Why has music been historically the most abstract art form?

I had an art professor in college who argued that all “representational” art is abstract, and all “abstract” art is representational. Any art has to refer back to sensory impressions of the world, internal or external, because that’s the only raw material we have to work with. Meanwhile, you’re unlikely to ever mistake a work of representational art for the object it represents. You don’t mistake photographs (or photorealistic paintings) for their subjects, and even the most “realistic” special effects in movies require willing suspension of disbelief.

Music seems more abstract than other art forms because it represents emotional states, symmetry and repetition, and other intangibles. But just because you can’t see or touch these things, doesn’t make them any less real. In preliterate societies, music was probably one of the best methods for storing and conveying complex stories and information.

Also, I dispute the idea that visual art started representational and then “progressed” toward greater abstraction. Architecture, textiles, tile work, face and body decorations and jewelry all use pattern, color and texture for their own sake, without any representational content.

Any one of the above images could pass as a music visualization or notation. I see a strong parallel between this kind of decorative art and the mathematical patterns in music — there’s the interest in interlocking patterns and symmetry for their own sake. Symmetry is a fact of the world, and both abstract art and music represent that fact clearly.

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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.

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The brain is a pattern-recognition machine. We like repetition and symmetry because they engage our pattern-recognizers. But we only like patterns up to a point. Once we’ve recognized and memorized the pattern, we get bored and stop paying attention. If the pattern changes or breaks, it grabs our attention again. And if the pattern-breaking happens repetitively, recursively forming a new pattern, we find that extremely gratifying.

Good breakbeats are just complicated enough to challenge our pattern recognition ability without totally overwhelming us. Repeating a complex and unpredictable rhythm in a simple, predictable structure, and then sometimes breaking that structure, holds our attention without completely dominating it. A good breakbeat ties the room’s attention together while still leaving enough bandwidth for people to dance, rap, sing, socialize or daydream. Breakbeats are good for social music because your attention can wander away to the other people with you, and then easily pick the thread back up.

For further reading about how music is defined by the limits of our attention spans, I recommend Music And Memory: An Introduction by Bob Snyder.

Also, I’ve written a few blog posts about programming your own beats:

• How to make a hot beat
• Drum machine programming

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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.

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To make a diminished chord, you start on any note, go up a minor third, then another, then another. Here are the notes in C diminished — the scale tones are in red.

Here are some good guitar fingerings for diminished chords.

Diminished chords are highly symmetrical, which gives them a peculiar property. The circle above shows C diminished, but the same notes also make Eb, F# and A diminished. The only difference between these four chords is their respective bass notes. This symmetry means that there are only four diminished chords total. The diagrams below show what I mean. On the left is the circle of fifths; on the right is the circle of half-steps. Each square is a diminished chord.

To play blues you mostly only need to concern yourself with the diminished chord on the root of the key. In C, that’s Cdim7 (though you can also substitute Ebdim7, F#dim7 and Adim7.) Here are the most common uses of diminished chords in the blues in C.

C diminished

To make Cdim7, you slide every note in C7 down a half step except for C itself.

C7:    C  E  G  Bb
Cdim7: C  Eb Gb A

Any time you have an uninterrupted stretch of C7, you can liven it by dropping briefly to Cdim7 and then sliding back up to C7. Robert Johnson did this a lot on the first four bars of twelve-bar blues. Instead of this:

| C7 | C7 | C7 | C7 |

Robert Johnson played this:

| C7 | Cdim7 | C7 Cdim7 | C7 Cdim7 C7 |

In “Kindhearted Woman Blues” you can hear this riff on the line “Now there ain’t but the one thing that makes Mr Johnson drink, I swear by how you treat me baby, I begin to think.” Listen at 1:18.

See guitar tab for a good voicing of this lick in the key of A.

The individual notes in C diminished make a great melodic line. C is the root, naturally. Eb and F# are from the blues scale. A is from the major scale, and it forms a nicely dissonant tritone.

Eb diminished

This chord is part of a ubiquitous blues and jazz lick that I know as the Blue Monk lick.

C7  Dm7  Ebdim7  C7/E

There are some variations you can use on the second chord:

C7  Dm7(b5) Ebdim7  C7/E
C7  Ddim7   Ebdim7  C7/E
C7  Bb/D    Ebdim7  C7/E

You can freely insert the Blue Monk lick anywhere you have a couple of bars a single dominant chord. Instead of:

| C7 | C7 |

Play:

| C  Dm7 | Ebdim7  C7/E |

This riff has been the basis for a lot of songs, most notably (surprise!) “Blue Monk” by Thelonious Monk.

You can also hear it in the bridge of “Honeysuckle Rose” by Fats Waller, under the line “You’re my sugar.” Here’s a live version by Ella Fitzgerald, listen at 0:47.

The Blue Monk lick works equally well backwards:

C7/E  Ebdim7  Dm7  C7

Wikipedia calls this the How Dry I Am lick; I associate it more with Bob Dylan’s “Rainy Day Women #12 & 35.”

Robert Johnson used the descending Blue Monk lick for his characteristic intro — grab the tablature here.

F# diminished

Use this chord after F7 to get what I call the gospel lift. Use it in bar six of the twelve bar blues and feel the spirit. Instead of:

| F7 | F7 |

Play:

| F7 | F#dim7 |

Jazz loves the gospel lift. Hear it in Duke Ellington’s “In A Mellotone” as sung by Lambert, Hendricks and Ross — listen at 1:05 and try to ignore the goofy video.

The gospel lift also shows up in a turnaround commonly used in bars eleven and twelve of twelve-bar blues.

| C  C7/E  F7  F#dim7 | G7 |

This turnaround makes a nice intro, and with a slight tweak, it also makes a swell ending.

| C  C7/E  F7  F#dim7 | C  Db7 C7 |

I haven’t yet talked about A diminished. That’s because it doesn’t get a lot of action in the key of C except as an alternative voicing for the other diminished chords.

The other big diminished use case: minor-key V chords

The other major use case for diminished chords is for dominant chords in minor keys. In C minor, the dominant chord is G7(b9). This chord includes B diminished (or D, or F, or Ab diminished, however you want to think about it.) This is good to know for minor blues. It’s also handy anywhere you encounter a minor chord. Just insert the diminished chord a half-step below the root and you can get some nice passing chords and chromatic basslines. For example:

| Cmaj7 | C#dim7 | Dm7 | G7 |

This isn’t blues, but the Roots use the minor-key dominant diminished idea heavily in their awesome song “Don’t See Us.”

Okay. So. The Higgs boson is involved in the weak nuclear force, which is the weirdest and least famous of the basic four forces in the standard model of particle physics. I have a pretty firm handle on the other three. There’s gravity, you know what that is. There’s electromagnetism, which is behind pretty much everything in our direct experience aside from gravity. And there’s the strong force, which sticks quarks together into protons and neutrons, and sticks those together into atomic nuclei.

But then the weak force. This one is harder to nail down in a single pithy sentence. When you get to the section on the weak force in most popularly-oriented physics texts, the language becomes vague and evasive. There’s usually a feeble bit about how the weak force “is involved in certain kinds of radioactive decay.” This is true, but it doesn’t begin to tell the story. What the weak force really does is transform one kind of particle into another.

Here’s the weak force at work, transforming a neutron into a proton.

This might be happening inside an unstable atom, like nitrogen-16 (nitrogen with too many neutrons.) Time goes from bottom to top, as indicated by the arrow. At the bottom is the neutron, with its three quarks: up, down and down. As the nucleus wobbles, it’s possible for its components to come within the weak force’s extremely short range. A weak force carrier particle, represented by the wavy line labeled W-, changes the flavor of one quark from down to up. That changes the neutron into a proton, and in the process spits out an electron and an antineutrino. With its new proton, the former nitrogen atom is now oxygen. Shazam!

Weak interactions are part of the fusion reactions powering the sun. They’re the reverse of the one pictured above, since the sun turns protons into neutrons, spitting out positrons and neutrinos. Weak interactions produce some of the heat coming from the Earth’s core, and there are more weak interactions in the upper atmosphere as high-energy particles slam into air molecules. Aside from nuclear reactors and particle accelerators, there isn’t too much weak force happening in our day to day lives. Your best chance to experience the weak force first hand is in a hospital PET scanner. Anna asks, looking over my shoulder, if it scans to see if you have any pets. Um, no.

Before you lie down in the scanner, you get injected with a radiotracer containing unstable isotopes of oxygen, nitrogen or some other biologically-oriented element. These isotopes come attached to glucose or water molecules. You lie in the scanner, and as your body metabolizes the radiotracers, weak interactions emit positrons (thus the term Positron Emission Tomography.) The positrons are antimatter, and they don’t get far before they smack into electrons, mutually annihilating into pairs of high-energy photons that zip away in exactly opposite directions. The scanner ring registers all the photons hitting it, and devotes mammoth amounts of computer power to ignoring all of them except the ones originating on opposite sides of the ring. From there, the computer can deduct where the photons are originating, and voila, you get a 3D animated picture of your metabolism in action.

There are a couple of weird and cool things about the weak force. One is that it has a preferred handedness. All particles spin, either clockwise or counterclockwise. Physicists call these spin directions right-handed and left-handed. If you think of your thumb as your spin axis, then your fingers curl in the direction of spin. The weak force defies common sense by only acting on left-handed particles (and right-handed antiparticles.) This is a startlingly odd asymmetry. Gravity and electromagnetism act the same on left and right-handed particles and there’s no obvious reason why the other forces shouldn’t behave the same way. Could this asymmetry could be related to the slight imbalance between matter and antimatter produced by the big bang? Is it necessary for a universe that’s hospitable to our existence? What do you say, scientists?

Another weird and cool thing about the weak force is its relationship to electromagnetism. They turn out to be different aspects of the same force. This is where the Higgs boson comes in. It’s the particle aspect of the Higgs field, which is thought to pervade all of space. The standard model of particle physics credits this invisible energy field with giving the various force-carrying particles their various masses. The idea is that the Higgs field gives the universe a weak force charge, the way electric charge pervades a cloud before a thunderstorm. The weak force has such a short range because the W and Z particles that convey it drag against the Higgs field and quickly lose their juice. Photons have an infinite range because they don’t interact weakly, so they pass right through the Higgs field.

So here’s the thing. At very high temperatures, the Higgs field evaporates. W and Z particles no longer drag, so they become massless and indistinguishable from photons. In other words, electromagnetism and the weak force reveal themselves to be different aspects of the same force, the electroweak force. The standard model predicts this, and experiments have confirmed it. This fact gives physicists hope that at higher energy levels still, the electroweak force will unify with the strong force, and at even more ridiculously high energy levels, they’ll all unify with gravity. Sadly, testing the unification of the electroweak and strong forces is very far out of our technological reach. Testing to see if the other forces unify with gravity would require a particle accelerator bigger than the solar system. That hasn’t stop physicists from dreaming of finding a single unified theory of the forces, a mathematical description of the entire universe that would fit on a t-shirt. Einstein spent decades of his life searching for such a theory, without success.

The Higgs boson is the particle form of the Higgs field, the way the photon is the particle form of the electromagnetic field, and the electron is the particle form of the lepton field. The Higgs boson has never been spotted. It’s assumed that it takes more energy to produce Higgs bosons than particle accelerators have been able to bring to bear. A major mission of the Large Hadron Collider is to produce Higgs bosons.

Here’s what Higgs boson production would look like on the LHC computers:

And so who is this Higgs guy? Here’s what he looks like.

He was one of the major movers behind the electroweak theory and is presumably twiddling his thumbs in a university office somewhere, waiting to see if they do indeed find his particle. I’m rooting for him.

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.

Before the mid-sixties, it was a different story. Pop and jazz artists were mostly interpreting existing, familiar material, and only rarely writing new stuff. Even the most prolific and brilliant jazz composers like Miles Davis and Thelonious Monk devoted album after album to arrangements of standards. Nobody arranged standards more radically and personally than John Coltrane.

My Favorite Things

The emblematic Coltrane remake is “My Favorite Things” from his classic album by the same name. Here’s a live rendition:

Coltrane’s arrangement of this tune bears the same relationship to the one in The Sound Of Music as “Hard Knock Life” by Jay-Z bears to Annie. Jazz arranging uses different technology than sampling and remixing, but it makes the same musical statement. It’s a stamp of personal ownership on a familiar piece of public musical property.

I bought Coltrane’s album when I was eighteen or nineteen after hearing Jerry Garcia and many other musicians rave about it. On the first pass, I wasn’t impressed. A corny showtune played on soprano sax, whee! Now I experience Coltrane’s version of “My Favorite Things” as the mind-expanding flight of imagination I was promised, but I had to grow up a little to appreciate it. I eventually developed such an obsession with it that when I had a jazz band, I insisted that we perform it regularly, and that we include it on our one CD.

Coltrane and looping

Coltrane had a way of anticipating what music would sound like in the future. He was particularly prescient about the importance of looped basslines. Jazz bass is usually a complex semi-improvised stream of quarter notes. But Coltrane liked to have his bassists play strictly structured two-bar loops. On “My Favorite Things,” Jimmy Garrison plays a a simple pattern on the note E identically for almost the entire duration of the song. This kind of bassline anticipates the looped, sequenced and sampled bass parts in hip-hop and other electronic music. The idea was probably inspired in part by the Ravi Shankar albums Coltrane was listening to at the time.

Coltrane was also prescient in his liking for open-ended loops on a single chord, or a few repeating chords from a single scale. This is the basic structure of nearly all forms of electronic music. Like James Brown and the hip-hop artists he inspired, Coltrane relied a lot on the “repeat until cue” instruction. The E major and E minor parts in “My Favorite Things” are open-ended loops. You play each one as long as you feel like playing it, and then signal the band that it’s time to continue to the next section by playing the “raindrops on roses and whiskers on kittens” melody.

But Not For Me

The album My Favorite Things is most famous for its title track, but it also includes three other startling reinterpretations of standards. “Every Time We Say Goodbye” implies a doubletime feel in places and stretches the melody like silly putty. “Summertime” is played fast, with an aggressive feel and crunchy, dissonant chord voicings. Finally, “But Not For Me” gets transformed almost as radically as the title track. Here’s a conventional version by Chet Baker:

And here’s Coltrane’s arrangement.

Should we consider Coltrane’s arrangement to be the same piece of music as the Gershwin original? The most obvious change is the first four bars. In the Gershwin tune, the line “They’re writing songs of love but not for me” runs over a simple ii-V-I progression in E flat. Coltrane’s first four bars are a sprint through the keys of E flat, B and G via those keys’ respective dominant chords. The bassline spells out the descending E flat whole tone scale: Eb, F#7/C#, B, D7/A, G, Bb7/F, Eb. Coltrane rewrites the melody completely to fit this new chord progression.

Coltrane inserts some other new structural elements into “But Not For Me.” He adds a long tag section where he lifts unexpectedly up to a few distant minor keys for eight bars each. There’s also the extremely extended open-ended tag on the ii-V-iii-VI turnaround. If you call this tune on the bandstand and you expect the Coltrane arrangement, you’d better come prepared with charts and a lot of explanation.

Jazz and modularity

Every jazz arrangement of a standard is an analog remix. Where do you draw the line between an arrangement, a new melody written to existing chord changes and an improvised solo? The line is blurry at best. Should we consider “Whispering” and “Groovin’ High” to be the same song? How about “I’m In The Mood For Love” and “Moody’s Mood For Love?” Or “I Got Rhythm” and the zillion bebop heads it inspired?

Jazz was largely built on a scaffolding of showtunes and other pop songs. The crucial ones known as standards have certain musical characteristics that make them more amenable to jazz adaptation: a modular structure amenable to being dissassembled and reassembled, like a good Lego kit. Jazz compositions and improvisation look to me like different combinations from a giant box of musical legos, rearrangeable at will on paper or on the bandstand.

The most jazz-friendly standards have singable melodies with rhyming lyrics accompanied by a simple chord progression (or sometimes not so simple, but always intelligible to the ordinary person’s ear.) They’re repetitive and predictable. They follow a small set of conventions in their structure: four, eight and sixteen-bar phrases, repeated two or three or four times, with the larger grouping of phrases repeating more or less intact for the entire duration of the tune. There are a lot of interchangeable modular forms: the cadence, the turnaround, the counter-clockwise trips around the circle of fifths.

As with harmony, there’s a finite toolbox of riffs, patterns and scale runs you can use to build your jazz melodies and solos. Blues is particularly heavily based on Lego-like modular riffs. Intros and endings are few, highly standardized and interchangeable. One much-recycled ending is the one Count Basie uses in his performance of “Fly Me To The Moon” with Frank Sinatra:

Another basic Lego is the Duke Ellington ending, as in “Take The A Train.”

Modules and samples

I think that the distance between a jazz module like the Duke Ellington ending and a sample like the Funky Drummer break is short. The technology changes but the underlying musical statement is the same. Writing a jazz tune based on licks and progressions from existing songs feels very much the same to me as producing a track based on samples and loops. I doubt there’s ever been much originality in the most creative music, and I see a smooth continuity from the practices of my musical forebears to the ones used by me and my contemporaries.

Even Coltrane’s “original” music draws heavily on other sources. His classic tune “Impressions” is a mashup of “So What” by Miles Davis and “Pavane” by Morton Gould. If the most creative artist in the history of jazz is sampling, I think everyone should feel emboldened to do the same.

Here’s my remix of Coltrane’s “Venus” — enjoy.

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The color-coding system started as a simple information-management technique, but it ended up improving my ears. Spending so much time looking at these colorfully abstracted representations of so many songs, I couldn’t help but notice some patterns. I’ve done enough tracks now that I can lay something out in the sequencer and know that it’ll basically work without having to listen to it first. Classical and jazz musicians get to the point where by glancing over a score, they can hear it quite clearly in the mind’s ear. The Reason sequencer has a much shorter path into the brain’s deep sense-data processing centers because it’s dynamic, animated, and responsive to my thoughts in real time.

So here are three representative tunes. The rows are instruments, mostly sample players along with the odd drum machine or synth. The columns are groups of eight bars, sixty-four beats according to the dance music convention of a bar comprising eight eighth notes. You can see that every phrase in these tunes is two, four, eight or sixteen bars long. This is no accident. Powers of two sound good. Each colored brick is a phrase worth of sequencer data. My system is to color intros and outtros pale yellow, the verses blue, choruses green, instrumentals and breakdowns orange, and bridges purple. The colors are chosen soley on the basis of what looks good together on the screen.

The Sign – Revival Revival vs Ace Of Base vs Super Mario Bros vs Scientist

Even though this track is a freakshow sonically and memetically, its underlying structure is total pop boilerplate. Every phrase is eight bars long. The intro is mostly identical to the verses, each of which is followed by the chorus. The breakdown is modeled on the verse, but twice as long, and is followed by a triple chorus to end the song. The outtro is the last chorus spaced out and with no drums, plus a little tag on the very end.

Tomorrow Never Knows – Revival Revival vs the Beatles vs M.I.A. vs Missy Elliot

Tomorrow Never Knows by ethanhein

Since this is a fake Ravi Shankar tune, it has a more open-ended, less narrative structure. The single-chord jam fits electronic music like a glove, and fake Middle Eastern and Asian music usually translates better to computers than Western linear tunes with definite beginnings, middles and ends. Tomorrow Never Knows is a single mixolydian scale to infinity, verses interspersed with open-ended passages of swirling modal chaos. I have a few different versions of the basic loop with different densities, but functionally they’re all interchangeable. The colors are more general landmarks for me.

Love Her Madly – Revival Revival vs the Doors vs James Brown

We like this tune so much that we extend it like crazy in performances. The recording only goes to the bridge once, but live we do a breakdown and then go back into the bridge, sometimes a few times. The outtro is when I rap.

MIDI sequencers like Reason have done for music notation and composition what word processing and the internet did for the written word. Especially intriguing is the way you can move the loop markers around during playback. My one sadness with Reason’s sequencer is that while there are many operations you can perform during playback and live recording, you can’t copy and paste in the sequencer window without stopping first. Maybe there’s some unavoidable software constraint here, or maybe it’s just lazy coding, I’ll give the Reason guys the benefit of the doubt and assume the former. I’m finding so much inspiration in their software, it feels ungrateful to criticize.

Reblogged on Hysysk’s Delicious