Fractal music

Continuing my series of posts on the ways that science might explain why we like the music we like. See also my posts on the science of rock harmony, harmony generally, and Afro-Cuban rhythms.

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.

Mandelbrot zoom

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Why is son clave so awesome?

One of the best discoveries I made while researching my thesis is the mathematician Godfried Toussaint. While the bookshelves groan with mathematical analyses of western harmony, Toussaint is the rare scholar who uses the same tools to understand Afro-Cuban rhythms. He’s especially interested in the rhythm known to Latin musicians as 3-2 son clave, to Ghanaians as the kpanlogo bell pattern, and to rock musicians as the Bo Diddley beat. Toussaint calls it “The Rhythm that Conquered the World” in his paper of the same name. Here are eight different representations of it as rendered by Toussaint:

Toussaint - visualizing son clave

And here it is in my preferred circular notation:

circular son clave

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Can science make a better music theory?

My last post discussed how we should be deriving music theory from empirical observation of what people like using ethnomusicology. Another good strategy would be to derive music theory from observation of what’s going on between our ears. Daniel Shawcross Wilkerson has attempted just that in his essay, Harmony Explained: Progress Towards A Scientific Theory of Music. The essay has an endearingly old-timey subtitle:

The Major Scale, The Standard Chord Dictionary, and The Difference of Feeling Between The Major and Minor Triads Explained from the First Principles of Physics and Computation; The Theory of Helmholtz Shown To Be Incomplete and The Theory of Terhardt and Some Others Considered

Wilkerson begins with the observation that music theory books read like medical texts from the middle ages: “they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases.” We can do better.

Standing waves on a string

Wilkerson proposes that we derive a theory of harmony from first principles drawn from our understanding of how the brain processes audio signals. We evolved to be able to detect sounds with natural harmonics, because those usually come from significant sources, like the throats of other animals. Musical harmony is our way of gratifying our harmonic-series detectors.

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Toward a better music theory

Update: a version of this post appeared on Slate.com.

I seem to have touched a nerve with my rant about the conventional teaching of music theory and how poorly it serves practicing musicians. I thought it would be a good idea to follow that up with some ideas for how to make music theory more useful and relevant. The goal of music theory should be to explain common practice music. I don’t mean “common practice” in its present pedagogical sense. I mean the musical practices that are most prevalent in a given time and place, like America in 2013. Rather than trying to identify a canonical body of works and a bounded set of rules defined by that canon, we should take an ethnomusicological approach. We should be asking: what is it that musicians are doing that sounds good? What patterns can we detect in the broad mass of music being made and enjoyed out there in the world?

I have my own set of ideas about what constitutes common practice music in America in 2013, but I also come with my set of biases and preferences. It would be better to have some hard data on what we all collectively think makes for valid music. Trevor de Clerq and David Temperley have bravely attempted to build just such a data set, at least within one specific area: the harmonic practices used in rock, as defined by Rolling Stone magazine’s list of the 500 Greatest Songs of All Time. Temperley and de Clerq transcribed the top 20 songs from each decade between 1950 and 2000. You can see the results in their paper, “A corpus analysis of rock harmony.” They also have a web site where you can download their raw data and analyze it yourself. The whole project is a masterpiece of descriptivist music theory, as opposed to the bad prescriptivist kind.

Jimi Hendrix, common practice musician

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Hereditary units in music

Another thought-provoking Quora question: Are there any hereditary units in music? The question details give some context:

In his blog post “The Music Genome Project is no such thing,” David Morrison makes an edifying distinction between a genotype and a phenotype. He also makes the bold statement “there are no hereditary units in music.” Is this true?

Morrison’s post is a valuable read, because it’s so precisely wrong as to be quite useful in clarifying your thinking.

Nas -

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Frank Ocean’s Real Love

Frank Ocean is the R&B singer of the moment. Does he merit all they hype? There’s no doubt but that the man can sing. I first heard him in Jay-Z and Kanye West’s tremendous “No Church In The Wild,” which owes a lot of its intensity to Ocean’s vocals. He’s been releasing some good mixtapes too. Some of his sudden fame is also due to his implicit coming-out moment, a remarkable Tumblr post talking openly about his feelings for another man. In a world where Jay-Z’s voicing ambiguous support for gay marriage is headline news, Ocean’s open love letter is bold indeed.

The online Frank Ocean buzz reached such a pitch that I finally took the plunge on his first major-label release, Channel Orange. It’s the first full album of new music I’ve bought since The Archandroid by Janelle Monáe. Does it merit the hype? I don’t know yet. I think so. It’s strange and idiosyncratic. Some of it is boilerplate R&B, some of it is wildly experimental, Most falls somewhere in between. One song that jumps out at me is “Super Rich Kids,” featuring the utterly affectless rapping of Earl Sweatshirt.

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My NPR debut

On Tuesday, July 17, I appeared on the Colin McEnroe Show on Connecticut Public Radio to talk about my pet topic, remixes and mashups. The great DJ Earworm was on the show too, which I was totally geeked out about. You can stream or download the show here. Or listen to my remix of it:

My friend Jesse had a lot to say about the discussion on the program. Read his response (and my response to his response.)

At NY NPR HQ

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Originality in Digital Music

This post is longer and more formal than usual because it was my term paper for a class in the NYU Music Technology Program.

Questions of authorship, ownership and originality surround all forms of music (and, indeed, all creative undertakings.) Nowhere are these questions more acute or more challenging than in digital music, where it is effortless and commonplace to exactly reproduce sonic elements generated by others. Sometimes this copying is relatively uncontroversial, as when a producer uses royalty-free factory sounds from Reason or Ableton Live. Sometimes the copying is legally permissible but artistically dubious, as when one downloads a public-domain Bach or Scott Joplin MIDI file and copies and pastes sections from them into a new composition. Sometimes one may have creative approval but no legal sanction; within the hip-hop community, creative repurposing of copyrighted commercial recordings is a cornerstone of the art form, and the best crate-diggers are revered figures.

Even in purely noncommercial settings untouched by copyright law, issues of authorship and originality continue to vex us. Some electronic musicians feel the need to generate all of their sounds from scratch, out of a sense that using samples is cheating or lazy. Others freely use samples, presets and factory sounds for reasons of expediency, but feel guilt and a weakened sense of authorship. Some electronic musicians view it as a necessity to create their tools from scratch, be they hardware or software. Others feel comfortable using off-the-shelf products but try to avoid common riffs, rhythmic patterns, chord progressions and timbres. Still others gleefully and willfully appropriate and put their “theft” of familiar recordings front and center.

Is a mashup of two pre-existing recordings original? Is a new song based on a sample of an old one original? What about a new song using factory sounds from Reason or Ableton Live? Is a DJ set consisting entirely of other people’s recordings original? Can a bright-line standard for originality or authenticity even exist in the digital realm?

I intend to parse out our varied and conflicting notions of originality, ownership and authorship as they pertain to electronic music. I will examine perspectives from musicians and fans, jurists and journalists, copyright holders and copyright violators. In so doing, I will advance the thesis that complete originality is neither possible nor desirable, in digital music or elsewhere, and that the spread of digital copying and manipulation has done us a service by bringing the issue into stark relief.

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