Aleatory.

A term applied to music whose composition and/or performance is, to a greater or lesser extent,
undetermined by the composer.
1. Introduction.
2. History.
3. Aleatory composition.
4. Mobile form.
5. Indeterminate notation.
6. Graphics.
7. Texts.
8. The role of the performer.
9. The aesthetics of chance.
PAUL GRIFFITHS
Aleatory
1. Introduction.
As defined above, the term aleatory (aleatoric is an etymological distortion) applies to all music: it is
impossible for a composer to prescribe every aspect in the realization of a composition; even the sound
result of a tape playback will depend on the equipment used and the acoustic conditions. However, the term
is usually restricted to music in which the composer has made a deliberate withdrawal of control, excluding
certain established usages which fall within this category: for example, keyboard improvisation, the
cadenza, the ossia, the ad libitum, unmeasured pauses, alternative scorings and the provision of sets of
potentially independent pieces (e.g. the Goldberg Variations). Three types of aleatory technique may be
distinguished, although a given composition may exhibit more than one of them, separately or in
combination: (i) the use of random procedures in the generation of fixed compositions (see 3); (ii) the
allowance of choice to the performer(s) among formal options stipulated by the composer (see 4); and (iii)
methods of notation which reduce the composers control over the sounds in a composition (see 57). The
liberty offered by these various means can extend from a choice between two dynamic markings to almost
unguided improvisation. Some theoretical considerations and practical consequences are outlined in 89.
Aleatory
2. History.
Until the mid-20th century Western composers were constantly seeking notational developments that would
enable them to determine sounds with greater exactness, an attitude entirely opposed to the aleatory. There
were, however, some trivial examples of aleatory music in the 18th century, when schemes were published
for generating simple pieces in response to the results of dice throws. These games usually left only one
aspect to guided chance: the ordering of bars supplied with the scheme, for instance, or the melody to be
placed over a given rhythmic-harmonic pattern. Mozart and Haydn were sometimes claimed as authors, but
probably without any more than commercial justification. One might also consider the art of keyboard
improvisation as a precursor of aleatory music, but here the creator and the performer are identical; once an
improvisation is published for performance by others, it has to be respected as much as any other printed
score. In most aleatory music, on the other hand, the creator provides a score which gives a degree of
freedom to any performer. Similarly, other improvised musics, such as jazz and folk traditions, were not
initially the most important influences on aleatory music.
The first composer to make a significant use of aleatory features was Ives, whose scores include
exhortations to freedom, alternatives of an unprecedentedly important character, and unrealizable notations
which silently invite the performer to find his own solution. From the 1930s Cowell followed Ivess lead in
such works as the String Quartet no.3 Mosaic (1934), which allows the players to assemble the music from
fragments provided. He used other elastic (his own word) notations to introduce chance or choice into the
performance, occasionally instructing the performers to improvise a certain number of bars or ad libitum.
His sometime pupil Cage began to use what he called chance operations in composition during the early
1950s, notably in the Music of Changes for piano (1951). At first Cages work had most influence on his
immediate associates: Feldman wrote a number of graph pieces, such as the Intersection and Projection
series, in which notes are replaced by boxes, determining pitch only relatively; and Brown abandoned all
conventional notation in, for example, December 1952, consisting of 31 black rectangles printed on a single
sheet.
European composers were more hesitant in taking up aleatory techniques. Such early examples as
Stockhausens Klavierstck IX (1956) and Boulezs Piano Sonata no.3 (19567) allow the player no more
than limited freedom in the ordering of composed sections. By this time Cage had gone much further in
abandoning the control exercised by the composer, or even the performer(s), reaching an extreme point in 4'
33'' (1952), whose only sounds those of the environment are quite unpredictable. About 1960 purely
verbal scores were introduced by LaMonte Young and others, and the following decade saw the pursuit of
aleatory methods to a wide range of ends throughout the world. Composers such as Henze and Lutosawski
used aleatory incidents in otherwise determined compositions, while Rzewski, Globokar, Stockhausen and
others produced scores that give only a few specifications to stimulate improvisation.
After an explosion of interest in the late 1960s, coinciding with a revolutionary period in Western culture
generally, aleatory music became a dead or at least dormant issue. Stockhausen returned to conventional
notation in his Mantra (1970). Boulez began to write fully determined works again, and even to rescind
some of the freedoms of earlier pieces, such as his Improvisation sur Mallarm III (1959), whose revised
score, made in the 1980s, removes alternatives of material and flexibilities of ordering. And though Cage
remained true to non-intention, even he went back to staff notation in Cheap Imitation (1969) and many
later works. A kind of superficial looseness (represented, for example, by ad libitum repeats of figures, or by
time-space notation, in which duration is determined by length on the staff) remained as part of the lingua
franca of moderate modernism, and improvisation continued as the mainstay of experimental music. But
Cage's later music is unusual in the period for the precision of its invitations to chance.
Aleatory
3. Aleatory composition.
As here defined, aleatory composition involves the use of random procedures in determining musical aspects
that are to be notated; unless other aleatory techniques are also used, the resultant score is no less fixed than
a conventional composition. Chance procedures in composition have been most fully and diversely
exploited by Cage. In producing the Music of Changes, for example, he tossed coins to decide how he
should make choices from charts of pitches, durations, intensities and other sound aspects, deriving his
chance operations from the I Ching, the Chinese book of changes. Similar methods were used in
assembling Williams Mix for tape (1952) and in notating the parts for 12 radio receivers in Imaginary
Landscape no.4 (1951). (The latter work is inevitably unusual, in that the sounds heard in performance are
out of the control of both composer and players, depending on the broadcasts that happen to be received.)
Other random techniques employed by Cage include placing notes on imperfections in the music paper
(Music for Piano, 19526) and using templates drawn from maps of the constellations (Atlas eclipticalis,
19612). An example of random composing combined with other aleatory features is Cages Winter Music
(1957), in which from one to 20 pianists may use any quantity of the chance-composed score.
Atlas eclipticalis is one of the few Cage scores from between the mid-1950s and the end of the 1960s to use
traditional notation. When Cage returned to such notation, it was with new chance procedures, such as the
use of time brackets to define not specific durations but rather the intervals during which sounds must start
or stop.
Xenakis's principle of stochastic composition is different. In such works as ST/4 for string quartet (1956
62), he used a computer in producing music modelled on stochastic processes, where events on the smallest
scale are indeterminate though the shape of the whole is defined. Thus randomness is introduced as a
necessary part of a willed product, and Xenakis retained the right to modify the computer result. Few
composers other than Cage have made much use of true aleatory composition.
Aleatory
4. Mobile form.
By contrast with Cage and his chance operations in composition, other composers have avoided introducing
any randomness into their composing or notation, but have permitted the performer some flexibility in
realization by means of the provision of alternative orderings. Sometimes, as in Stockhausens Klavierstck
XI, the player is instructed to pick from the alternatives on the spur of the moment; other works, such as
Boulezs Piano Sonata no.3, suggest a more considered choice. The sonata is in five parts which may be
played in any of several permutations, and each part contains sections which may be variously ordered
and/or omitted. Fig.1 shows the Troisime texte, one of the tiniest satellites of Boulezs mobile-form
Structures II for two pianos (195661); note that the ordering of events is to some extent free, and that
durations and dynamics are variable. Other notable works of mobile form include Boulezs Pli selon pli for
soprano and orchestra (195762), Stockhausens Momente for soprano, chorus and instruments (19624)
and Pousseurs fantaisie variable genre opra Votre Faust (196067), which draws the audience, too, into
the decision-making. All of these works provide comprehensive rules for the assembling of a performance,
whereas when Cage used formal variability, as in Winter Music or the Concert for Piano and Orchestra
(19578), he left options as open as possible: any amount of the solo part of the Concert may be omitted, as
may any or all of the orchestral parts, and the piece may be performed simultaneously with others by the
composer.
Aleatory
5. Indeterminate notation.
The types of aleatory music so far described use conventional notation to determine sounds, although, in
compositions of mobile form, new signs may be necessary to guide performers in choosing a route. Many
composers have introduced new notations which render the sounds themselves indeterminate, frequently by
abandoning traditional signs for graphics or texts, each of which is considered below. But it is possible to
use conventional notation in an indeterminate manner. An early example is Stockhausens Zeitmasse (1955
6), whose tempos depend on the physical capacities of the five wind players: the duration of a single breath,
or the fastest speed possible.
The composer can also allow flexibility in the interpretation of conventional symbols by giving alternatives
or by specifying sound aspects in only relative terms. Alternative tempos, dynamic degrees and so on have
been extensively used by Boulez. Relative notation has often been employed to specify a more or less
narrowly defined register rather than a determined pitch, particularly in vocal music. Boulezs Structures II
contains an analogously imprecise notation of durations (fig.1), and Boulez has frequently specified a range
of tempo rather than a definite figure, so setting limits to a fluctuating rubato.
Greater indeterminacy is introduced, still with conventional notation, when performers are asked to
improvise on the basis of given pitches or rhythms, to interpret a given pitch sequence with any rhythm, to
interpret a given rhythm with any pitches, and so on. All these possibilities have been used by composers as
different as Kagel and Lutosawski.
The most systematic use of newly invented symbolic notations is to be found in Stockhausens process
compositions, which specify how sounds are to be changed or imitated rather than what they are to be. The
first of these compositions was Plus-Minus (1963), whose title indicates the two principal signs that
Stockhausen introduced for these purposes: the plus sign means that a sound is to be increased in some
parameter with respect to some preceding sound (i.e. it may be louder, higher in pitch, longer, more
subdivided etc.), and the minus sign has the reverse significance. Fig.2 shows this notation in a fragment of
Spiral for solo performer (1969). The number of plus and/or minus signs in any event indicates the number
of parameters to be changed; other signs refer to articulation (e.g. POLY indicates a polyphonic event).
Aleatory
6. Graphics.
Graphic notation which may be distinguished from the preceding by the fact that it signifies, if at all, by
analogy instead of by symbol has been employed to supplement conventional notation where the latter
proves inadequate. For example, the shape of a glissando (i.e. the variation of pitch with time) can be
shown by a curved line on a staff; though the aleatory character of such notations is an inevitable
concomitant rather than a deliberate addition. A more truly aleatory use of graphics occurs in Stockhausens
Zyklus for solo percussionist (1959), a compendium of quasi-conventional graphic notation used in
conjunction with traditional signs. Fig.3, from Haubenstock-Ramatis Tableau II for orchestra (1970), shows
some examples of this type of graphic notation.
Alternatively, graphics may be used as a total replacement for standard symbols, as in Browns December
1952. Logothetis, Cardew (in Treatise, 19637) and other composers continued in this direction, raising
graphic notation to the level of visual art, but beyond the level of musical intelligibility, since such scores
often provide the performer with little or no information as to how the signs are to be interpreted, and the
possibilities for sound realization are exceedingly diverse. Fig.4 is an example of graphic notation from
Cage's Fontana Mix (1958), a score consisting of transparent sheets to be superposed, and used by the
composer originally to make a tape composition. In this case, although the notation looks enigmatic, the
rules given with the design offer exact (though chance-determined) means by which sounds are to be chosen
and assembled.
Aleatory
7. Texts.
Like graphics of this latter sort, verbal texts can be used to give the performer a very large degree of
freedom in determining both form and content. The text may be a straightforward instruction for action
often a far from conventionally musical action, as in Youngs Composition 1960 no.5, whose principal
requirement is Turn a butterfly (or any number of butterflies) loose in the performance area. Other text
scores are more inscrutable; Youngs Piano Piece for David Tudor no.3, for example, consists of the text:
most of them were very old grasshoppers. More usually, texts have been used to give a more or less clearly
stated basis for ensemble improvisation; notable examples include Rzewskis Love Songs (1968) and
Stockhausens Aus den sieben Tagen (1968).
Aleatory
8. The role of the performer.
Aleatory music implies a quite new inventive role for the performer, and its evolution has been closely
linked with the technical innovations and accomplishments of individuals, such as Tudor or Boulez, and of
ensembles.
In some respects, compositions of mobile form introduce the fewest new problems, since the material can be
fully composed. It is significant that the earliest European efforts in this direction Stockhausens
Klavierstck XI and Boulezs Piano Sonata no.3 are each for a solo player, who is in a position to make
spontaneous or rehearsed decisions about the ordering of the music. When more performers are involved
and when the composer does not want an anarchic result, either the performers must make all decisions in
advance, as in Stockhausens Momente, or else the composer must supply a system of cues and other
signals. This was the procedure adopted by Boulez in writing for two pianos (Structures II), for chamber
ensemble (explosante-fixe ) and for orchestra in several works (Pli selon pli, Eclat, Domaines) which
expand the conductors function.
Where the notation, or lack of it, renders the music still more indeterminate, the performers responsibility
becomes weightier. It is often difficult for the composer to make his intentions clear without hampering the
player more than he wishes, so aleatory scores have frequently to be understood against the background of a
composers more determinate work or within an implicit cultural milieu; but a performer may choose to take
the score out of that background or milieu as, for example, when the English composer Gavin Bryars made
a realization of Stockhausens Plus-Minus with fragments from Schuberts C major String Quintet and a pop
song and so draw attention to the new division of labour between composer and executant.
The common reaction to this problem in the 1960s was the establishment by composers of performing
traditions within their own ensembles, of which the Sonic Arts Union (consisting of the four composers
Ashley, Behrman, Lucier and Mumma) and the Stockhausen Ensemble were prominent. Such groups were
able to develop collective qualities of reaction previously rare outside long-established string quartets, and
composers in turn made use of these group characteristics. Sometimes this meant that very little had to be
specified in the score Stockhausens Aus den sieben Tagen texts represent an extreme case. Other
composers welcomed the extreme variability with which minimally notated scores may be interpreted, and
made no attempt to form a tradition of performance. Their interest was, rather, in exciting the players to
awareness of their own and their colleagues potentialities, a position exemplified by Wolffs work.
Some performing ensembles dispensed even with this unassuming stimulus from a composer, and engaged
in free improvisation, though most continued to play composed music as well. Among the groups which
had some success in this field were Musica Elettronica Viva (Rzewski and others) and New Phonic Art
(Globokar and others). It was only at this point that other improvisatory musics had much direct influence
on aleatory practice in Western art music, and some players, among them Michel Portal and Barry Guy,
involved themselves concurrently in jazz and free improvisation.
Aleatory
9. The aesthetics of chance.
The introduction of chance into a work of art undermines the notion that creation requires, at each moment
and on every level, a definite choice on the part of the artist. One implication of Mallarms Un coup de ds,
a work that had a great influence on European aleatory composers, is that each creative decision gives rise to
a multiplicity of possible continuations, and in the projected Livre he was to provide for alternative
continuations to be realized. But in general the Western work of art was, until the mid-20th century,
supposed to have an ideal identity, and, in the case of performed arts, a performance might be judged by the
extent to which it was held to correspond with that identity.
In the works of most European composers, the operation of aleatory technique does not fundamentally
disturb that conception. The composition is still the product of an individual mind, though some aspects are
left indefinite; the performer has still to realize the composers intentions. (One problem in aleatory music is
that of whether the performance should communicate the fact of indeterminacy. The flexible features of a
work may not be perceived as such if the listener does not hear frequent different performances, still less if
the work is heard most usually in a single recording. In some disc issues, such as that of Pousseurs Votre
Faust, the difficulty has been tackled by having the listener take decisions about operating balance and
volume controls during the playing.) And the roots of the aleatory in European music are principally within
the European tradition itself. If composers were impressed by the freedom of performance in oriental
musics, their reaction was to attempt to establish some equivalent in Western terms. In doing so, they found
more immediate stimulus in literary parallels (particularly Mallarm and Joyce) and in the principle of
serialism as it had been developed in Europe up to the mid-1950s. This development had brought about the
avoidance of large-scale formal processes, and so the ground was laid for forms in which sections could be
moved about without disrupting the whole. In addition, the permutational character of serialism was seen as
implying permutable forms. Yet another field of activity within European music which stimulated aleatory
innovations was electronic music: first, composers had observed that a sound is partly determinate and
partly indeterminate (Boulez was to write of the main parts of his Piano Sonata no.3 as its formants), and
second, there was the desire to achieve in instrumental music what had proved obstinately unobtainable in
electronic music, namely variability with performance.
Aleatory music in Europe might, in general, be considered as a matter of choice rather than chance, and the
most significant choices have usually remained with the composer, whether he exercised them in notating a
score or in directing a performance. In either event, the criteria for judging the result as a work of art are
barely altered. Even improvisation groups in Europe customarily retained a traditional regard for
achievement, finish and the expression of defined ideas (whether musical or political), although few
succeeded in establishing a code of practice, such as exists in most jazz, within which their improvisations
may be understood.
Cages use of chance was, from the first, more destructive of the traditional notion of a work of art (just as,
previously, his automatic procedures had been). Influenced by Zen Buddhism as well as by the musics of
the east, his aim was to remove the barrier of his discrimination: any sound was to be admitted, freed to be
itself. It was a persistent search for means of avoiding willed choice that led him to investigate procedures
that took music out of the control of both composer and performer. Although certain of Cages associates,
notably Brown and Feldman, found a parallel for their ideas in the work of visual artists (Calders mobiles
and Pollocks action paintings, for example), the central Cagean idea was to remove from music any
reference to tradition or any trace of subjectivity, and chance, not choice, was the obvious means. This
extreme aleatory position was stated at its most exact in Cages lecture Indeterminacy:
Finally I said that the purpose of this purposeless music would be achieved if people
learned to listen; that when they listened they might discover that they preferred the
sounds of everyday life to the ones they would presently hear in the musical program;
that that was alright as far as I was concerned.
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