FRACTAL AESTHETICS

The 'Flow' of Music

'Unlike poetry ... music and all energetic arts work
through time.'
(Music and Aesthetic ideals, p.13, 1984)

As Deleuze and Guattari wrote, 'It has been said that sound has no frame' (What is Philosophy?, p.189). By 'frame', they mean the interlocking artifacts which make up a composite whole. For example, the wall, window, roof, the ground floor must join together to create a house, just as the bricks must join together to create the wall. They argue that music perhaps 'embodies the frame even more powerfully' (p.189). This is because compounds of sensation arising from a musical stimulus 'equally possess sections or framing forms'. Of course, an entire symphony is not interpreted solely on its completion, it is subject to ongoing temporal blocs of cognition throughout its performance - these cognitive blocs arise from the differing musical frames inherent in the work itself. Such a conception of sound undermines the populist notion of a linear 'flow of music'. Deleuze and Guattari do not negate this notion; they incorporate it in their theory. A composer's objective is to use these differing frames of mmusical expression to create a theme, a continuity in the piece. The theme then is the overall composition or 'great refrain' (What is Philosophy?, p.191) - the unification of differing sonorous units. Music then is a deterritorialization of frame and theme - of closure and opening. The deterritorialization produces an ambiguity which, as Rapp suggests, stimulates the strange attractor in the listener's brain. Such stimulation accounts for music's emotive effect on the brain. I believe that music must reproduce ambiguities at differing scales - for example, at the scale of a movement, a passage, a bar - in order to create the intense stimulus provided by an artform. I shall illustrate my claim through an examination of Mozart's Requiem d-moll KV 626 (1791).

Requiem

In the sixteenth century, composers were obliged to use a formal layout when considering the Catholic High Mass. Mozart used the five principal musical parts: Kyrie, Gloria, Credo, Santus-Benedictus and Agnus Dei to underpin the Requiem's brief individual movements. These movements act as frames within 'the great refrain'. But this separation or 'closure' is off-set by Mozart use of text. Pius V's decision to prescribe a text for use in the requiem mass left little artistic freedom to the composer. Yet, Mozart uses the repetition of expression over wide spaces in the mass to highlight the linguistic theme, and to develop an overall consistency. The Domine Jesu begins with cantabile ease, but in bar 3 it is preceded by a sudden rhythmic change during the words 'Rex gloria' (Ex. 1).

Rhythmic change in the Domine Jesu.
Example 1 Rhythmic change in the Domine Jesu.

The rhythm reminds us of the trochaic homophony in bar 6 of the Rex tremendae (Ex. 2) on the words 'Rex tremendae majestatis':

Homophonous 'pulse' in the Rex Tremendae
Example 2 Homophonous 'pulse' in the Rex Tremendae.

As Deleuze writes, 'musicians compensate for their individuating closure by an openness created by modulation, repetition' (What is Philosophy?, p.190,). The repetition of Catholic worship and its evocation in the rhythm across movements contributes to the Requiem's theme - its consistency. Yet, both sections remain different in melody and tempo. This repetition then is not a simply cloning, but a repetition of self- similar properties. In this way the composer can deterritorialize the closure/opening dichotomy. This allows him to compensate for both the closure of movements and their opening onto the composite whole. Although Mozart's Requiem was incomplete on his death, analysis of its overall structure is not problematic because:

'There is no evidence to suggest that the overall layout of the Requiem
as completed by Sussmayr, departs in anyway from Mozart's plans.'
(Johann Micheal Haydn, p.132, 1979)

Restricted by technical conditions, Mozart was still able to bring a vocal texture to the mass abounding with aesthetic intensity. In bar 14 of the Recordare the alto solo begins the word 'Recordare'; bar 15 introduces a bass repeating the same word but his melody acts as counterpoint. Paradoxically, attention is drawn to distinctiveness (the closure) of each melodies as they overlap opening onto one another in bars 17: 're', 18: 'je' & 19: 'pi' (Ex. 3).

Deterritorialization of alto and bass melodies in the Recordae
Example 3 Deterritorialization of alto and bass melodies in the Recordae.

This vocal texture offers the listener a stimulus which is neither fragmented nor unifying and one time, both fragmented and unifying at another. Its ambiguities cannot be resolved, thereby creating reflectaphoric tension within each bar. This tension is increased as bar 20 introduces an abrupt key change (Ex. 4).

The unification of soprano-tenor (and alto-bass).
Example 4 The unification of soprano-tenor (and alto-bass). Tension between examples 3 & 4.

Yet, the progressiveness of such a key change (emphasized by the higher pitch) is offset, because soprano and tenor repeat alto and bass melodies. This has significant effect on the listener's compound of sensation (remember, it too possesses 'sections or framing forms'). Once confronted by a tension between alto and bass lines, the listener now groups (closes) alto-bass together in its own frame because they share the same key - a paradoxical 'opening' between alto and bass. Such closure-opening must apply to soprano-tenor too. The original tension is not diminished, far from it, rather intensified through another musical texture operating at a different scale in the piece. This process of intensification can be clarified:

'[The reason why] compounds of sensation become more complex is that
[a frame's] closure and shutting off ... is accompanied by a possibility of
opening onto an ever more limitless plane of composition.'
(What is Philosophy?, p.190)

I have illustrated, that deterritorialization operates at the scale of movement, bar and passage in Requiem. This complements the deterritorializing feature inherent in every musical whole, as previously explained. If the ambiguities generated by deterritorializations did not operate through these differing scales, the original stimulation of the brain's strange attractor to music would remain constant. This is because the music does not consist of other stimuli which would induce further complexification. In agreement with Deleuze and Guatarri, music which is structured by self-similair deterritorializations operating at differing frames is aesthetically intense. The artform is a whole, composed of potentially infinite frames (transversing all scales) and each frame consists of ambiguity caused by deterritorialization. Therefore, reflectaphoric tension is experienced by the listener in every frame, offering increasing stimuli to the brain. As the Requiem is performed, the brain's strange attractor responds by an ongoing complexification, it resists habituation. This potentially infinite complexification is actualized by a finite source: the Requiem is approximately 70 minutes in length. In summary then, I would argue that Mozart's artistic density relies on the successful composition of fractal-like, not linear, structures.

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