One quite short piece that is a notorious challenge to most listeners is John Cage's 4'33. The name it goes by is simply the total duration of the piece. It doesn't actually have a title. It is in three sections, each with a specified duration and they add up to 4 minutes and 33 seconds. Each section or movement consists of a rest and the word "tacet" meaning, don't make any sounds. So it is a piece consisting simply of silence for four and a half minutes. Cage has said that the "music" is whatever sounds happen to occur during this timespan: crickets, a cough, passing jet overhead, stomach rumblings, whatever. The piece is a kind of Zen meta-composition. Very easy to listen to, but philosophically or aesthetically challenging.
Another way for a piece to challenge the listener is to present themes, rhythms and harmonies that are complex in themselves and not easily identifiable. Many movements of the very large piece for piano, Catalogue d'oiseaux by Olivier Messiaen are difficult in this sense. His thematic material consists largely of transcriptions of birdsong interspersed with musical soundscapes of the scenery and environment. Each piece is set in a particular time and place. Here, for example, is "Le chocard des Alpes", the first of the thirteen pieces that make up the work. The first section depicts the mountain landscape of chasms and precipices, from about the 50 second mark we start to hear the call of the alpine chough. The silences represent the enormous spaces and distances of the mountain landscape.
It takes quite a bit of listening before this music becomes familiar and enjoyable--not because of anything unpleasant in the vocabulary, but simply because of its complexity. There are no simple themes and harmonies.
Another kind of challenge can present even with short pieces. Arnold Schoenberg, before he developed his serial method of composition, went through a period when he was exploring the possibilities of the dissolution of tonality. He wrote a set of six tiny pieces for piano, labeled op. 19. These are so short that all six take only five minutes to play. But they are so enigmatic, that, again, it takes a lot of listening to start to understand them. Each is like a tiny complex jewel from another planet. They do have a structure, but it is rather enigmatic. Perhaps the second one is easiest to access as a lot of it is repeated thirds that are expanded outwards. There are analyses of these pieces that essentially turn them into mathematical set theory. It is probably better to just listen to them! They offer a unique set of introspective moods:
Finally, there are pieces that are not only enigmatic, but also long and emotionally draining. The symphonies of Allan Pettersson are certainly an example. Perhaps the most accessible of his fifteen symphonies is Symphony No. 8 composed in 1968/9. It is the only one of his symphonies that is divided into sections, all the others are in one long movement. One structural feature that the listener can hang onto is the recurring motif of a rising minor second. At the beginning it is in eighth notes in the accompaniment. Later on, it appears more prominently in half notes. You can see both forms in this example, which is from the notes to the CPO recording:
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Here is the recording by the Baltimore Symphony Orchestra conducted by Sergiu Comissiona, 1980.