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.

Self-reference makes loops possible, which is great for programming. But sometimes the computer gets stuck in those loops. XKCD gives a playful illustration of how this can happen, using ducks.

We experience these infinite loops as computer crashes. The computer isn’t “stuck” when it crashes; it’s just running the same few instructions over and over.

The computer can’t break its own loops by “stepping outside of itself;” it needs an external agent to intervene, like you hitting the reset button.

The operations of our minds are also heavily recursive and self-referential. But unlike computers, we aren’t prone to getting stuck in loops, and we seem to be unfazed by logical paradoxes. Some of us even find them beautiful. Nature is full of self-similar, “paradoxical” structures like fractals.

Biological systems are especially self-similar and fractal-like.
Our brains are full of recursive loops. The brain’s representation of itself to itself is probably the basis of our consciousness.

The profoundest truths take on the quality of strange loops, GEB’s useful shorthand for recursive paradoxes. Here’s a diagram I made of the “heterarchy” of human knowledge.

Bach isn’t the only musician to use recursion and self-reference. Hip-hop and other sample-based music use it too, in the form of artists sampling their own songs within their own songs. Here are some blog posts digging into this idea.

• Biggie Biggie Smalls Is The Illest
• Eric B and Rakim
• Nas Is Like
• In A Silent Way is a remix of itself
• Self-reference in computer programming and hip-hop
• Take it to the bridge

Hofstadter also tackles the concept of emergence, the way that an intelligent mind can arise from the interaction of unintelligent component. He compares the mind to an anthill — the collective ant colony has intelligence, even though the individual ants are dumb.

Finally, the book is the best introduction to Zen Buddhist thinking that I’ve come across. Hofstadter observes that westerners are used to thinking in terms of neat Manichean categories — profound truths are unambiguously true or false. Zen prepares the mind to deal with Gödelian paradoxes, strange loops, fractals and the like.

I don’t think I’ve ever succeeded in reading GEB from cover to cover. It’s not really that kind of book. I prefer to just open to a random page and struggle with whatever concept I find there. I recommend a similar approach.

Original post on Quora

And here’s the full song — contains much explicit language.

The hook samples the line “Biggie Smalls is the illest” from “The What” on the same album. It’s twenty-three seconds in.

Sampling is a severely underappreciated songwriting tool. Even if you have moral or legal issues with sampling from others, sampling from yourself is still a good idea. Biggie’s line about himself being the illest is just part of a verse in “The What.” The producer on “Unbelievable,” the great DJ Premier, was smart enough to recognize that Biggie’s line could stand on its own as a hook. DJ Premier also produced “Nas Is Like,” and built its chorus through similar means.

The word “Unbelievable” itself comes from R Kelly, sped up a little and raised in pitch to sound female. Listen at 0:58.

Sampled vocals aside, the chopped-up keyboard part is the most musically sophisticated aspect of the track. Its original source is “Remind Me” by Patrice Rushen — I’m pretty sure it comes from the end of the solo section around 4:10.

Premier chopped up this little keyboard phrase and resequenced it beyond recognition. The result is a hip angularity that a normal keyboard player would probably not have arrived at organically.

The beat in “Unbelievable” is an old standby, “Impeach The President.”

The string ambiance in the background comes from the very odd Quincy Jones song “Kitty With The Bent Frame.” Listen at 1:08.

Quincy’s record is a favorite for hip-hop producers looking for an uneasy mood.

Here’s a diagram showing the sample genealogy of “Unbelievable.”

The meaning of self-sampling

Like I said above, self-sampling is so interesting to me because it’s recursive, self-referential. Most of the music we like is full of self-reference, and generally, the more self-referential it is, the more structured and meaningful it feels. Even simple-seeming nursery rhymes can be recursive and self-similar. Here’s a visualization by Lee Byron showing self-similarity in the nursery rhyme “Hickory Dickory Dock.”

Self-similarity makes for compelling visual art, too. One reason we find nature attractive is its rich fractal self-similarity. Here’s a leaf I photographed in my neighborhood; notice how the same veiny structure repeats itself at different size scales:

Even very simple recursive mathematical equations can produce stunningly complex, biological-looking forms, like the classic fractal known as the Mandelbrot set.

Recursion isn’t just attractive. It’s fundamental to computer science — self-reference is a key programming technique. Recursion may be essential to the very nature of consciousness itself. Some neuroscientists think that your entire sense of self emerges out of recursive self-referential loops as your brain represents different parts of itself to itself.

No wonder recursive music is so fascinating. Keep on sampling yourselves, musicians; let’s see what other recursive truths we can uncover.

Wave mechanics

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.

Symmetry

See this delightful paper by Vi Hart about symmetry and transformations in the musical plane.

Combinatorics and graph theory

Generating diatonic chords from a scale is basically just an exercise in combinatorics. Seventeenth-century European bellringing introduced one of the earliest nontrivial results in graph theory, change or method ringing.

Discrete mathematics

The pitch continuum is, well, continuous, but tuning systems and scales are discrete. The voice, fretless stringed instruments and trombones produce continuous pitches. Keyboards, fretted string instruments and saxophones produce discrete pitches. Great intuitive preparation for the concepts of discrete vs continuous generally.

Modular arithmetic

Once you’ve dealt with the circle of fifths, and with scales and modes, extending the idea to generalized modular systems is no problem.

For example: What is the mathematical relationship between the circle of fifths and the circle of half-steps?

Recursion

Maybe you’d consider this more a computer science topic than a math topic. Regardless, the best music is very recursive. See Gödel, Escher, Bach by Douglas Hofstadter.

Some speculation

My experiences in both music and math have convinced me that music is a severely underutilized resource for math teaching. There are many ways to learn besides manipulating symbols on a page or computer screen. In his book Anathem, Neal Stephenson imagines monks solving proofs and running cellular automata by chanting melodies that evolve by systematic rules.

When I was trying to learn how wrap my head around binary numbers, I eventually just wrote a song that counts in binary from one to sixty-four and back down. It works great, and also turns out to be a highly relaxing and meditative exercise. Maybe if more kids felt relaxed and meditative in math class, they’d learn the material a lot better.

Original question on Quora

To keep all the symmetry from getting oppressive, you can throw a few multiples of three or five in there, for example with triplet figures or ten-bar phrases, knowing that listeners can easily parse these against the powers-of-two baseline. Even in 3/4 time, you usually subdivide beats and group phrases by powers of two.

As Laszlo B. Tamas says, there’s a limit to the number of discrete pieces of information we can keep in our working memory at any one time. I don’t know what it’s like to be a Bulgarian or Indian musician, but like Laszlo, I can only conceive of the more complex time signatures in terms of groups of simpler ones, like thinking of 11/8 as 3+3+3+2. Four is a big enough number to be subdivided interestingly, but still small enough so as to not be overwhelming.

Original post on Quora

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:

It makes sense that I first encountered Rakim Allah in the context of a sample, because he and Eric B pretty much wrote the book on sample-based music. “I Know You Got Soul” is named for the Bobby Byrd song, written and produced by James Brown, that you hear looped throughout the track. Sampling James Brown has become a basic part of the musical toolkit, but it wasn’t such an obvious choice back in 1987. Stetsasonic said it best in their song “Talkin’ All That Jazz:”

Tell the truth, James Brown was old
’til Eric and Ra came out with “I Got Soul.”

Now, thanks to eighties hip-hop, James Brown will be cool forever. Sample-based music is supposed to be “fake,” but paradoxically, sampling made funk authentic again after disco had turned it corny. Michael Krimper observes in his blog post Future Funk: Searching For The Lost Groove that by removing music from its original social context, sampling frees it to be heard and experienced in new and unexpected ways.

The aesthetics of the hip-hop beat — one of recycled recorded sounds and reinvented roles for samples clips repeated on loop — spawned a whole new social practice of archiving. A new culture of crate diggers, both collectors and enthusiasts, grew obsessed with finding and archiving dusty, lost vinyl from a previous generation… It’s almost as if these producers began, nearly 20 years later, where the previous musicians had left off. Those funk sounds, once dulled down by over-saturated commercial mediation, became fresh again and pregnant with a wave of creative potential. The early hip-hop generation didn’t grow up during the golden age of the funk era, but they listened and absorbed at home as children. They grew familiar with the sounds without enduring the same forces of marketing as their parents. Maybe that opened up enough free space for them to imagine the music differently.

Eric and Ra have a futuristic electronic sound based almost entirely on samples and turntable scratching, but its futurism is balanced by the rich network of associations they build in with their choice of sampled records. Here’s a map of all the samples on the album Paid In Full – click to see it bigger:

Fittingly, Eric B and Rakim have themselves been a rich source of samples for other artists, starting with Coldcut’s epic remix of “Paid In Full.” Eric and Ra themselves have sampled the songs on Paid In Full many times as well. The phrase “follow the leader” at 1:03 in “I Know You Got Soul” is the basis for, you guessed it, “Follow The Leader.”

Eric and Ra sample “Eric B Is President” in both “Eric B Never Scared” and “Move The Crowd.” This kind of extreme self-reference has been an inspiration for subsequent self-samplers, like Nas on “Nas Is Like” and Fugees on “The Score.” And by the way, “The Score” includes a sample of Eric and Ra’s “My Melody,” which heavily features a sample of itself. How’s that for recursion?

Eric and Ra also inspired the recording of mine that I’m most proud of. “Eric B Never Scared” samples “Those Shoes” by the Eagles. When it came time for my band Revival Revival to work up our arrangement of “Those Shoes” it seemed logical to work in a sample of “Eric B Never Scared.” This is easily the nastiest groove I’ve ever put together.

Revival Revival – Those Shoes Never Scared by ethanhein
I had a teenage guitar student who loves hip-hop, and he asked me for some recommendations. He was underwhelmed when I played him “Follow The Leader” — he thought it sounded old-fashioned and unsophisticated. I was shocked; what could be fresher than Eric B and Rakim? But I’m from a different generation. High school kids now were born into a world where hip-hop is a given. They take it for granted that artists like OutKast and Common and Lauryn Hill will pack their flows with dense internal rhymes and tumbling streams of imagery. Rakim doesn’t sound so groundbreaking now that every halfway decent emcee has absorbed his techniques. It’s like the way the radical innovations of Jimi Hendrix have been turned into standard rock cliches. It takes some historical context to imagine how stunning he must have been back in the sixties.

Rakim came by his connection to the musical past more personally than most, since he’s the nephew of the great R&B singer Ruth Brown. In an interview with Planet Ill, he talks about how his musical upbringing impacted his flow:

I think playing in the bands and learning how to read music; learning the theory of music breaks it down a little more and you get to understand it better. It helped me a lot with my rhythms and my syncopations… I played the sax in school. I play alto all the way up to baritone sax. Coming up in the house my older brother played piano, my middle brother older than me played saxophone, the drums.  I tried to get my hands on whatever I could.

You can clearly hear the bebop in Rakim’s deadpan delivery and his long chains of eighth notes, starting and ending on unexpected beats. His flat affect holds a lot more swagger than if he was yelling and screaming. It lets you focus on the complex musicality of the words. For the first couple of albums, he uses every single song to rap about how awesome he is at rapping, which he proves by being awesome at rapping, even when he’s just rapping about how awesome he is at rapping.

I’m a member of the first hip-hop-listening generation and I still hear Eric and Ra as hot. All that minimalism and repetition and empty space — I know plenty of musicians who are still catching up with it. The eighties hip-hop sound feels urgent to me, it’s so confident in itself. It becomes timeless by being so unapologetically of its time.

Some of the musicians I work with are very anxious about not being too fresh. There’s this need to imitate the masters of the past, to not stray too far from the territory marked out by the Beatles or Led Zeppelin or John Coltrane or whoever their idols may be. This results in weak music. How can you tell the truth about yourself when you’re too timid to belong to your own time and place? I want to grab any musician now who’s obsessed with sounding like Zeppelin, and ask: would you care about them if they were anxiously imitating the music of thirty or forty years before them? There were plenty of bands in 1975 who only played big band jazz, does anyone care about them now? Led Zeppelin took big risks in 1975. Now that their sound has become acceptable, there’s no risk in sounding like them, and no reward either. It’s 2010, better to play and write and produce like it’s 2010.

That doesn’t mean you have to forget or ignore the past. Far from it. Best to follow Eric and Ra’s example and study the past, incorporate it and transform it. The Biz Markie sampling lawsuit may have thrown a wet blanket onto sample-dense music as a commercial enterprise, but the artistic genie is out of the bottle. I, for one, plan to keep doing as much sampling as I can get away with.

Meanwhile, Eric and Ra continue to make their presence felt. The list of hip-hop and techno artists who sample or quote them is too long to go into, and it runs right up to the present. They’ve even crossed over into video game territory — DJ Hero lets you mash them up with MIA, Tears For Fears and David Axelrod.

Hear my mashup of “I Know You Got Soul” with “Pump Up The Volume” and “Follow The Leader.”

I Know You Got Soul Megamix by ethanhein

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:

Primo tells the story of the track, including the serendipitous discovery of the killer orchestral string sample, in The 14 Deadly Secrets by DJ Premier:

A transcript:

The day I made this record, I was at my house in Long Island, and I found this old record that I was gonna throw away. It was a ten inch record from a Lutheran church, and it was pink with a black fish on it. And I was gonna throw it in the garbage, ‘cuz it didn’t look like it had anything hot on it. But somethin’ told me “before you throw it away, put it on the turntable, see if you can find something on it.

And I found that sample of “Nas Is Like”, and I broke it into 3 parts, scratched it live to the drumbeat that I already had, with the little chirpin’ birds and from there, “Nas Is Like” was born, man…

The birds twittering during the intro beat are from “Why” by Don Robertson. And here’s the Lutheran record Primo’s talking about, “What Child Is This.” Very unlikely hip-hop source material.

Most of the lines in the chorus come from Nas’ breakout hit “It Ain’t Hard to Tell.” The “life or death” line is at 0:32, the “Nas is like” that gives the song its title is at 0:44, and the “half man half amazin’” comes in a few seconds later. “My poetry’s deep, I never fell” is at 2:41.

“It Ain’t Hard To Tell” includes some hot samples of its own, including the synth intro from “Human Nature” by Michael Jackson and a saxophone riff from the much-sampled “NT” by Kool & The Gang (listen at 3:12.)

The other source for the “Nas Is Like” chorus is Nas’ “Street Dreams” from 1996. Samples are at 3:16 (“I’m a rebel) and 3:18 (“no doubt.”)

This track is also a composite of different memes – it quotes “Sweet Dreams” by Eurythmics and samples its beat from “Never Gonna Stop” by Linda Clifford.

Maybe the most inventive sample in “Nas Is Like” is a single syllable from “Nobody Beats the Biz” by Biz Markie. It’s the line “highly recogNIZED as the king of disco-in’” at 2:06. Out of context, “NIZED” sounds like Biz is saying “Nas.” That might be the single most creative sample usage in hip-hop history.

No wonder DJ Premier loves Biz — both like using a lot samples and allusions. Biz’s chorus is a play on a commercial jingle that’ll be familiar to anyone from the NYC region who grew up in the eighties (or has watched Seinfeld.) Biz also samples the drums from by “Hihache” by the Lafayette Afro Rock Band, “Fly Like An Eagle” by Steve Miller and, to heighten the self-reference even more, one of his own classic tracks, “The Def Fresh Crew” with Roxanne Shanté.

To add yet another layer of reference, there’s a bit in here where Biz quotes the jingle for Meow Mix! Biz is so much bigger than copyright law.

Nas does a lot of bragging in his rhymes. I learned excessive self-deprecation as a virtue from both my Jewish and middle American Protestant sides, so swagger feels deliciously subversive for me. There’s nothing more balling than sampling yourself in your own songs. Any sample-based song carries a dense web of associations, and I love the complexity that gets introduced when people sample themselves, or when they sample tracks containing samples, or best of all, both. “Nas Is Like” has a complex family tree, a set of allusions to allusions to allusions. This is as it should be. Fundamentally, all music is built of reshuffled bits of other music. Hip-hop makes this fact an explicit part of the music’s message, and that’s the biggest reason why I love it.

Hear a mashup of “Nas Is Like” with “It Ain’t Hard To Tell,” “Human Nature” and “Right Here” by SWV.

Human Nature Megamix by ethanhein

Muppet Silly Songs came out in 1984. I was in fourth grade. I think my dad got it for us. He had us on Wednesday nights, when the Muppet Show was on, and I associate the Muppets with him. It must have been weird originally to have him living in his own apartment a few blocks away from us rather than under the same roof, but by fourth grade it had been a few years and the whole thing felt normal. The next year Dad met my stepmother and moved to Roosevelt Island, still in NYC but a much longer and more complicated trip than a walk down 181st street. So Muppet Silly Songs represents the end stage of a happy time for me. A lot of complex feelings there.

I’m at the age where if I were going to be a rock star, it would have happened a while ago. My musician contemporaries are dealing with the end of the rock star years in different ways. Some continue to rock, though maybe on a schedule limited by careers and families. Some move into teaching or music therapy or just set the whole enterprise regretfully aside. And some move into making music for kids. Kimberly West and Daniel Cole, two singers I used to play lead guitar for, have reinvented themselves as a kids’ group called the Rock Doves. It’s an idea that appeals to me. I have some ideas for songs about math and science aimed at geeky kids like myself in the pipeline.

What makes for good kids’ music? First and foremost it has to be good music, period. As a kid, I couldn’t have explained to you why I liked Michael Jackson or the Beatles, but I knew that there was something truer and more important about their music than other stuff I was hearing. The Muppet people know from good music. Behind their silly delivery they had strong tunes with catchy melodies. They drew on a wide palette, centering on showtunes but bringing in everything from jazz to country.

I can see the roots of a lot of my present interests in Muppet Silly Songs. Both “The Rhyming Song” and “I’m My Own Grandpa” are strongly recursive. In “The Rhyming Song” the joke is simple: the song doesn’t rhyme, at all.

“I’m My Own Grandpa” is a more ambitious joke, a logical pretzel knot that wouldn’t be out of place in Gödel, Escher, Bach.

The Muppet guys loved Tin Pan Alley songs. In their version of “Who?” by Jerome Kern, the question in the title is asked by an owl.

The album also includes Kermit The Frog’s rendition of “Lydia The Tattooed Lady.” The Muppet Wiki informs me that it was written by Harold Arlen and Yip Harburg (who also wrote the songs in The Wizard Of Oz) for the Marx Brothers movie At The Circus. Kermit’s version is less saucy.

As a kid I had no idea what the lyrics were talking about, I just liked the complex rhymes. (I guess it warmed me up for the brainy hip-hop I like now.) Shortly after graduating from college I moved back to New York City. I went to a party at my older stepbrother’s place in the Meatpacking District, and then on my way home roamed around the West Village. It was summer, a warm night, people were out. A guy in a bunny suit rode by on an enormous tricycle singing “Lydia The Tattooed Lady” and I felt that weird mixture of adult sophistication and childishness that I feel often in NYC. It’s the way I feel now, listening to Muppet Silly Songs. Not a comfortable feeling, but one I like.

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.

Why is Bach’s music so much cooler than anything else of his time and place? There are plenty of beautiful melodies and interesting thematic developments in other Baroque music, but they’re usually buried under tweedly curlicues. I get exhausted from all the jumping up and down between adjacent scale tones.

You never get the sense that Bach is just throwing notes at you to fill the space between ideas. This spare, economic quality shows most clearly in his solo instrument stuff. The single lines spell out both the melodies and the chord progressions clearly, using the spaces between the melody notes to deploy fragments of basslines or arpeggios. Bach gives your imagination just enough data to easily fill in the rest. Leaving notes out is a great way to draw in the listener. It invites us to participate in our heads.

Nowhere does Bach build more attractive melodies out of arpeggiated chords than in his cello suites. The first movement of the G major suite is a total cliche thanks to its heavy TV and film exposure, but for good reason. I can’t think of a better use of a melody to spell out harmony. You can have your Pablo Casals and your Yo-Yo Ma; as far as I’m concerned, Mstislav Rostropovich owns the cello suites. I can’t embed the video of him playing the first movement, sadly; click here to enjoy it.

Bach has huge geek appeal. He favored puzzle-like musical forms, canons and fugues, where the melody gets repeated as its own accompaniment. Even outside of such self-referential formalities, Bach’s music is dense with references and quotations, of other works, and of itself. Bach’s love of recursion inspired Douglas Hofstadter to write a whole computer science book about him (and Gödel and Escher.) Fans of Gödel, Escher, Bach might enjoy the Tumblr devoted to it. Here’s a nice quote from the New York Times review of GEB:

A theme enters, then appears again, inverted or reversed or in a different key or a different tempo; the transformed melody then blends with its original. Figure and ground may unexpectedly change roles. Even though each of the notes is heard distinctly–and in Bach the notes have a logic only slightly less formal than that of the Russell-Whitehead language — the ear cannot always resolve their relationship.

Bach was a great quoter of the popular music of his time and place: hymns and regional dances. Since most of the music he was paid to write was for church services, it’s no big surprise that Bach did so much reworking and embellishing of hymns.

There’s a cool album called Morimur by Christof Poppen and the Hilliard Ensemble. It combines the chaconna from Bach’s violin partita in D minor with the hymns it derives from. Poppen plays the violin music, the Hilliard Ensemble sings the hymns, and then they do them both simultaneously. The effect is haunting and gorgeous. You couldn’t ask for a better education in what it means to embellish a theme than to hear Bach’s lines superimposed on the simple hymns. No wonder jazz musicians love him so much, the effect is similar to the way Charlie Parker sounds improvising on a showtune. (Bach was known in his lifetime as an improviser, which adds to his jazz cred.)

Morimur’s liner notes go on at length about all the elaborate numerical codes embedded in the music, but who cares? This is the kind of dry and tedious pedantry that scares people with feelings away from classical music. On the other hand, I’m both convinced and moved by the theory that Bach wrote this melancholy piece based on hymns about death in tribute to his first wife, who had died a year before.

The chaconna is a dance form. It doesn’t sound rhythmically very much like what we’re dancing to now, but there are some structural similarities. A short theme repeats continually, with variations, over a predictable and simple chord progression spelled out in a looped bassline. Bach’s chaconna implies the bassline more than stating it, but your ear fills it in easily. Bach’s use of repeated modules evokes grid-based electronic music. There’s something very algorithmic about the rule-oriented forms he wrote in, the canons and fugues, all that complex counterpoint. Every note that Bach ever wrote is on the web in MIDI format. His music sounds pretty decent when played by robots (though it’s still livelier when it’s played by humans.)

Bach wasn’t very highly regarded in his lifetime outside of a small devoted circle of groupies. He didn’t hit the cultural big time until a hundred years after his death. He’d probably be amazed now at his elevated stature. His music probably works better outside of its original context than it did inside it. No context shift is too radical. Wendy Carlos’ 1968 all-synth album Switched-On Bach is goofy, but it still makes its own weird kind of sense.

There have been plenty of other sassy modern interpretations of Bach. Apollo 100 did a groovy retrofuture pop version of “Jesu, Joy Of Man’s Desiring” in 1972 that shows up in The 40-Year-Old Virgin soundtrack.

I guess Bach makes so much sense in the present because he combines rigorous formal logic with the spirit of an improviser. I can’t think of a better way to describe the rest of the music I like listening to.

Update: see the connection between Bach and Paul Simon.

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? Each time through, the chant affects me a little differently. The forty-third time through might be musically indistinguishable from the forty-second but it feels different. My attention drifts and snaps back in. There’s a feeling of tension through each group of four or eight that gets resolved on the first repetition in the next phrase. A cumulative tension builds across all the repetitions.

Some western listeners get anxious from this tension. I’ve seen loops make people surprisingly angry. The loop reaches deep into the brain stem, and not everybody likes having their consciousness altered so heavily. I’ve also seen loops bring groups of people into ecstatic states with an afterglow lasting for days, weeks, even months.

Loops make me happy

In retrospect, I look back at stuff I liked the best instinctively before I was a musician, still just a fan, and what ties it all together is loop-oriented structures.

• Riff-based Ellington, Monk and Coltrane tunes
• “Once In A Lifetime” by Talking Heads
• “Not Fade Away” and “Fire On The Mountain” by the Grateful Dead
• “Stir It Up” by Bob Marley
• “Wanna Be Startin’ Something” by Michael Jackson
• Everything by Run-DMC
• The first few minutes of “Chameleon” by Herbie Hancock

On paper, these tunes are all very boring pieces of music. But living in my ears, they’re bottomlessly gratifying.

People with a casual relationship to music tend to enjoy loop-based material, especially on the dance floor. But many if not most of the trained musicians I’ve worked with are resistant to the loop. Whether they come from jazz or classical, schooled musicians tend to equate quality with complexity, density and unpredictability. This to me is one of the great pathologies afflicting the music academy. Making good music takes a lot of study and focus, but that’s different from effort. Some of the best music is easy. After struggling with all the intricacies of music theory, we musicians get too suspicious of simple truths. That suspicion gets in the way of our main job of connecting to listeners and making their lives more bearable.

A few years ago I went to hear a highly respected quartet led by a saxophonist who the jazz nerds speak of in hushed tones. I got to the club early enough to catch the soundcheck. While the sound guy fiddled with levels, the band played an open-ended funk groove on one chord. It was exhilarating: the loose interplay between the band members was anchored by the straightforward groove to make a satisfyingly tight sonic knot. I was all excited for the actual set, which turned out to be… a snooze. The material was full of startling key and time signature changes at unpredictable intervals. The band maneuvered through these sonic mazes masterfully, and I’m sure they enjoyed themselves, but for me it was like watching someone else play a difficult video game. And these are jazz musicians, supposedly the warm, emotionally connected wing of intellectual music. The situation is even worse in the classical world.

All music is based on repetition

The definition of a rhythm is a patterned sound that repeats (or, for that matter, any patterned event that repeats.) Pitched sounds are produced by regular sine-wave vibrations as an air column’s pressure cycles back and forth.

Repetition and recursion

Nearly all world music uses repeating phrases grouped into longer phrases, and groups those metaphrases into meta-metaphrases. Entire sections get repeated to form still higher level structures. For my ears, the most satisfying music is the most modular and recursive.

Loops and thermodynamics

Repeated events are surprising because they’re thermodynamically improbable. Usually the rock falls off the mountain and just sits there. For the rock to roll around and around in a circle, some unusual force must be driving it. When we come across something improbable, we instinctively want to find a meaning for it. Symmetrical repetition creates structure and gratifies our pattern-recognition systems, the same ones that enjoy parsing out the meaning of a text or the rules of a video game.

Structure acts very strongly on our emotions, often without our realizing why. One reason the Beatles and Michael Jackson sell so many more records than their seemingly equally talented peers is their mastery of structured repetition. Their best work repeats phrases exactly the right number of times, in exactly the right sequence. This aspect of songwriting is harder to quantify in rule sets than rhythm or harmony, but that hasn’t stopped the music industry from trying. Here’s an excerpt of an entertaining McSweeney’s series, Dispatches From a Guy Trying Unsuccessfully to Sell a Song In Nashville by Charlie Hopper.

To me, it appears that Music Row’s devotion to form and formula is not strictly venal. It’s just the smartest way to send a song into the Machine without you being there to defend it. “The first rule of songwriting is, there are no rules,” Barbara Cloyd, a Songwriting Tutor, likes to declare at the outset of her class. Then she takes a fairly deep breath: “Having said that…”

And she goes on to explain the three or four acceptable formulas.
It all proceeds from the notion that there are basic truths about how people like to get information. Barbara quotes someone she knows as saying, “We like to hear something, then hear it again. Then we want to hear something different for a while. After that, we’re ready to hear the first thing again.”

That would be Verse Chorus, Verse Chorus, Bridge, Verse Chorus.

I knew John spoke the Universal Language of Beatles. “So the basic formula is like, oh, ‘Ticket to Ride.’ Or ‘Day Tripper.’”

I might have been a little didactic. “Then, if you want, you can start with two verses. That gives you an option to have one or two verses after the first chorus. But you never put two verses after the first chorus unless you had two at the beginning. That screws with the formula.”

John was laughing and shaking his head in a way that meant he couldn’t believe I had bought into this seriously.

“Like ‘Yellow Submarine,’” I said. “Two verses, chorus, one verse, chorus, the farting around in a submarine during the bridge, verse, chorus. Actually, the bridge is optional. I’ve heard publishers say, ‘Do you really need a bridge here? There’s no new information in it…’”

The other form that’s generally acceptable, though less prized because it has no soaring chorus, is the “A A B A” form. The hook comes as the end line of each A section. It might show up at the end of the B section, but doesn’t have to. Most songs that are written with no thought of formula tend to be in this form. “Yesterday” is A A B A. “Back in the U.S.S.R.” is. “Girl” is. Most Bob Dylan songs are.

Repetitive music teaches itself to you as you listen

Repetition creates familiarity, which is a prerequisite to emotional connection. Cognitive scientists use the word “rehearsal” to describe the process by which the brain learns through repeated exposure to the same stimulus. As they like to say, neurons that fire together wire together. Repetitive music builds rehearsal in, making it more accessible and inclusive.

Africa vs Europe

In America, our musical culture is a hybrid of mostly western European, African and Caribbean traditions. Our musical ancestors have some philosophical differences around repetition. The western European classical music term for a continually repeated phrase is an ostinato, from the Italian word for “stubborn.” It’s related to the English word obstinate. This is not an attractive quality in a person and the European classical world doesn’t think too highly of it as a quality of music either. Theodor Adorno criticized the repetitiveness of popular music as being “psychotic and infantile.” He was outspokenly contemptuous of jazz and dance music generally. From his book Prisms:

Considered as a whole, the perennial sameness of jazz consists not in a basic organization of the material within which the imagination can roam freely and without inhabitation, as within an articulate language, but rather in the utilization of certain well-defined tricks, formulas, and cliches to the exclusion of everything else.

Adorno is factually correct. But he’s wrong that this is a defect of the music. The tricks, formulas and cliches are the basic grammar of pleasure. Cooking tofu with sesame oil, ginger and soy sauce is a cliche too, and for good reason, it consistently makes the tofu taste good.

Fortunately, we in America are blessed with the strong African and Caribbean influences, and the musicians of these cultures hold circularity as a high virtue. To pick one example out of a vast many, Fela Kuti’s “Beasts Of No Nation” repeats the chords G minor to F for about half an hour. It doesn’t get old.

Sample-based hip-hop is the music most exciting my ears right now. The best beatmakers find fragments that were part of a linear stream and bend them into unexpected loops.

I don’t know the provenance of this RZA quote beyond wikipedia, but it’s a good one:

For hip hop, the main thing is to have a good trained ear, to hear the most obscure loop or sound or rhythm inside of a song. If you can hear the obscureness of it, and capture that and loop it at the right tempo, you’re going to have some nice music man, you’re going to have a nice hip hop track.

This is good advice for any musician, not just hip-hop beatmakers.

Historically, search engine results were ranked based on the frequency and proximity of keywords in the page text. But as the web grows, there are tons and tons of pages out there with the same or similar keywords. Any Google search on any remotely mainstream topic is going to return thousands and thousands of hits, most of which are useless to you. Another problem is that the keyword system is easy to game. Unscrupulous web designers can load up a page with invisible keywords repeated over and over, by putting them in the same color as the background off to the side of the page.

To make its results more useful, Google tries to rank its keyword-based search results in the order of their relevance. They do this using a complex proprietary algorithm called PageRank, the real heart of their search engine. One of PageRank’s most heavily weighted factors is the number of links pointing to a page. If more people link to your site, presumably that’s because it’s more useful or authoritative. PageRank also recursively factors in the number of links going into those pages that link to you.

So the key to a higher Google rank is getting other pages to link to you. The question is, how do you get those precious inbound links?

The first step is to do a lot of linking to yourself. Using blogs, Twitter, Delicious, Flickr and other social networks, you can link to your own site with impunity. A single Twitter post is a full-fledged web page unto itself and any links within it count just as much toward your Google PageRank as any other.

Internal links from one page within your web site to another all count towards your PageRank total. This is why blogs are so great for SEO. They create tons of internal links automatically: tags, categories, previous/next post links, and so on. WordPress users can get even more SEO benefit from plugins like Random Posts, Calendar and Most Commented.

Another way to get your URL out there is to comment on other people’s blogs. Nearly all blog platforms give you a chance to add a link to yourself when you post a comment. This SEO strategy has given rise to the automated blog-commenting spambot, a program that generates a human-seeming comment from keywords in your site with a link back to some online vitamin seller or what have you.

In addition to links, you still need to make sure your keywords are in place in your page copy. What search terms are people likely to use when looking for your site? Put yourself in the shoes of a stranger out there on the internet. Do some Google searches in character as this stranger. Make sure the phrases that you’re searching with appear verbatim in your page text.

Freshness of content matters too. Google ranks newer material higher than older material. This is yet another reason why blogs are better than static web sites for getting yourself noticed. Twitter is even better for keeping your presence up-to-date.

Plain-English URLs and page titles help too. Notice that the addresses of the posts in this blog spell out what the post is about. If your page titles and URLs give some indication of what’s on the page, that helps both humans and the Google robots identify them properly.

SEO companies have all sorts of esoteric methods and tricks, technical stuff like alt tags and XML sitemaps. By all means, try these things, they can’t hurt and might marginally help. But fundamentally, SEO is all about having well-written content that’s genuinely useful or interesting to other people, and having lots of links pointing at your site. These more basic approaches take time and effort, but ultimately, they really work.