Repetition defines music

Update: there’s a lively discussion of this post happening on Synthtopia’s Facebook page.

Musical repetition has become a repeating theme of this blog. Seems appropriate, right? This post looks at a wonderful article by , investigating the reasons why we love repetition in music in Aeon Magazine.

The simple act of repetition can serve as a quasi-magical agent of musicalisation. Instead of asking: ‘What is music?’ we might have an easier time asking: ‘What do we hear as music?’ And a remarkably large part of the answer appears to be: ‘I know it when I hear it again.’

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What are the main ideas and highlights of Gödel, Escher, Bach?

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.


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Biggie Biggie Smalls Is The Illest

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.

[iframe_loader width="480" height="360" src="http://www.youtube.com/embed/IdL2e1MrTgY" frameborder="0" allowfullscreen]

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What is the relationship between music and math?

Music is richly mathematical, and an understanding of one subject can be a great help in understanding the other.

Geometry and angles

My masters thesis is devoted in part to a method for teaching math concepts using a drum machine organized on a radial grid. Placing rhythms on a circle gives a good multisensory window into ratios and angles.

Wave mechanics

The brain turns out to be adept at decomposing sinusoids into their component frequencies. We can’t necessarily consciously compare the partials of a sound, but we certainly do it unconsciously — that’s how we’re able to distinguish different timbres, and is probably the basis for our sense of consonance and dissonance. If two pitches share a lot of overtones, we tend to hear them as consonant, at least here in the western world. There’s a strong case to be made that overlapping overtone series is the basis of all of western music theory.

The concept of orbitals in quantum mechanics made zero sense to me until I finally found out that they’re just harmonics of the electron field’s vibrations. I wasn’t at all surprised to learn that Einstein conceptualized wave mechanics in musical terms as well.

Logarithms

Octave equivalency is really just your brain’s ability to detect frequencies related by powers of two. The relationship between absolute pitches and pitch classes is an excellent doorway into logarithms generally. You also need logarithms to understand decibels and loudness perception.

Symmetry

Music is really just a way of applying symmetry to events in time.  See this delightful paper by Vi Hart about symmetry and transformations in the musical plane.

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Why is so much music written in 4-4?

I have a theory that what people find most interesting in music is self-reference, recursion and fractal-like scale-invariance. Rhythms based on powers of two are a great way to get this kind of recursion because they can be compounded or subdivided so easily. A bar of four can be treated as two bars of two, or half of a bar of eight. You can further subdivide your bars into quarter, eighth and sixteenth notes. You can group your bars of four or eight into four or eight or sixteen-bar phrases. Here’s a visual representation of this kind of powers-of-two recursion:

Modular group - fundamental domain

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Eric B and Rakim

In 1987 I remember having my ears grabbed by this thing on the radio called “Pump Up The Volume” by MARRS.

Now that mashups are so common, this track doesn’t sound particularly remarkable. But in seventh grade it was startling to hear a house music track full of random samples. “Pump Up The Volume” was part of the same UK dance music movement that spawned the KLF’s “Doctorin’ The Tardis” and “Rush” by Big Audio Dynamite. I wasn’t enough of a hip-hop head in 1987 to recognize where the phrase in the title comes from, but now I do, it’s from “I Know You Got Soul” by Eric B and Rakim. Listen at 0:43:

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Nas Is Like

If I had to pick a single track to explain to an alien or time traveler what hip-hop is and why it’s so awesome, I think I’d pick “Nas Is Like.”

Nas has a great flow full of powerful imagery, but what truly sets this track apart for me is DJ Premier’s production. It’s a complex web of samples and scratches that tie together so seamlessly as to be much greater than the sum of their parts. A lot of the samples are from other songs by Nas himself. Here’s a diagram of all the samples, click to see it bigger:

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Muppet Silly Songs

For my 35th birthday, my sister gave me a CD of Muppet Silly Songs, a favorite of ours when we were kids. It’s been out of print for years and last time I checked wasn’t even available on the web, legally or not. We unearthed the vinyl at our mom and stepfather’s place when we were there over Mother’s Day, and Molly converted it to digital with the help of our friend Leo.

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Bach to the future

I’m not a big classical music guy for the most part, but I never get tired of Bach.

This stodgy eighteenth century Lutheran doesn’t seem a likely inspiration for a hipster electronica producer like me. There aren’t too many other wearers of powdered wigs in my record collection, and Bach is the only one in the regular rotation. Why? When I studied jazz guitar I was encouraged to learn some Bach violin and cello music. I learned a lot about music theory that way but I had a surprising amount of fun too. Those pieces are complex and technical, but they’re easy to memorize – it’s one catchy hook after another after another.

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Repetition, repetition, repetition, repetition

I’ve had a lot of music teachers, formal and informal. The best one has been the computer. It mindlessly plays anything I tell it to, over and over. Hearing an idea played back on a continuous loop tells me quickly if it’s good or not. If the idea is bad, I immediately get annoyed, and if it’s good, I’ll cheerfully listen to it loop for hours.

There’s something in the cumulative experience of a loop that makes it greater than the sum of the individual listens. Good loops create a meditative, trance-like state, like Buddhist mantras you can dance to. As far as I’m concerned, if it’s the right groove, there’s no such thing as too much repetition. Take “Hey Jude” by the Beatles.

At the end, they repeat “Naah, na na nanana naah, nanana naah, hey Jude” over and over for four minutes. I could listen to it for forty minutes. Why don’t I get bored? Continue reading