Four bars of Mozart explains everything humans like in music

I’m not arguing here that everyone loves Mozart, or that I’m about to explain what all humans enjoy all the time. But I can say with confidence that this little bit of Mozart goes a long way toward explaining what most humans enjoy most of the time. The four bars I’m talking about are these, from “Eine Kleine Nachtmusik.”

What these four bars of music demonstrate is that humans like:

  1. Repetition
  2. Breaks in the repetition
  3. Repetition of the breaks in the repetition
  4. Breaks in the repetition of the breaks in the repetition
  5. Recursive layers of patterns of breaks and repetitions

In order to prove this to you, I’m going to talk you through these eighteen notes one at a time.

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The Vocoder, Auto-Tune, Pitch Standardization and Vocal Virtuosity

Writing assignment for History of Science and Technology class with Myles Jackson. See a more informal introduction to the vocoder here.

Casual music listeners know the vocoder best as the robotic voice effect popular in disco and early hip-hop. Anyone who has heard pop music of the last two decades has heard Auto-Tune. The two effects are frequently mistaken for one another, and for good reason—they share the same mathematical and technological basis. Auto-Tune has become ubiquitous in recording studios, in two very different incarnations. There is its intended use, as an expedient way to correct out-of-tune notes, replacing various tedious and labor-intensive manual methods. Pop, hip-hop and electronic dance music producers have also found an unintended use for Auto-Tune, as a special effect that quantizes pitches to a conspicuously excessive degree, giving the voice a synthetic, otherworldly quality. In this paper, I discuss the history of the vocoder and Auto-Tune, in the context of broader efforts to use science and technology to mathematically analyze and standardize music. I also explore how such technologies problematize our ideas of virtuosity.

Ableton vocoder

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The vocoder and Auto-Tune

This post documents a presentation I’m giving in my History of Science and Technology class with Myles Jackson. See also a more formal history of the vocoder.

The vocoder is one of those mysterious technologies that’s far more widely used than understood. Here I explain what it is, how it works, and why you should care. A casual music listener knows the vocoder best as a way to make that robot voice effect that Daft Punk uses all the time.

Here’s Huston Singletary demonstrating the vocoder in Ableton Live.

This is a nifty effect, but why should you care? For one thing, you use this technology every time you talk on your cell phone. For another, this effect gave rise to Auto-Tune, which, love it or hate it, is the defining sound of contemporary popular music. Let’s dive in!

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QWERTYBeats design documentation

QWERTYBeats logoQWERTYBeats is a proposed accessible, beginner-friendly rhythm performance tool with a basic built-in sampler. By simply holding down different combinations of keys on a standard computer keyboard, users can play complex syncopations and polyrhythms. If the app is synced to the tempo of a DAW or other music playback system, the user can easily perform good-sounding rhythms over any song. 

This project is part of Design For The Real World, an NYU ITP course. We are collaborating with the BEAT Rockers, the Lavelle School for the Blind, and the NYU Music Experience Design Lab. Read some background research hereContinue reading

Syncopation

I have a whole lot of explanatory writing about rhythm in the pipeline, and thought it would be good to have a place to link the word “syncopation” to every time it arises. So here we go. Syncopation is to rhythm what dissonance is to harmony. A syncopated rhythm has accents on unexpected beats. In Western classical music, syncopation is usually temporary and eventually “resolves” to simpler rhythms. In the music of the African diaspora, syncopation is a constant, in the same way that unresolved tritones are constant in the blues.

Syncopation is not just a subjective quality of music; you can mathematically define it. Before we do, it helps to visualization a measure of 4/4 time, the amount of time it takes to count “one, two, three, four.”

Radial syncopation

The more times you have to subdivide the measure to get to a given beat, the weaker that beat is. When you accent weak beats, you get syncopation. Continue reading

Scale necklaces and symmetry

While I was doing some examination of rhythm necklaces and scale necklaces, I noticed a symmetry among the major scale modes: Lydian mode and Locrian mode are mirror images of each other, both on the chromatic circle and the circle of fifths. Here’s Lydian above and Locrian below:

C Lydian mode

C Locrian mode

Does this geometric relationship mean anything musically? Turns out that it does.

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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 it is as programmed by me on a drum machine:

The image behind the SoundCloud player is my preferred circular notation for son clave. Here are eight different more conventional representations as rendered by Toussaint:

Toussaint - visualizing son clave Continue reading

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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