Throughout much of classical music's history, the principle of goal-orientedness undergirds much of musical form. Sonata form introduces listeners to a series of ideas in the exposition, followed by a protracted exploration of these themes in the development, and finally resulting in their closure in the recapitulation. Theme and variations takes a motif, and manipulates its musical elements in various ways. The fugue likewise explores a single subject and takes it on a musical journey across various voices.
All of these formal structures are like narratives. They begin with a setting or introduction with a 'cast of characters'. This is followed by world-building, character development and plot twists. At the end, the narrative 'wraps up' and concludes the tale being told.
Stockhausen, perhaps one of the most radical composers of the late 20th century, had a very different idea of music. To him, music could step out of this goal-oriented, story-like structure. He calls this new type of structure 'Moment-form'.
Moment-form presents a few musical segments, or moments, where each one is individual and able to take on an independent musical existence. There wouldn't be a pre-determined beginning and inevitable end. Each individual moments are not merely consequences from (and precursors to) other moments. It is basically a series of musical 'portraits', much like how paintings in an art gallery might be thematically linked, but they are individual works of art and can be appreciated in isolation from the rest.
One of my favourite examples of Moment-form is the aptly named Momente, composed in 1965.
Apart from employing individual 'moments' of music that can be appreciated as standalone miniatures, I most particularly enjoyed the humour (whether intentional or not) of the first segment. The first time I heard this work online, the clapping of hands sounds like the obligatory applause at the start of a concert, only for me to realize that it was part of the music, which comically repeats several times, as if the audience had forgotten when is it appropriate to clap!
It is also important to recognize that Stockhausen was not dispensing with unity. He was not composing a pastiche of incongruous works and conjoining them into a disjunct Frankenstein. It is more accurate to say that the individual moments are quasi-independent. They can be taken apart and listened as they are, but they can also fit together into a wider work.
Another composer who radically rethought form and structure is the Greek polymath Iannis Xenakis. Apart from being a celebrated composer, he was also an architect, engineer and mathematician by trade, which influenced his compositional procedures.
Xenakis' compositions employs 'stochastic form', which is derived from the Law of Large Numbers as defined by the mathematician Jacques Bernoulli. The idea here is that when one performs the same probability event a large number of times, the average of the results will tend towards the expected value as more events are carried out. Take for example a coin toss with a probability of 50%. The more one tosses the coin, the closer the average of all the tosses would gravitate towards the equilibrium of 50%.
Stochastic form thus involves a sense of equilibrium between highly contrasting musical alternatives. Extreme contrasts between musical elements (e.g. texture, dynamics, articulations) are juxtaposed beside each other. Through such extreme contrasts, some form of unified idiom can be derived when the piece is heard as a whole, even when from moment to moment, one hears great disparity. In other words, equilibrium is achieved when the whole piece is heard, but not when one hears a small segment of the entire work.
Through stochastic form, Xenakis hopes to create 'the greatest possible asymmetry', where highly disparate elements of music are present within each section. An example of this form employed could be found in his work Morsima-Amorsima (1962):
This work, for strings and piano, begins with an extreme diversity of register, duration and dynamics. Notes of long duration are juxtaposed with brief flickers of pitches. This is done alongside quasi-pointillistic dynamics, where fortissimo pitches and motifs are juxtaposed with near silent phrases.
Such radicalism from Xenakis is not without its consequences. As Arnold Whittall wisely observes, such asymmetry results in the near-complete absence of more relaxed moods. From my perspective, even for the seasoned listener of contemporary music, Xenakis' works remain as abstruse as James Joyce's Finnegan's Wake.
Ng Yu Hng, 2020
Find out more about Ng Yu Hng at https://www.ngyuhngcomposer.com/
Whittall, Arnold, 'Music of Change: Seven Europeans', in Musical Composition in the 20th-Century. pp. 286 - 324