So, what would most musicologists supposedly argue? According to mathematician Scott Rickard in a TEDx Talk from 2011,
Most musicologists would argue that repetition is a key aspect of beauty. The idea that we take a musical idea, we repeat it, we set up the expectation for repetition and then we either realize it or break the repetition. If repetition and patterns are key to beauty, then what would the absence of patterns sound like—if we wrote a piece of music with no repetition in it?
Rickard claims that it would be the least beautiful, therefore The Ugliest Piece of Music. Tim Edwards of Classic FM ran with that idea when he reported on Rickard's talk in an article titled, "This is the most monumentally ugly piece of music ever composed, according to science."
Yes, this is another blog post about "science" and music, and once again it involves Classic FM. In my previous post, I looked at the ways in which Classic FM reports on scientific studies involving classical music in order to confirm their readers' cultural biases. This article reveals a different problem involving music in science: when the scientist (or mathematician) misrepresents musicology (or music theory).
Rickard presents an interesting mathematical challenge: finding a way to arrange 88 pitches so that there would be no repetition—as I understand it, no repeated interval between any given pair of pitches. As he points out, this is much more difficult than randomization, as a truly random collection will almost always contain some repetition.
As math problems go, this one is interesting and has some practical application, since the problem arose from developing the perfect sonar ping. Applying it to music is a logical next step, as it's already about pitch. But when Rickard takes that additional step of applying an aesthetic judgment on his creation and saying it's a musicological claim, that's when he raises my hackles.
Is repetition a key aspect of beauty? I definitely agree that repetition in music is important, however I would say that it has more to do with "coherence" than "beauty." Our brains specialize in finding patterns. When listening to a piece of music, I do listen for repetition, latching onto motives. The recapitulation can be the most satisfying parts of a work in sonata form because it's the return of a theme. If Rickard had claimed that this is the "most disorienting" piece of music, I wouldn't argue.
Beauty, however, is much more difficult to quantify. Aesthetics in music has a looooong history, appearing in writing as early as Greek antiquity, with heavy-hitters like Kant and Hegel weighing in. Rather than getting sucked in by the gravity of a philosophical black hole, I'll just offer a few counterexamples to explain why I disagree that "repetition is a key aspect of beauty." There are pieces that I consider beautiful within the first few moments, before there is even time for anything to repeat. For example, the first two chords of Brahms's third symphony, or the first few notes of The Beatles' "Blackbird." I think the harmony is what strikes me as beautiful in the former and the timbre in the latter. Music is too multifaceted to reduce "beauty" to any one factor.
Not only does Rickard reduce beauty in music to one facet (repetition), when creating his "ugly" piece, he only eliminates repetition for two elements: pitch and rhythm. But his piece is played on a piano, keeping the timbre fairly consistent throughout. There aren't major fluctuations in dynamics, either. There is repetition, but in factors that Rickard apparently did not consider, perhaps because he is not a music theorist or musicologist.
Rickard also spends about a minute talking about Arnold Schoenberg and his tweleve-tone method, suggesting his mathematical approach has precedent because Schoenberg eschewed tonality by ensuring that no pitches repeated before all twelve pitches were used. His casual invocation of Schoenberg in this context has a few problems: First, he seems to imply that serialism is built on a lack of repetition. In practice, however, works using the twelve-tone method feature a lot of repetition in order to make the music coherent. The tone row saturates the piece. Next, though Rickard doesn't say it outright, mentioning Schoenberg in this context makes it seem like he's saying Schoenberg writes ugly music, or that he intended to write ugly music. I don't believe Schoenberg would always agree with that.
I'm not claiming that Rickard's piece is beautiful. I am saying that a musicologist would not proclaim it "The Most Monumentally Ugly Piece of Music Ever Composed," because that's not really what musicologists do.
I commend Rickard for applying a mathematical concept to music. I also know of several pieces based on the digits of pi (which also don't repeat!), and even a bagpipe solo based on the Fibonacci sequence. But Rickard does not understand musicology, and Classic FM was once again too dazzled by the authority of "Science!" to think better of repeating his claims.
To invoke Rickard's specialty and translate his next statement into mathematics (or at least symbolic logic), "If repetition and patterns are key to beauty, then [this piece without repetition is ugly]" is p→q, where p is false. If a conditional has a false hypothesis, then the conclusion can be anything and the conditional is considered true—but it cannot be used to prove anything. It is meaningless.
Thanks again to Robert Fink, who is ever vigilant toward dubious scientific claims about music.
Sources:
"This is the most monumentally ugly piece of music ever composed, according to science" by Tim Edwards on Classic FM
http://www.classicfm.com/music-news/ugliest-music/#3BFIjrTWBzHriKbz.97
I commend Rickard for applying a mathematical concept to music. I also know of several pieces based on the digits of pi (which also don't repeat!), and even a bagpipe solo based on the Fibonacci sequence. But Rickard does not understand musicology, and Classic FM was once again too dazzled by the authority of "Science!" to think better of repeating his claims.
To invoke Rickard's specialty and translate his next statement into mathematics (or at least symbolic logic), "If repetition and patterns are key to beauty, then [this piece without repetition is ugly]" is p→q, where p is false. If a conditional has a false hypothesis, then the conclusion can be anything and the conditional is considered true—but it cannot be used to prove anything. It is meaningless.
Thanks again to Robert Fink, who is ever vigilant toward dubious scientific claims about music.
Sources:
"This is the most monumentally ugly piece of music ever composed, according to science" by Tim Edwards on Classic FM
http://www.classicfm.com/music-news/ugliest-music/#3BFIjrTWBzHriKbz.97
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