yet beautifully elegant in effect, where the clearly deterministic algorithmic thinking lends itself quite naturally to software implementation;

Algorithmic composition. Ligeti was
a major composer, admired by experts
and non-experts alike, and is gener-
ally not associated with algorithmic
composition; indeed, Désordre was al-
most certainly composed “algorithmi-
cally” by hand, with pencil and paper,
as opposed to at a computer keyboard.
As such, Désordre illustrates the clear
link in the history of composition to
algorithmic/computational thinking,
bringing algorithmic composition into
mainstream musical focus; and
tial data states is instructive and fun.

Figure 9. Foreground rhythmic pattern (quaver/eighth-note durations) of Désordre. 26

right hand:
cycle 1: a: 3 5 3 5 5 3 7
a’: 3 5 3 5 5 3 7
b: 3 5 3 5 5 3 3 4 5 3 3 5
cycle 2: 3 5 3 4 5 3 8
3 5 3 4 5 3 8
3 5 3 4 5 3 3 5 5 3 3 4
cycle 3: 3 5 3 5 5 3 7
3 5 3 5 5 3 7
3 5 3 5 5 3 3 4 5 3 3 5
cycle 4: 3 5 3 4 5 2 7
2 4 2 4 4 2 5
2 3 2 3 3 1 1 3 3 1 1 3
cycle 5: 1 2 1 2 2 1 3
1 2 1 2 2 1 3
1 2 1 2 2 1 1 2 2 1 1 2
...

left hand:
3 5 3 5 5 3 8
3 5 3 5 5 3 8
3 5 3 5 5 3 3 5 5 3 3 5 3 5 3 5 5 3 8
3 5 3 5 5 3 8
3 5 3 5 5 3 8
3 5 3 5 5 3 3 5 5 3 3 5 3 5 3 5 5 3 8
3 5 3 5 5 3 8
3 5 3 5 5 2 7
3 4 3 4 4 2 2 4 4 2 2 3 2 3 1 3 3 1 4
1 3 1 2 2 1 3
1 2 1 2 2 1 3
1 2 1 2 2 1 1 2 2 1 1 2 1 2 1 2 2 1 3
1 3 1 2 2 1 3
1 2 1 2 2 1 3
1 2 1 2 2 1 1 2 2 1 1 2 1 2 1 2 2 1 2
...

the middle of the piano outward, to the high and low extremes.

The foreground rhythmic process consists of slower-moving, irregular combinations of quaver-multiples that tend to reduce in duration over the melodic cycle repeats to create an acceleration toward continuous quaver pulses (see Figure 9).

The similarity between the two hands’ foreground rhythmic structure is obvious, but the duration of seven quavers in the right hand at the end of cycle 1a, as opposed to eight in the left, makes for the clearly audible decoupling of the two parts. This is the beginning of the process of disorder, or chaos, and is reflected in the unsynchronized bar lines of the score starting at this point (see Figure 10).

In Désordre we experience a clear, compelling, yet not entirely predictable musical development of rhythmic acceleration coupled with a movement from the middle piano register to the extremes of high and low, all expressed through two related and repeating melodic cycles with slightly differing lengths resulting in a combination that dislocates and leads to metrical disorder. I invite the reader to investigate this in more detail by downloading my software implementation. 12

 

Figure 10. Désordre. First system of score © 1986 Schott Music Gmbh & Co. KG, Mainz, Germany. Reproduced by permission. All rights reserved.

Conclusion

There has been (and still is) considerable resistance to algorithmic composition from all sides, from musicians to the general public. This resistance bears comparison to the reception of the supposedly overly mathematical serial approach introduced by the composers of the Second Viennese School of the 1920s and 1930s. Alongside the techniques of other music composed from the beginning of the 20th century onward, the serial principle itself is frequently considered to be the reason the music—so-called modern music, though now close to 100 years old—may not appeal. I propose that a more enlightened approach to the arts in general, especially those that present a challenge, would be a more inward-looking examination of the individual response, a deferral of judgment and acknowledgment that, first and foremost, a lack of familiarity with the style and content may lead to a neutral or negative audience