Quora user Marc Ettlinger recently sent me a paper by Sherri Novis-Livengood, Richard White, and Patrick CM Wong entitled Fractal complexity (1/f power law) determines the stability of music perception, emotion, and memory in a repeated exposure paradigm. (The paper isn’t on the open web, but here’s a poster-length version.) The authors think that fractals explain our music preferences. Specifically, they find that note durations, pitch intervals, phrase lengths and other quantifiable musical parameters tend to follow a power law distribution. Power-law distributions have the nifty property of scale invariance, meaning that patterns in such entities resemble themselves at different scales. Music is full of fractals, and the more fractal-filled it is, the more we like it.
Gödel, Escher, Bach by Douglas Hofstadter describes and defines the concept of recursion, and discusses its applications in computer science, consciousness, art, music, biology and various other fields.
Recursion is crucial to writing computer programs in a compact, elegant way, but it also opens the door to infinite loops and irreconcilable logical contradictions.
I always enjoy when hip-hop artists sample themselves. It makes the music recursive, and for me, “recursive” is synonymous with “good.” You can hear self-sampling in “Nas Is Like” by Nas, “The Score” by the Fugees and many songs by Eric B and Rakim. The most recent self-sampling track to cross my radar is “Unbelievable” by Biggie Smalls, from his album Ready To Die. Here’s the instrumental.
Writing a song is a lot like writing a computer program. They both require clever management of loops and control flow.
The simplest sheet music reads as a straightforward top-to-bottom list of instructions. You start on measure one and read through to the end sequentially. That’s fine unless the music is very repetitive, which most popular music is. The loop is the basic compositional unit of nearly every song you could dance to. The problem is that writing loops out sequentially is very tedious.
Rather than writing the same passage over and over, you can save yourself a lot of laborious writing by using repeat markers. They’re like the GOTO instruction in BASIC. Here are the first four bars of “Chameleon” by Herbie Hancock. This four-bar phrase repeats hundreds of times over the course of the song. You wouldn’t want to write them all out. With repeat markers, you don’t have to. Repeat markers give sheet music the topology of a clock face.