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