will happen, always busy and never stopping'. The structure might not be as transparent here as, say, in a Bach fugue where you hear a theme superimposed upon itself, but it is an indicator of the new directions into which these formal concepts, these intricacies of musical architecture, were being taken in the latter half of the 20th century. It was bringing a system of organisation and formalism to what might otherwise be heard only as chaotic, shapeless noise. It can be hard to remember that this was created in the mid-1960s – now half a century ago – drawing on musical concepts that had themselves grown from two and a half centuries earlier.

Karlheinz Stockhausen: KREUZSPIEL (1951)
Written when Stockhausen was only 22 years old, KREUZSPIEL ('Cross-Play') is one of its composer's earliest pieces and was often the one he cited as the first of his really serious works. The spirit of Bach is found not only in its focus on a set of structural rules to shape it but also in its religious symbolism where the image of the Christian cross is represented in the movements of notes between registers. Six high notes and six low notes continually interchange, at first six octaves apart, but gradually moving closer to each other, and then crossing so that, by time the process ends, about a third of the way into the piece, the six pitches that began in the low register are now heard in the upper register, and the six pitches from the upper register are now heard in the lower register. The pattern of the movement is a complex one, as different numbers of notes from each register are exchanged each time, and the notes that are left behind are then rotated into new and different pitch-rows, in their original register, while the other notes change registers. The process is transformed in the middle section into one where the movement is from the centre outwards, and then in the final section where the two processes occur side by side. The durations and dynamics that are assigned to each note shift as well, so that overall there is movement, in different instruments and registers, in patterns that move faster or slower, louder or softer, shifting direction like the pitches. As always with Stockhausen (as indeed with Bach also) these patterns and structures are not always observed strictly, and the rules are always broken if the music seems to call for something different. Stockhausen, like Bach, never allowed form to dictate his musical outcomes, but rather to guide it, shape it. The musical proportions and structural plans in Stockhausen, as in Bach, was rather like the genetic code of a person – determining much, but still leaving place for individual choice, and environmental factors, to change and steer things differently.

You can look at the form schemes of works like this, and any of Stockhausen's pieces, where he sets out these structural ideas, and you can be astounded by the ingenuity and invention of ideas within it, but you will still be a long way from knowing what the piece will sound like. This is how it was with Bach, too – you can read the densest and most detailed analysis of how a fugue or a chorale or a canon is constructed, but you still won't know how it sounds as music. This is where the magic becomes part of the mathematics.

Perhaps Bach's greatest gift to us is not so much that his music is so perennially wonderful to listen to, but that there is so much to learn from it. It teaches us how music can be something in which every minute bit, every little connection, every note that progresses from one to another, contains within it a possibility for something new. It teaches us the value of the bits and it urges us to keep creating something else with them. It sets out its formulas and codes and invites us both to colour them in and to write our own.

The boundless constructive energy of Bach might have begun 333 years ago, but it continues to generate innovation and freshness today, as new musical edifices emerge, beyond anything he could possibly have foreseen, but always within the endless enormity of what he imagined.

Don't forget to checkout the playlist and audio for details of the recordings and to listen back to the show!

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