Modernism and Mirrors

The opening movement of this piece uses a compositional technique which Gould refers to as 'Spiegelbild' (Mirror image). Each complete statement of the tone row is followed by the same material in retrograde. For example, the piece opens with four rhythmic groups of four. The first two groups of four contain the complete row, the third group is a retrograde of the second and the fourth of the first. Visually we could represent it something like this, with each number representing a semiquaver beat:

1234   5678   8765   4321

The entire first movement is constructed along similar lines.

The use of mirror image techniques is not combined to the literal mirroring of phrases in the first movement. The second movement is a canon in strict contrary motion. Whatever melodic interval is featured in the right hand, the left hand features exactly the same interval in the opposite direction.

Similar symmetrical principles can be found throughout Webern's works. The row for the second movement of the second movement of his Symphony Op. 21, for example is as follows:

F - Ab - G - F# - Bb - A - Eb - E - C - C# - D - B

If we count the number of semitones between each note we get the following:

3 - 1 - 1 - 4 - 1 - 6 - 1 - 4 - 1 - 1 - 3

From this it can easily be perceived that the second six notes of the row are formed from the retrograde of the first six, transposed by six semitones (This interval forms a comparison with the tonic-dominant relations central to tonal music).

The structure of the piece itself consists of a theme, followed by seven variations, and then a coda. The initial presentation of the theme consists of the row being played by the clarinet, while the horns and harp play an accompaniment derived from the retrograde of the row. The first variation consists of the row, transposed up a fifth to begin on C, stated melodically by the first violin. The accompaniment in the second violin is the retrograde of the row beginning on F#, the viola plays the inversion beginning on E, and the cello plays the retrograde inversion beginning on Bb. Each of the lines consists of the melody, followed by an exact mirror, but because the entries are separated in time and the phrases are of differing length, the overall mirror is not exact (The first violin entry begins the variation while the cello ends it, for example).

The fourth variation, which forms the center of the piece, has a kind of mirrored construction, which Webern himself makes much of in his lecture series The Path to New Music. In the same work he makes much of the analogy with the Sator Square:

SATOR
AREPO
TENET
OPERA
ROTAS

This material should be enough to show the importance that Webern placed on Palindromic procedures.

An analogy presents itself to the technique of another composer working at the same time, Olivier Messiaen. In his book 'The Technique of my Musical Language', Messiaen discusses the use of two related concepts - non-retrogradable rhythms and modes of limited transposition. A non-retrogradable rhythm is a rhythm which is the same whether read forwards or backwards. Their construction is exceptionally simple, the total rhythmic unit consists of a rhythm immediately followed by the retrograde and joined to it by a common central rhythmic value. The basic example given by Messiaen is Semiquaver-Quaver-Semiquaver.

Messiaen relates the principle presented by non-retrogradable rhythms in the rhythmic dimension to modes of limited transposition in the melodic dimension. A mode of limited transposition is a group of notes which can only be transposed a limited number of times before repeating itself. The principle of construction is very similar to the construction of non-retrogradable rhythms, the mode actually consists of a combination of a smaller group of notes and it's transposition, with the transposition beginning on the last note of the first group.

Apart from the fascination with palindromic principles of musical construction, Messiaen and Webern share the unfortunate fate of having had their works analysed as if the technical principles of it's construction was the point. One can point to two extreme points of view in the music of the second half of the 20th century by way of contrast. Milton Babbitt came increasingly to regard the musical score as the central point of focus, with compositional technique becoming a central concern, and audibility essentially irrelevant. Steve Reich on the other hand attempted in his early works to utilise only those technical means which are directly perceivable to the listener.

The principles of construction which Messiaen and Webern utilise are not directly audible to the listener. Nonetheless, for neither composer, the point of the music always remains on some level the aural result, and this aural result is always shaped by technique, whether or not the technique is directly identifiable. The listener unacquainted with technical discussions of 20th century music is unlikely to have heard the terms non-retrogradable rhythm or mode of limited transposition, much less be able to identify their use in a piece of music simply from hearing it. None the less, the use of these techniques obviously lends a certain quality to the music and is deployed in the service of an identifiable aesthetic conception:

"Let us think now of the hearer of our modal and rhythmic music; he will not have time at the concert to inspect the nontranspostions and the nonretrogradations, and, at that moment, these questions will not interest him further; to be charmed will be his only desire. And that is precisely what will happen; in spite of himself he will submit to the strange charm of impossibilities: a certain effect of tonal uniquity in the nontransposition, a certain unity of movement (where begginning and ending are confused because identical) in the nonretrogradation, all things which will lead him progressively to that sort of theological rainbow which the musical language, of which we seek edification and theory, attempts to be."

Webern himself seems to have harboured similar sentiments, emphasising in his comments to performers the importance of the expressive value of the music as opposed to it's formal and constructivist qualities.

This is not to deny the striking aesthetic dissimilarities between the music of Webern and Messiaen. Messiaen's music is undoubtedly incredibly rich and sensual, the product of French and Russian influences, particularly Debussy and Stravinsky, as well as the influence of his Roman Catholic faith, while Webern's music is often stark and austere, reflecting his German roots and the existentialist mode of his faith.

The use of 'mirror' techniques in the music seems to be incredibly suggestive, not only from the technical but from the higher theoretical point of view. A mirror image is something which is identical yet not identical. It is a unity on some level of identity and difference. The identity of identity and non-identity is of course one of the ways in which Hegel phrased his philosophical mission statement.

Hegel's discussion of these issues is of course difficult to separate from mysticism. In his Metaphysics Aristotle discusses the law of identity as a foundational principle and rages against the perceived absurdities which those like Heraclitus who deny must originally fall into. If a thing can be both A and not-A, then we lose any kind of foundation for discussion. What is to prevent us from such absurdities as saying that a tree is a boat, a sheep and a mountain range? Indeed, Aristotle claims that all that is recquired to refute Heraclitus is for him to speak. Those who deny the law of identity can only be taken seriously if they retain a plant-like existence.

The mystical identity of identity and non-identity, formulated in terms of the unity of opposites, of which latter day Marxists were to make so much of, is the principle by which he attempts to bring us out of the realm of reflective philosophical abstractions towards a vision of the transcendent freedom which he saw as being central to his vision of human nature or 'Spirit'.

Of course for Hegel there have been three primary modes through which humanity has come to consciousness of this freedom. Apart from philosophy, art and religion have also expressed this vision of freedom, although in which ways which are deficient when compared to philosophy.

One can begin then to form an understanding of the fundamental mysticism which underlies the music of Webern and Messiaen, the unity of identity and non-identity, a contradiction which drives towards a result which expresses the transcendent freedom of the human spirit.

The Twelve Tone System and Tradition

"I think it has to be a stupid blog, the rest are taken." - ZeroNowhere

Duly noted. Riffing on the theme of stupidity being doing the same thing multiple times and expecting different results, here's a riff on themes, more specifically thematic material (Get it? Riffing? Themes? Music?).

The twelve tone system is often seen as a 'revolutionary' turning point in the history of music. According to Howard Goodall, who has a degree from Oxford or something, and writes terrible music, and books justifying the existence of his terrible music, the tradition which developed out of Schoenberg's system has produced 'not a single piece in 100 years that any normal person could listen to.' This is high praise indeed, but we shouldn't get too excited yet.

I think the significance of the twelve tone system can be easily understood in the context of western music up to that point. The characteristic texture of that tradition is (or was) contrapuntal. Beginning with the medieval proscription of parallel fourths and fifths, the gradual recognition of the third as a consonant interval, and the developing preference for contrary motion, the initial development of polyphonic technique reached a peak in the music of the 16th century.

This 'modal' style of counterpoint is marked by very limited concern for harmonic progression. Typically cadences only occur at the very end of a piece, every other harmony is simply a result of the relationship between the melodic lines. This is why students since the early 18th century have been introduced to the study of counterpoint through the Palestrina style - it allows for a pure focus on the treatment of consonance and dissonance without adding the extra complication of having to produce 'correct' harmonic progressions except for in the final cadence.

The development of the sense of harmonic progression and key, referred to generically as 'tonality' or sometimes 'functional harmony', which was to remain a part of music until the first half of the 20th century, produced a change in contrapuntal style, reaching an original peak in the music of JS Bach. The sense of stability provided by 18th century tonality, as well as the facility provided by writing instrumental rather than vocal music, allowed for much greater freedom in the use of chromaticism and dissonances. In the most famous example, the B minor fugue from Book I of the WTC, Bach writes a fugue with a theme which uses all twelve notes of the chromatic scale.

By the end of the 19th century the development of chromaticism threatened to destroy the tonal foundation which it had grown out of. Beginning with Debussy composers rapidly began to abandon the rules on which the development of the previous 200 years of music had been based. In the Debussian style, any chord is allowed to follow any other chord, with the only consideration being, for Debussy at least, the beauty of the sound.

Schoenberg characterised the prior history of music as a gradual process of the emancipation of the dissonance. Audiences had been accustomed to hear more remote key relations and more elaborate dissonances as an integral part of musical style. But the dissonance was still treated as dissonance, that is, as something to be resolved.

The essential element of the contrapuntal style, whether of Palestrina, Bach or even Wagner, is the treatment of dissonances. The kinds of extended chords which we accept as an integral element of the style of Debussy would sound peculiar or even discordant if inserted at random into a piece by Mozart, because the Mozartean style treats those relationships as dissonances, not as free sonorities.

But what happens when, as in Debussy's music, chords other than the triad can be treated as consonant, and the momentum provided by the need for harmonic resolution becomes lost as all chords can be treated as equally good at any point in a piece as any other?

This is not to say that a contrapuntal style of sorts is not possible without the traditional methods of treating dissonance. In fact, if no interval or chord is considered dissonant or in need of resolution, it would seem that initially we are provided with the greatest possible contrapuntal freedom. We can write any melodic line against any other and the result will always be harmonically 'correct', because we have given up entirely any notion of harmonic correctness.

Yet in another sense the emancipation of the dissonance completely destroys the contrapuntal style, because the essence of that style consists precisely in it's treatment of dissonances. When dissonance ceases to be a concern of musical style, that means the death of contrapuntal art. No technique is required to arbitrarily combine any given melodic line with any other.

This is where the twelve tone system comes in. And although it was indeed at the time a 'revolutionary' conception, I think in one sense it is perhaps one of the most conservative developments in the history of 20th century music. I mean in this way - the twelve tone system is an attempt to rescue contrapuntal technique from the apparent abyss into which it seems fated to fall once musical style ceases to regard any combination of notes as dissonant.

It is well known that Schoenberg first developed the technique in the early 20's, a time which also saw the development of 'neo-classicism' and the 'new objectivity'. As Stravinsky and his cohorts sought to beat back the expressionistic excesses of romanticism and return to Baroque and Classical ideals of proportion and clarity of line, Schoenberg introduced the world to the twelve tone system with his Suite for Piano Op. 25. It might seem peculiar that such an innovation in technique should be introduced to the world in a piece which is formally modeled on a Baroque dance suite. But as we have already detailed this is one of the most conservative artistic 'revolutions' that could be imagined.

Schoenberg's pupil Webern is often regarded as the bridge between the style of the former and the music which emerged after WWII written by composers like Boulez, Stockhausen and Luigi Nono. Certainly Webern seems to have been the most enthusiastic advocate adopter of the twelve tone system. The music of Schoenberg and Alban Berg always has a fundamental tension between the new style and an immense nostalgia for the old, a nostalgia which would lead Schoenberg himself to return occasionally to writing tonal music. Webern's music is often praised or derided because he alone seems to lack affection for the romantic past.

And yet, Webern embodies the contradiction between revolution and reaction which is present in the Second Viennese school to the most extreme extent. He had gained his musical education under the tutelage of the musicologist Guido Adler, and had become enthralled by the musical technique of the renaissance contrapuntal masters. He alone threw himself heart and soul into the twelve-tone system because he saw in it the way back to the strict contrapuntal technique which he had so admired in the 15th and 16th century masters.

Hopefully this gives a general idea of the significance of the music of the Second Viennese school. Generally, as I have said, it is music which in it's fundamental aesthetic should give no issues to the listeners of Classic.fm. That it has not made headway here is I believe a simple matter of historical contingency. I have no doubt that in a few years hence pieces such as this will make their way into the Classic.fm hall of fame, once it is seen correctly as a bulwark against modern degenerate forms of music: