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.