Fascinating Rhythm:
John C. Adams as Metametric Pioneer

Keynote address to the "Inside the (G)earbox: John Adams @ 70" symposium at UCLA, March 4, 2017

By Kyle Gann

I am going to talk today about the aspect of John C. Adams’s music that most fascinates me, and that, in my view, most closely relates him to the music of my own slightly younger generation. To the next generation of composers after mine, I think, his music has meant something different, and they have drawn a different kind of influence from him. For my generation he was the first to realize that minimalism made a certain kind of rhythmic texture possible that composers had been thinking about for a long time. Being devoted to the kinds of structural issues composers like to think about, my paper will be rather technical in nature, but I am going to make it as clear and interesting as possible, and play you some nice music.

I became aware of minimalism in the summer of 1974, between my freshman and sophomore years of college, the summer that the music of Steve Reich and Philip Glass started appearing on widely available records. From the beginning, I thought that the stupidest and most inaccurate criticism of minimalism was that it was simplistic, a dumbed-down music suitable for only unsophisticated listeners. Quite the contrary. Already in the out-of-synch repeating loops of Reich’s Come Out and Piano Phase, and the additive processes of Glass’s Music in Fifths and Music with Changing Parts, I was becoming excited about the new kind of rhythmic complexity minimalism was making possible. Of these two processes, loops going out of sync and additive process, today I am going to talk about loops, because this is partly where Adams’s rhythmic sense resides, as the very title of his Shaker Loops suggests. I’m not really talking about repetition, which so many people think is the primary characteristic of minimalism, but about the kind of rhythmic complexity that repeating loops can make when they’re overlayered at different rates of speed. The first piece I know of that began to make this aspect of minimalism explicit was arguably Adams’s China Gates (1977) and Phrygian Gates (1978), but even more dramatically Shaker Loops (1978).

The kind of rhythm I’m addressing was actually anticipated by the 1920s. Between 1919 and 1921 the young Henry Cowell (1897-1965) wrote a book, not published until 1930, called New Musical Resources, which outlined a new theory of rhythm. He theorized about having different meters, or tempos, or phrase lengths going out of phase with each other at the same time, and referred to them as “metrical links.” Around the same time, an emigré theorist and composer born in the present-day Ukraine, Joseph Schillinger (1895-1943), developed a theory that the basis of musical beauty was mathematical in nature; from this, he drew a system for composing that was a big influence on certain composers, especially Tin Pan Alley songwriters. George Gershwin studied with Schillinger from 1932 to 1936, and the technique is evident in certain passages of his opera Porgy and Bess. The most elementary rhythmic principle of Schillinger technique was that a hidden feature of many aesthetically satisfying rhythms was that they contained different-length pulses going out of synch with each other, like three against four or four against five. Schillinger’s term for these was, forbiddingly enough, “interference of periodicities,” since the total rhythm was made by two steady beats (or periodicities) interfering with each other. Gershwin had been interested in these kinds of rhythm even before meeting Schillinger, and perhaps the clearest and most famous example of such rhythms is his 1924 song “Fascinating Rhythm.”

As you can see, the rhythm referred to in the title and text is actually a pattern seven eighth notes long superimposed across a half-note harmonic rhythm and a 4/4 meter. Schillinger called conflicting pulses only one note long “monomial periodicities”; when each rhythm was two notes long, he called them “binomial periodicities,” and so on. In this Gershwin example, then, we have a binomial periodicity in the piano against a periodicity of six notes in the voice, maybe a sexonomial periodicity.

The influence of Schillinger’s and Cowell’s rhythmic ideas was not very widespread in the next couple of decades, although Conlon Nancarrow was working away on them in his isolation in Mexico City, and Elliott Carter explored them in more abstract contexts in which they were difficult to hear. Then minimalism happened. The repetition of short phrases that started up in Terry Riley’s In C (1964), and the phase-shifting effects Steve Reich achieved with tape loops in Come Out (1966) and then with pianists in Piano Phase (1967) provided the fertile ground in which Cowell’s and Schillinger’s ideas could take root. Most importantly, minimalism made them clearly audible. Mid-century modernism, with its atonality, pointillism, and mercurial rhythmic variety, was too complex a context for pulse-shifting subtlety to have much of an impact. But the spare tonality and steady beats of minimalism, together with a grounding in continual repetition, suddenly made phase-shifting loops a seductive musical phenomenon. Far from being simplistic, minimalism made subtle levels of complexity audible and perceptible that had been only obliterated in the gross and obvious context of dissonant modernism.

From everything I can tell, it was John Adams who first realized the implications for rhythm implicit in minimalism’s alleged simplicity. We first see the idea in China Gates. At the beginning there are two phrases of seven eighth-notes length running parallel to each other in 4/4 meter, much like our Gershwin example. But soon he begins altering the phrase with fewer notes until it is only three quarter-notes long, for a six-against-seven rhythm that Schillinger would have called an interference of trinomial and septinomial periodicities.

Already this is expanding the idea beyond anything Reich would have done.

In his now-famous piano piece Phrygian Gates (1978), which I first heard at the New Music America festival in 1980, Adams expanded the idea further. Here, for instance, you can see phrases of four notes and five notes running against each other and going out of phase:

The numbers were still simple, but the idea of using loops to make texture (rather than gradual process as in Reich’s works) had been breached.

In Shaker Loops for string sextet, written that same year, the idea bursts onto a wider stage. Here you can see that, beneath a consistent tremolo in the first two violins, the third violin starts repeating an accented note every eleven beats. That switches to every six beats as the viola enters with the same accented note every nine beats. The first cello starts playing an accented E every 13 beats, and the second cello an accented E every 10 beats. You’ll notice that the loops are not uniformly consistent in length. One of the things you quickly learn composing this way is that mathematical consistency is not a conspicuous virtue, nor are deviations noticed by the listener; it is, of course, more important for the music to sound good than for the numbers to exhibit ideological purity. In art, appearances are more important than reality.

The pattern of accented notes can be graphed as follows, and you can both see and hear the satisfying effect of a mathematical pattern that is unpredictable to the ear and yet follows an underlying logic that the intuition might be able to grasp subliminally. This is quite like some of the examples in Schillinger’s book The Schillinger System of Musical Composition, some of which are marked out on graph paper.

With Short Ride in a Fast Machine (1986) Adams transferred this effect to the orchestra. The numbers are once again simple, mostly groups of three against four against six, but with these intricate rhythms reinforced by brass and wind choirs the effect is quite exciting. The impression of competing rhythmic levels is audible enough without a chart to analyze it.

It was the orchestra piece Lollapolooza (1995), though, that made it really obvous to me how abundantly Adams’s ideas were grounded in principles that Cowell and Schillinger had theorized about, and that made me realize how relevant he was to the music of New York composers of my generation. Lollapolooza is a great, galloping machine of repeating melodic loops, audible in its methods and quite complex in its overall rhythmic effect. The piece is driven by an ostinato in 3/4 meter, a repeating figure in the bassoons and bass clarinet. Here in this long reduction of the work’s opening section I have marked each loop with the number of beats that elapse before it repeats. The ostinato is punctuated by notes in the bass, contrabassoon, and piano every five to six beats, though with an occasional syncopation of only two and a quarter beats. The oboes and clarinets enter with a quick figure repeated every four beats at first, though after a few repetitions they fall into sync with the ostinato every three beats. The piccolo, flutes, and piano then enter with a falling figure that repeats irregularly every three and a half to four and a half beats.

Then, at measure 24, the harmony switches from G to C, and the trombones and tuba start playing the “lollapalooza” motive every five beats. This heavy bass motive has so much influence over the perceived overall rhythm that the security of the 3/4 meter is strongly challenged. At measure 28, the piano, doubled by winds, starts up a new phrase every six beats, against the implied 5/4 of the brass. At measure 31, the ostinato itself starts to lengthen and become irregular, and a 3/4 meter is no longer evident. The impression is unmistakably like a powerful machine held together by gears working together in complex ratios and then gradually breaking down and running out of order.

In the 1980s and ‘90s this tendency to run looping rhythms or melodies in out-of-phase patterns became the basis of a style centered in New York City that was known for awhile as Totalism. The name was partly a nod to Henry Cowell in that it realized his plan to create harmonies of rhythms analogous to the way we create harmonies of pitches, thus the totality of the music had an arithmetical basis. Since so many of the composers in the movement had also been involved in rock music, the term also had a connotation that the music was open to classical, jazz, pop, and other influences. In 2006, Dutch composer Samuel Vriezen coined a new term for the central rhythmic technique involved: metametrics, kind of a masculine, steel-cut-sounding term. The idea of metametrics is that rhythmic complexity of quite a high order can be obtained by superimposing meters and tempos in relation to some central meter that might not even be articulated in the music. This was in contrast to the previous kind of rhythmic complexity found in serial music, which seemed chaotic and irregular, even arrhyhmic. In metametrics, one can hear regular pulses, but because there are several going on at the same time it is impossible to regard any particular one as primary.

There is also a relationship between Lollapalooza and the music of Morton Feldman. In the 1950s, Feldman and Earle Brown were rather in a contest to see who could express in music the kind of shifting relationships between musical objects that would be analogous to the shifting forms in the mobiles of Alexander Calder. Feldman’s solution, which I think won the contest, was to have each instrument repeat a phrase or note at his or her own tempo, so that there was no synchronization. In some of Feldman’s music, such as Crippled Symmetry and For Philip Guston, the same melodic figures float by in different instruments at different rates of speed, often superimposed but always in changing relationships. For Feldman, such incidences were haphazard. In metametrics, as Lollapalooza abundantly and audibly proves, the changing relationships are locked into an overall mathematics that offers its own delightful perceptual challenges.

Lollapalooza is the most obvious example of metametrics in Adams’s music that I know of (there may be others, but he puts out so many new works that I haven’t been able to keep up with them all). After Lollapalooza, though, he has continued to explore metametrics in ever more subtle directions. My next two examples involve melodies that are quite free and metrically ambiguous, played over Schillinger-style backgrounds of pulses at conflicting tempos. In Naive and Sentimental Music (1997-98), an active and entirely rhythmically ambiguous flute melody, and a slower and soaring line in the violins, are heard over repeated chords playing at different tempos. As you can see in the example, the harps play chords in steady dotted eighth-notes as the bassoons hit a chord every fifth sixteenth-note, for a three-against-five rhythm. Over this, the piano plays those same chords in an irregular pattern of three, four, or five sixteenth-notes; in the background, the violas pluck a lonely, off-beat octave every dotted eighth-note. One can hear some constancy in the different rhythm levels, but their lack of relation to the flute melody makes it sound like the instruments are all playing independently; and still, they all change harmonies at the same time, like some miracle of collective inspiration, like a flock of birds at different speeds but all changing at the same moment. The audio example begins at the point where the bassoon chords enter, and will continue a little past the notated example here.

Another technical point I can’t resist making is that, you may notice, the harmonies are D minor, F# minor, and Bb minor, three triads with roots separated by major thirds that move to each other so chromatically that the ear has trouble relating them to each other. This kind of chromatic movement among closely spaced chords is a type of harmony that is now referred to as neo-Riemannian. It was common among certain composers of the 19th century, notably Bruckner and Liszt, and has become common again among postminimalist composers who want to use triadic harmonies without any of the conventional syntax of tonal music. Neo-Riemannian harmony is a branch of theory that only started in the late 1980s, and that has since developed into a major branch of mathematical music theory. In fact, I first heard of it at a minimalism conference where analytical papers were presented on the music of Gavin Bryars and on Adams’s 1996 clarinet concerto Gnarly Buttons. This colorful style of harmony, revived again after a hundred-year hiatus, has proved very fertile for music coming out of the minimalist tradition.

The last Adams work I want to look at is The Dharma at Big Sur (2003), a concerto for electric six-string viola. Just before the viola enters, the piano starts repeating a low B at a metronomic tempo of one beat per second, unsynchronized with the orchestra which is being conducted at a tempo of quarter-note equals 52. (The notation given in the example is therefore inexact, matching an alternate notation Adams provides in the score.) Relative to the orchestra, that low, pulsing beat approximates a double-dotted eighth-note, equal to seven 32nd-notes. The harp enters playing B’s and F#’s in a three-against-two pattern. Above this, harmonics are passing back and forth among the string sections in a rhythm of dotted eighth-notes. Below it, the basses are plucking octaves every seven and a half eighth-notes, or every fifteen 16th-notes. A gong plays a note approximately every eleven or twelve eighth-notes. The whole rhythmic continuum of pulsing notes is quite complex with its multiples of twos, threes, sevens, and fifteens. Over this, the viola enters with a wandering, growing line that is conventionally notated but sounds completely improvisatory with respect to rhythm, since there is no one pulse in the orchestra that it relates to.

As the viola continues, (and the viola melody is omitted from this example) the piano begins a chord, and then a chord and a D# octave, pulsing every five 16th-notes, as the strings begin a quiet 3/8 pattern, the harp articulates triplet half-notes, and the winds come in with a sustained F# every six beats. For all its rhythmic complexity, the gentle pulsing of this B-major scale is quiet and subtle, and you might not hear all the detail beneath the viola solo, but it creates a magical background. Let me also add that the piano and harp are tuned to just intonation, and that this is probably the most important, and certainly the most well-known and successful, work that’s ever been written for an orchestra in an alternate tuning. I’ll play this whole passage, and you can hear the orchestral texture gradually metamorphose in the background from my first example to my second.

For comparison I now want to turn now to a few examples of pieces by younger composers whose music resembles Adams’s in this respect – although since these composers are all now around sixty, don’t get too excited about the word younger. Whether these pieces were influenced by Adams’s example, or whether they resulted from teasing out the same implications of minimalist rhythm that he had explored earlier, I won’t pretend to know, but they do provide, I think, a suggestion that Adams and the totalist composers of the 1990s had some interests in common.

First, here is a page from Spooks (1999) by my Bard colleague John Halle (b. 1957). This entire piece is a thorough exploration of metametrics, but I offer this climax in which we find quarter-notes against dotted quarter-notes against triplet quarter-notes against septuplets against chords five quarter-notes long, with a rather Adams-like flute melody moving back and forth among various tempos. I will play the section leading into this musical example.

Next, a piece by Los Angeles’s own late and lamented Art Jarvinen, called Murphy Nights (1989). The piece’s first section is based on two ostinatos running out of phase with each other, one in the electric keyboard that repeats every 32 16th-notes, and one in the bass that repeats every 33 16th-notes. Over this, the other instruments enter with a melody in a different metrical organization, and in which the different instruments start going out of phase. The title Murphy Nights came from a suggestion Jarvinen read that if someone gave the same public lecture an infinite number of times that at some point the audience might be made up of an audience whose names were coincidentally all Murphy (although at the moment it occurs to me that an audience all named John Adams might be more likely). At first we hear only the bass alone, and then the keyboard enters after two repetitions of the 33/16 line.

Michael Gordon’s Yo Shakespeare (1992) likewise starts with two ostinatos, one of them five beats long and the other four and 2/3 beats long, for a phasing pattern of 14 against 15. Note that Gordon uses the practice, first suggested by Henry Cowell and also employed by Pierre Boulez and myself, that triplet quarter-notes do not always have to appear in groups of three. At the end of the printed example, the violin enters in phrases five 16th-notes long.

Since the late 1980s, John Luther Adams has written in an idiom that overlays rhythmic layers in tuplets of three, four, five, six, and seven notes per measure. This rather typical example from In the White Silence (1998) has soloists from the orchestra playing languidly in all these rhythms.

Finally, if you will indulge a selection of my own music, here is a passage from “Venus” (1994) from my suite The Planets. As in Lollapalooza the basic meter is 3/4, but the flute melody and the bass outline a meter of 25/16, that is, a beat of five 16th-notes in phrases five beats long. [I provide more of the piece here than I played at UCLA.]

I can say in my own case that I had absorbed my own minimalist influences before hearing the first Adams works I really fell in love with, which were Grand Pianola Music, Harmonielehre, and Nixon in China, which did not exhibit the same kind of rhythmic tendencies. But then about fifteen or twenty years ago I heard Lollapalooza, and jumped up and shouted, “Holy cow, he’s doing the same things we’re doing!” Ever since that point I’ve been analyzing his works in more detail.

I hope to suggest with these examples, which I could easily multiply, that a fascination with out-of-phase loops – metametrics - became prevalent among several composers who came out of the minimalist tradition, and that Adams was not only the first to recognize and explore these possibilities, and the oldest to have made beautful use of them throughout his career, but also that he has continued to develop new ways of using them and thus created his own very distinctive kinds of floating, pulsing, yet metametric orchestral texture.

Copyright Kyle Gann 2017

Return to the Kyle Gann Home Page

If you feel moved to reply to any of this, email me

return to the home page