I recently came across a TEDTalk by a mathematician named Scott Rickard who set out to create the “ugliest” piece of music possible. It’s a fun clip, and can be viewed in its entirety here:
The basic premise is that “beauty” in music comes from patterns and repetition, and so our perception of “ugliness” results from the lack of these things. And this is basically true. As Rickard points out, the music we love is full of repeated patterns, and as listeners–consciously or unconsciously–we try to predict how these patterns will unfold. This is not to say that good music is endlessly repetitive (though some gets close)–just like a good book or film, there is joy both in the fulfillment of something we saw coming, and also in the surprise plot twist that subverts our expectations. Of course, we can only really have expectations when we are able to recognize a pattern in the first place.
At the end of the video, Rickard shares an original piece of music for piano where he has applied mathematical principles to ensure that no musical material is repeated. Not only is each note on the piano played only once, but the distance (the pitch interval) between each pair of notes is never repeated. Even the amount of time between two notes is unique to each pair.
You’d be hard-pressed to identify any patterns in this music, let alone predict which note was coming next (or when it would appear). It’s played for laughs in the moment, but it also raises an interesting question: would it be possible to use a lack of repetition to produce music that might be, in fact, beautiful?
Usually elements that are not pattern-based occur at an extremely local level in music, meaning that they are very brief in duration, or limited to certain instruments, but not others. For example, even though all popular music is built on top of a steady beat, there are (almost) always moments where the pattern is disrupted. Sometimes the same note of the beat is played on a different instrument for emphasis (for example, using the crash cymbal instead of the hi hat). Or the rhythm may change to make a passage more exciting, as in a fill at the end of a musical phrase. In both cases, it’s a momentary variation that the listener can compare directly with the pattern preceding and following it–it is meaningful to us to the extent that we can recognize its difference.
In jazz, this concept is taken a step (or two) further. In a typical jazz performance, players take turns playing solos over the same sequence of chords. This means that each section has different melodies and textures–often wildly different–but they are heard in relation to a repeated pattern of chord changes and a melody (the “head”) played at the beginning and end of the performance. It’s another way of finding a balance between the predictable and the unpredictable–what gets repeated, and what does not.
In the 1950s and 1960s, jazz musicians began to explore the limits of this balance. Free jazz, pioneered by Ornette Coleman, John Coltrane, and Cecil Taylor, exemplified one extreme through the use of less repetitive chord changes, more complex melodies, and greater rhythmic flexibility. But even before the emergence of free jazz, Miles Davis’s “Flamenco Sketches” (1959) presented an innovative take on the balance between repetition and non-repetition.
Apart from the opening piano chords, this composition is based entirely on improvised material. There is no identifiable melody that gets repeated–the structure of the piece comes from a sequence of five chords that are looped. However, unlike other jazz compositions in which the rhythm of the chord changes stays the same throughout the piece, in “Flamenco Sketches” the length of time spent on each chord varies according to the preferences of each soloist. It is an example of the principle of non-repetition expanded beyond the local level to shape the overall structure of the piece.
Of course, what is unique about Rickard’s composition is that it is arrived at mathematically, rather than intuitively. In other words, the raw materials of music–pitches, intervals, and rhythms–are organized according to a formula or algorithm whose results can’t be predicted until the formula is actually calculated. As it turns out, there are entire genres of music that use processes like these, often described (quite logically) as “algorithmic music” or “process music.”
One well-known example of process music is Steve Reich’s tape piece “Come Out” (1966). In this piece, multiple copies of the same short recording are played simultaneously on a loop at slightly different speeds. In the first few minutes of the piece, the difference is heard as a change in the quality or timbre of the sound, but a distinct echo quickly becomes audible. Later on, the echoes become more abstract, overlapping with one another in what is often described as a “phasing” effect.
What’s especially interesting about this example is that the basis of the piece is obviously the repetition of a short recording of someone speaking, but because of the process applied, no two repetitions sound exactly the same. Repetition itself, it seems, can be a form of variation under the right circumstances. And likewise, variation can sometimes sound a lot like repetition, based on how it is used. Rickard chose to apply a non-repetitive series to the notes of the piano, but what if the notes stayed the same and the it was the intensity of each attack that was varied eighty-eight times? Or the same note was played on eighty-eight different instruments? The perception of repetition or difference changes dramatically based on how it is applied to the music.
Brian Eno employs principles of non-repetition in his album Ambient 1: Music for Airports, often considered the progenitor of “ambient music.” Although the precise techniques vary from track to track, Eno makes extensive use of tape loops, in which a sound is recorded to a “loop” of magnetic tape that spools through the tape player over and over again. Instead of making the tape loop exactly as long as the sounds recorded, however, Eno adds a length of blank tape to each, creating repetitions that are interspersed with long silences.
A further layer of complexity emerges from the fact that Eno uses multiple tape loops at the same time and each tape loop has a different length. Additionally, the particular lengths that Eno chooses for the loops are not factors or multiples of one another. This means that the repetition of each loop is unsynchronized from the others–the beginning of each loop will always line up with a different part of every other loop. As Eno himself describes one track:
“There are sung notes, sung by three women and myself. One of the notes repeats every 23 1/2 seconds…The next lowest loop repeats every 25 7/8 seconds or something like that. The third one every 29 15/16 seconds or something. What I mean is they all repeat in cycles that are called incommensurable–they are not likely to come back into sync again.”
Just like in “Come Out,” even though the musical material is repetitive–recorded to tape and therefore fixed–the way in which the material repeats leads to a constantly changing musical texture. There is repetition of individual sounds, but their arrangement in relation to one another is always different. It’s certainly not “ugly” music, but in this case, it’s not necessarily repetition that makes it beautiful.