Grove article on Aleatory (APU Campus only).
A term applied to music whose composition and/or performance is, to a greater or lesser extent, undetermined by the composer.Grove
Grove article on Stochastic (APU Campus only).
A term used in music on the basis of its use in probability theory, where it applies to a system producing 'a sequence of symbols (which may... be letters or musical notes, say, rather than words) according to certain probabilities'W. Weaver: 'Recent Contributions to the Mathematical Theory of Communication', Etc.: a Review of General Semantics, x (1953), 261
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 Ives’s 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 Cage’s 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 Stockhausen’s Klavierstück IX (1956) and Boulez’s Piano Sonata no.3 (1956–7) 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 Lutoslawski 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 Mallarmé 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.Grove
Don't get too carried away by ideas of 'randomness' - distinguish what is genuinely random or disorganised from ideas that you just can't understand at a given time. Maybe if you spent a bit more time with the ideas they'd seem a little more rational. Genuine 'randomness' is quite difficult to achieve and usual rather dull. I can play the piano 'randomly' but there's automatically a huge amount of structure there - I'll probably use my hands which have a given number of fingers. These body parts can only do certain things and not others. The piano itself is a hugely organised thing. So whatever I play on the piano there'll already be lots of structure for interpretation.
Our brains weren't designed for big statistics, big time, big numbers, big anything. There were designed to work with small numbers, slow moving things. We often get things wrong because we imagine we understand big things - gambling often does not use huge numbers, but we still think that we can win. The chances of winning the National Lottery are miniscule, but many of us think that quite genuinely, it could be us. Of course, to all intents and purposes, it won't be.
If we lived for 1000 years, we'd never cross the road because it would be too dangerous. Or to put it another way, our roads would be radically different, because we wouldn't want to risk such a lot on such a mundane yet dangerous activity. The dangers on our roads are a balance between the convenience of road travel and the likelihood that we'll die there. If roads become substantially more dangerous then we'll try to institute rules to reduce that danger (as we often see happen).
In a pack there are fifty-two cards to which an order can be assigned (such as ace to king, hearts, clubs, diamonds, spades). What is the probability that given a proper shuffle the cards would end up in the order originally given? The case is a much simpler analogy than the molecules of gas in the clock, for here there are only fifty-two cards instead of something like 10^23 molecules. The calculated probability turns out to be one chance in 10^68 attempts. To put that into perspective, imagine every man, woman and child on this earth, each with a pack of cards, shuffling them once every second. How long would it take until someone shuffled a pack into the right order? The answer is about 10^50 years. As the universe is aonly about 10^11 years old, all those people would have to keep suffling those cards for about 10^39 lifetimes of the universe! To ascribe the word impossible to such a situation is, in the light of that answer, not a misuse of words.
On Time, Sallis, Burnett Books, 1982Many people think that chance or indeterminacy in music are twentieth century western concepts. To a degree this is true, but only from a very limited (and rather ill-informed perspective).
The basis for most western classical music, Gregorian Chant...