On The Ergonomics Of Music: Reflections On Flow In Steve Reich’s “Drumming”

“But how the paths sounded to me was deeply linked to how I was making them. There wasn’t one me listening, and another one playing along paths. I listened-in-order-to-make-my-way.”
-David Sudnow, Ways of the Hand (MIT Press 2001, p. 40)

Every once in a while warming up before a show I noodle around by playing a bit of Steve Reich’s Drumming on the marimba. Composed in 1971, Drumming is over an hour of continuous percussion music entirely built on just a few pitches arranged in a constellation of eight beats over twelve pulses. This is the core melo-rhythmic pattern:


As I played Reich’s pattern I thought about what makes it so idiomatic for the drummer’s hands. First, there its short-short-long-long rhythm whose composite sounding has the feel of a three against two polyrhythm. Next, the truncated scale: four notes of a minor one, but without the other three notes that would tell us more about specifics. Finally, Reich’s pattern on these four notes bring my left hand on an out-in-out motor pattern, moving from the g-sharp (out or away from me), up to the b-natural (in or towards me), and then from the b-natural down a semitone to the a-sharp (in to out). Simply put, while the right hand stays perched up on the c-sharp, the left hand motor pattern traverses a small in-out path that flows like crazy!

As I played and enjoyed the flow of the pattern I wondered how it would sound and feel in different keys, so I transposed it downwards one semitone at a time to try it out on eleven other starting pitches. But none of these transpositions felt nearly as natural as playing the pattern on g-sharp. Interesting. In fact, some of the transpositions–starting on b-natural, for instance–were seriously awkward to play. Now I wondered: Would Drumming have worked had it been done in a different key? Had it been tried in different keys? Was motor pattern flow a factor in deciding on its key? (So many questions.)

Playing the core pattern of Drumming had me thinking about some other matters related to composing and playing musical instruments. Had the pathways of this pattern, in this key, on this instrument (and not the tuned bongo drums that are featured in the piece’s opening movement), been the impetus for Drumming? I also reflected on how it is that a piece of music that works so well–that sits so well in the hands–can help define a lexicon of movements that are possible along the terrain of an instrument. If you write music for marimba, it’s difficult to ignore the enduring influence of Reich’s distinctive syncopated patterns on your understanding of the instrument’s idiomatic potentials and expressive sweet spots. Even if you’re just noodling around, warming up before a show by playing bits of Drumming, the fact that the piece continues to sound and feel as good as it does as ergonomic percussion music is enough to make you reflect anew on how closely writing and performing music are connected.

Here is part two of Drumming:

On Modular Grid Structures: Thinking Through Sol LeWitt’s Cubes

I recently saw a striking cube-based structure by Sol LeWitt (1928-2007) at the MoMa. When you stand in front of it and take it in, the work works on multiple perceptual levels. Here are few things that I noticed:

one large (about 5 by 5 foot) and shallow three-dimensional square;

twenty-five smaller (1 by 1 foot) three-dimensional cubes;

moving from any corner towards the center: five nested cubes, each larger than the previous one (1 by 1, 2 by 2, 3 by 3, 4 by 4, 5 by 5);

and a twenty-five square foot wall space divided by a superimposed grid.

There’s nothing hidden here: you can see not only the metal structure, but also right through it too–to the spaces inside the cubes (on whatever scale you see the cubes on) right onto the cube shadows on the wall itself. As art, it’s not trying to represent anything but itself. It is what it is: solid yet transparent.

LeWitt’s work also reminds me of structures I see (and hear) a lot in electronic music circles, specifically the grid matrix used on drum machines, sequencers, and samplers–instruments which, by the way, are increasingly one and the same piece of hardware. Consider the classic Akai MPC drum machine/sampler

or the more Novation Launch

or the Monome

or Native Instruments’ Maschine

or Ableton’s Push

We can move in other directions too. LeWitt’s cube structure also reminds me of beloved (musical) games from my childhood, including Mego Corporation’s Fabulous Fred (1980)

and Parker Brothers’ Merlin (1978).

LeWitt, widely regarded as the founder of both minimal and conceptual art, began making what he called his open and modular “structures” in the 1960s and the cube form was the basis of much of this work. Thinking analogically about LeWitt’s modular cube piece as I look at it, it feels like an early sign of the repetitive and grid structures of minimal and electronic dance musics (not to mention the grid structures of electronic music controllers). No, there probably isn’t a chain of direct influence here–though LeWitt was an influence on some minimalist composers, some of whom may in turn have influenced various electronic dance musicians. But maybe the significance of the modular cube as art idea lies in its calm anticipation and representation of the digital world many artists inhabit today.

Still Centers: On Harold Budd’s Piano Music

“I realized I had minimalized myself out of a career. It had taken ten years to reduce my language to zero but I loved the process of seeing it occur and not knowing when the end would come. By then I had opted out of avant-garde music generally; it seemed self-congratulatory and risk-free and my solution as to what to do next was to do nothing, to stop completely.”- Harold Budd

Born in Los Angeles in 1936 and raised in the Mojave Desert where he found early musical inspiration in the humming tones caused by wind blowing through telephone wires, Harold Budd is a singular American ambient composer who makes spacious and meditative music. In the four and a half-minute piece “Haru Spring” from his recent recording In The Mist (Darla 2011) we hear Budd arpeggiate wide open five-note chords and let them ring very, very long. The space between chords ranges from five to over fifteen seconds and this isn’t really silence per se, but rather the sound of the piano slowly diminishing and fading to almost nothing. Listening to Budd you’re reminded of the famous Rorschach ink-blot test

where you stare at it and see what comes to your mind’s eye. With a piece like Budd’s “Haru Spring” something similar happens to your mind’s ear as you listen to one chord decay and wonder when the next one will appear and where it might go. In that space of wonder various non-musical thoughts and impressions come to the foreground and then recede like images triggered by an ink-blot.

The fact that Budd’s music can trigger this kind of perceptual experience is part of what makes it so good. It’s a kind of music that hides its musicality–making you forget it’s composed/improvised out of just a few tones. In doing this it reminds you that one of the very best things music can be is not a demonstration of a particular technique or theory but a realization of a special kind of affective space, a conjurer of mood.

On The Musicality Of M.C. Escher

“Order is repetition of units.  Chaos is multiplicity without rhythm.”

“My work is a game, a very serious game.”

“Are you really sure that a floor can’t also be a ceiling?”

– M.C. Escher

I’ve long been curious about M.C. Escher’s (1898-1972) drawings and woodcuts because of their precision, their order and symmetry, their use of repetition and optical illusions, and the way they seem to point towards what could be called the infinite. Lately I’ve been thinking about what these qualities in Escher’s art have to offer those of us working in music (whether making it or writing about it). Let’s take a look.

First, Escher incorporated tessellations into his work, a technique he picked up in his study of tile mosaics while visiting Alhambra, a Moorish palace in Spain in the early 1920s. (Which reminds me of an article on the advanced geometry of 12-century Islamic art.) Seeing the tile mosaics inspired Escher to use geometric grids as the basis for his art as a way of gaining precision. Tessellations, by the way, are the composite result of geometric shapes that are repeated without overlaps or gaps. Honeycombs and interlocking pavement tiles are examples of tessellations. We see tessellations in Escher works such as these:

Second, Escher depicted in his work transformation/transmutations where we see one shape becoming another. These transformations appear most clearly in Escher’s tessellation pieces. In his woodcut Sky and Water, for example, we see birds becoming fish/fish becoming birds.

Or in this piece, Day and Night, a whole landscape shifting:

Third, Escher was fascinated by so-called “impossible constructions” or visual illusions such as the Necker cube and the Penrose triangle that take advantage of quirks of perception and perspective. You can see impossible constructions depicted in Escher’s famous “Relativity” piece that depicts people simultaneously ascending and descending stairs in an infinite loop. Are the figures moving up or down, sideways this way or that way? I like to rotate this piece onto its different sides to see how it holds up. Miraculously, Escher makes the work cohere no matter what viewing perspective we try to bring to it:

Fourth, and speaking of infinite loops, Escher’s works illustrate the idea of recursiveness—that is, something feeding back upon itself in a never-ending cycle. Relativity, above, depicts such infinite loops, as does the work Drawing Hands:

And this one that depicts lizards crawling to life/becoming tessellations:

These works and others present the viewer with a visual chicken/egg dilemma: Where does it all start and end? I like that.

Fifth, it’s been said that Escher’s art demonstrated an “intuitive” understanding of mathematical order and symmetry and perhaps this is the reason why his works are so pleasing to look at? What’s remarkable is that this intuitive understanding was so accurate that in the late 1950s the Canadian mathematician H.S.M. Coxeter said of Escher’s hyperbolic tessellations (regular tilings of a hyperbolic plane): “Escher got it absolutely right to the millimeter.” Here is his Circle Limit III:

This notion of Escher’s intuitive mathematical understanding reminds me of a quote from the philosopher-mathematician Gottfried Lebniz (1646-1716) that always made intuitive sense to me: “Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.”

Finally, there’s an intangible quality to Escher’s work that some critics have described as an interest in exploring infinity. The repetition, the tessellations depicting nature’s transformations and evolution, the impossible constructions playing with our perceptions, the infinite loops feeding back upon themselves—all of these characteristics of Escher’s art suggest an artist trying to represent that which can’t be represented, a reality beyond, a time-space outside our everyday experience of space-time. You even see it in tiny details, like when Escher draws a reflection of himself. In his work The Eye, for example, the reflection is twofold: there’s the mirror-image close up of his face where we see the folds around his eye, and there’s also that next level reflection deep in his eye’s pupil where we see Escher post-Escher–he’s already a corpse! It’s these kinds of little details that suggest that Escher was always somehow thinking beyond the Now even as he had intricate, and serious fun (“My work is a game, a very serious game”) constructing its beguiling representations:


For me, Escher’s work has musical resonances and looking at his pieces reminds me of the work of various composers, especially that of the American minimalists such as Steve Reich and Philip Glass. Over the years I’ve spent much time thinking through their work (you can read more about their work here; and you can view a Ventrilo-Dialogue with Reich here). Escher’s tessellations remind me of minimalist music that is similarly built out of small repeating units of sound strung together to make long rhythmic tapestries. (Now that I think of it, a lot of electronic dance music fits this bill as well.) Escher’s transformations/transmutations remind me of how minimalist music changes over time through subtle additive or subtractive procedures—adding or taking away a note here and there to transform one motive into another before our ears. (Ditto for electronic dance music.) And Escher’s impossible constructions remind me of minimal music’s perceptual artifacts—where as a listener you’re not sure if you’re listening to three groups of four beats or four groups of three beats, for example. Like Escher’s Relativity, a piece like Reich’s Drumming allows the listener to hear both perspectives at once. As for recursiveness, a lot of classic minimal music really does have an endless quality about it: a sense that it could, and just might, go on forever—or at least long enough for the listener to stop worrying about where it’s “going.” (It’s not going anywhere, just being something for a time.) Finally, to return to Escher’s intuitive understanding of math: Aren’t composers kinds of mathematicians too in that in one way or another they’re concerned with numbers and quantity, structure, space, and change? Like Escher, most composers frame what they do not in clinical terms (“I spend a lot of time exploring e-minor…” or “I do most of my compositional work in 5/4 time…”) but in intuitive and emotional terms (“In this song I was trying to capture the sadness of my break-up with a girlfriend…”)  And isn’t music a good example of a kind of equation in sound that presents not an argument or a “proof” but rather shares the results of a procedure, solving itself and bringing us along for the ride?

On Minimalism and Aural Illusions

One of the enduring contributions of the so-called American “minimalist” composers–particularly Steve Reich and Philip Glass–to global music culture was to re-introduce shape-shifting, metamorphosing aural illusions to our listening experience through intense repetition, polyrhythm and additive rhythms. These rhythmic devices are not new in music–you can certainly hear them in some African and Indonesian musics–but they were newly foregrounded in the concert hall back in the 1960s and 70s when minimalism burst onto the scene.

“Foregrounding” is an apt term in that the use of these musical devices reminds us of those perceptual puzzles from Psychology 101–like the picture of the two faces/vase that foregrounds one or the other depending on your interpretive listening stance:

A good percentage of the bliss in a vintage Reich or Glass piece derives from how the music plays with our senses, inviting the transformation of our (mis)perception to become part and parcel of the music’s affect. Reich’s early piece Drumming (1971), for instance, features perceptual artifacts the composer calls “resultant patterns” that arise out of the music’s polyrhythmic web. Reich found inspiration for this concept from his study of West African drumming.  (A similar concept, “inherent patterns” was discussed by ethnomusicologist Gerhard Kubik in the early 1960s.) Musicians performing Reich’s music foreground these patterns by playing or singing them to help us along in our listening. Moreover, the careful design of the music supports our multiple and shifting interpretations: Drumming is in a 12/8 meter which can be rhythmically perceived in a variety of ways (3 groups of 4 beats, 4 groups of 3, 6 groups of 2, 2 groups of 6)–often simultaneously.

Here are excerpts from a recent performance of Drumming (and you can forward the clip to 2:00 to hear the singers’ “resultant patterns”):

Glass’s early piece Music In Twelve Parts (1971-1974) works its perceptual magic not through polyrhythms but through additive rhythms. The composer structures his piece around short rhythmic units that repeat at a steady tempo but also grow in length incrementally. Glass found inspiration for this technique from his study of Indian music with Ravi Shankar. After sufficient repetition, these repeating rhythmic blocks induce subtle perceptual shifts–playing especially with our sense of time. The music can make you feel like it’s foregrounding a slower time dimension behind its frantic surface.

Here is Music In Twelve Parts:

In both cases, the composers use minimal techniques to yield maximal perceptual results.

On Alva Noto and Ryuichi Sakamoto’s Musical Duets

In one of the more austere corners of contemporary experimental electronic music resides a series of luminous collaborations between the musicians Carsten Nicolai (aka Alva Noto) and Ryuichi Sakamoto.  Over a series of five recordings, Vrioon (2002), Insen (2005), Revep (2006), utp_ (2008), and summvs (2011) the duo have explored mixing electronic and acoustic sounds into a meditative whole that is at once icy and expressive, breathing and precision-engineered.

Both musicians are polymath artists.  Nicolai, who is German, makes electronic music under his Alva Noto alias out of the barest of materials, looping tiny shards of sine tones, static, and fuzz to make a rhythmic music that is minimal in sound but alive with constant micro-changes.  Nicolai/Noto also runs the Raster- Noton label and creates sound art pieces that have appeared in art galleries worldwide.  Sakamoto, a pianist and composer, is music royalty in Japan.  He founded the electropop band Yellow Magic Orchestra back in the late 1970s, has written soundtrack music, scores for the opening ceremonies at the 1992 Olympic Games, designed ringtones, and collaborated with numerous other artists on projects ranging from operas to pop songs.

The Noto-Sakamoto collaborations were composed by the artists trading audio files back and forth.  While I have no idea how exactly the music was created, it sounds as if Sakamoto’s modal chord-based piano playing (improvisations?) were subjected to Noto’s digital treatments–looping the piano, stretching and repeating phrases, dissecting it into micro-slices–with some Noto static-fuzz percussion added in to make to make it all gel.  Sometimes the music sounds like a piano infected with digital viruses, scattering its notes into strangely ordered patterns guided only by the most minimal of frozen rhythms.  What I like about the music is that it merges Noto’s and Sakamoto’s distinct voices into something unique.  But let’s go deeper.

In electronic music making, one always runs the risk of succumbing to what could be called sound fetishism–that is, ascribing supernatural powers to particular sound timbres.  The electronic musical instrument industry certainly encourages this with their non-stop release of “new” sound presets that promise to take your music to the “next level.”  Everyone wants either the newest sound or, for the adventurous, to create their own never before heard sounds.  In this way, everyone wants to be a pioneer sound explorer, discovering treasures out of which to make new music.

And yet, here we have Noto and Sakamato using a deliberately limited sonic palette–basically just piano and digital sine tones and percussive static–which does two things.  First, it brings you, the listener, back onto familiar ground. There aren’t really any “strange” sounds on these recordings, and so the music, while unique, is never exotic for exotic’s sake.  Second, using a limited sonic palette allows Noto and Sakamoto to focus on really interesting structures and relationships between the sounds.  It’s amazing, actually, how much can be done with so few materials.

Listen to the track “Moon”:

If you’re interest is piqued, you can watch them perform live here:

Apple Commercials and Musical Minimalism

Apple computer makes magnificent TV ads for its products: the commercials are visual case studies in sleek minimalism, computer or iPhone set again a pure black or white background, a disembodied hand showing the viewer just how simple it is to work with this technology.  Carefully chosen music is part of what makes Apple’s commercials so effective, and in the ads for two recent products–the iPad tablet computer and the second version of the Macbook air laptop–we hear two pieces that to my ear at least, riff off of a very famous piece of musical minimalism: Steve Reich’s 1978 work Music for 18 Musicians.

The music for the iPad commercial is the first minute of a piece by Chilly Gonzales called “Never Stop.”

Gonzales (real name: Jason Beck) is a Canadian pianist, producer and songwriter who lives in Paris.  “Never Stop” is one of 15 songs from his recent album “Ivory Tower.”  The piece begins with a steady pulse in a four feel (or meter) played on shakers, with polyrhythmic finger snaps layered on top.  Ten second in, the main piano riff enters: a 9-note repeating pattern that steps through just three pitches (tonic, flat-3rd, 4th).  Rendered poetically you can hum the pattern as: bum, bum, bum, bum-bum bum, bum, bum-bum (!)  About 20 seconds in, a second piano playing in a higher register comes in with a counter rhythm that plays against the 4/4 feel–in fact, it makes it feel as if the whole piece is simultaneously in a slower-moving three feel.  (That’s the kind of weird perceptual work polyrhythms can do for the listener . . .)  Tucked in just behind the second piano is a third piano part that seems to come around every 5 beats or so, further blurring our sense of the music’s metric feel.  Things are getting dense!  Then, around 42 seconds, Gonzales introduces some strong hand claps on beats 2 and 4, bringing our ears back to the ground and anchoring the music in the 4 feel once again.  This is pop after all.

Listening to this piece (actually it’s just the first minute of a 4:49 song), I hear a whole lot of Section II of Reich’s Music for 18.

Reich’s sections unfold at a slower rate, but listen to the repeating patterns and whole flow of it; Gonzales really took one out of Reich’s book.  Even Gonzales’ use of patterns in different meters is a technique Reich has been using for decades.

Reich’s Music for 18 also makes itself felt in the music for the Macbook Air commercial.

The music for this ad is an original piece composed by Mophonics Music, a company that has scored for ads for Adidas, Reebok, AT&T and Sony.  In this 30-second spot, you can hear a piano part that begins with a single chord and begins to pulsate and multiply into higher registers.  To my ear, the music, although at a slower tempo, is reminiscent of the opening “pulse” section of Reich’s Music for 18.

So: What is the connection between musical minimalism and sleek computers?  Composer John Adams once said that he heard minimalism as a reaction to living with machines and maybe there is some truth to that.  Maybe Apple understands this connection.