Search Results for: www.kylegann.com

If you hurry and look right… now, the playlist for Postclassic Radio is currently accurate and up-to-date.

Oops, too late! You weren’t quick enough.

(New pieces by Frank Denyer, Peter Gena, Walter Zimmermann. At this point I’ve played well over 600 pieces, something like 130 hours’ worth of postclassical music. And there’s plenty more where that came from.)

I don’t understand why the electric guitar orchestra hasn’t become a compositional focus for more composers, for practical reasons alone. It certainly looked like it was going to in the 1980s, with works and ensembles by Rhys Chatham, Glenn Branca, John Myers, Wharton Tiers, Phil Kline, and Todd Levin. The old joke is,

Q.: How do you get a guitarist to stop playing?

A.: Put some sheet music in front of him.

and certainly dealing with guitarists who don’t read was part of the challenge, especially starting in 1989 when Rhys Chatham initiated the 100-guitar tradition with An Angel Moves Too Fast to See, premiered in Lille, France. “Guitarists who can’t read can at least count,” Rhys liked to say, and this insight led the guitar-orchestra genre into totalist territory, however inadvertently. Glenn Branca couldn’t read music himself until he had finished several guitar symphonies, and at least his Sixth Symphony (also 1989), notated on graph paper, has rhythmic grids showing some players how to change chords every four beats while others are changing every five beats and still others every six. His 1994 Tenth Symphony for nine guitars, more normally notated, contains at one point an approximated Nancarrovian tempo canon at tempos of 7:8:12.

In An Angel Moves Too Fast to See Chatham solved the reading problem by dividing his 100 guitarists into an inner and outer circle, with the musically literate in the inner circle. In the fifth movement (he now calls the piece his First Symphony, though I think he avoided that at the time because Branca was for some reason being criticized for calling his pieces symphonies), he divided the orchestra into six rhythmic layers, each repeating a chord or phrase at diverse regular intervals (monomial or binomial periodicities). As you can see in the example below, one rung of guitarists played E and B every 7 beats; another E and G# every 8 beats; another an octave A every 9 beats; another, after a pause, A and F# every 5 beats, and then two more groups on longer patterns:

Put them all together, and the following process-generated melody is clearly audible:

What you can’t get from the recording (excerpted here, and available on Table of the Elements) is the totally original correlation of space and pitch that resulted. (I just missed the Lille performance by hours, but heard the North American premiere in Montreal.) A hundred guitarists, each with an amplifier and enough room to swing around and look cool, take up a tremendous amount of space; and since each group was herded together, the E-B chord might come from the middle, while the A-F# came from 60 feet away on the left, and the G# an equal distance on the right. Note by note, the melody bounced over wide distances as though the audience members were ants sitting in the middle of an enormous keyboard. Listening was like watching an arrhythmic tennis game.

This is not new information, by the way; it’s all in my book American Music in the 20th Century. Now that Branca is gathering 100 guitarists to reprise his 13th Symphony in Los Angeles, it may be worth recirculating at the moment.

At about the same time I was experimenting with a similar process to generate textures in a considerably more modest setting. My Windows to Infinity for piano (1987) was a reflection on Nietzsche’s concept of the eternal recurrence. I had been amused to read philosopher Arthur Danto parse out the statistical likelihood of eternal recurrance in his book on Nietzsche, and in response wrote a piano piece stretching out to infinity, tracking a recurring combination of notes as it gathered coincidences through millions of repetitions. As you can see below, there’s a middle D# every 5 8th-notes, a middle C# every 7 8th-notes, a lower F# every 29 16th-notes, and so on up through four-digit primes. Every phrase comes back to the C#-D#-E-G# “theme” found in the 4th and 5th measures (a motif also used in my two-piano piece Long Night):

In theory, this nine-minute piece would eventually repeat itself if extended for thousands of years. No one’s ever played the piece but me, and as I’m not terribly satisfied with my one recording, I think I won’t post it here. I used a similar technique soon after in the first movement of Cyclic Aphorisms for violin and piano. I’m sure others have stumbled across this interference of pitch-periodicities concept, but I don’t know of any examples of such an atomistic totalist technique past 1989. It may be worth noting that Nancarrow used the interference of much longer, more complex periodicities in his Study No. 9, way back in the 1950s.

As an addendum to my post on 4-against-5 rhythms, I should mention Paul Epstein’s 1998 harpsichord piece, 57:4/5/7. I think of Paul as a postminimalist rather than a totalist, but he goes the totalists one better: the piece is based on interfering periodicities of 4-against-5-against-7. (I tend to call pieces postminimalist when based on a steady beat unit throughout, and totalist when conflicting tempos are implied. For the record, I don’t give a damn whether anyone joins me in this.) I don’t know a mnemonic device for figuring out 4:5:7 – if you’re dealing with durations of 4, 5, and 7 16th-notes, you’d need 70 syllables to fill out the 140 16ths it would take those rhythms to come back in phase, and you’d need a mnemonic to help you remember the mnemonic, and probably another mnemonic to help you remember that. (If you’re simply dividing a measure into 4, 5, and 7 simultaneously, layering tempos rather than durations, you’d only need 14 syllables, but how to space them would be a knotty problem.)

But you can see Paul’s compositional use clearly here at the beginning of the piece, the three lines moving in tempos of 4, 5, and 7 16th-notes, switching register at the points where the 4:5’s, 4:7’s, and 5:7’s coincide:

Since the piece is for amplified harpsichord, there are no dynamics indicated, though in every other respect the notation is meticulous. And before influencing your perception of the piece by reading how it works, you can hear the ten-minute piece here, performed by harpsichordist Joyce Lindorff.

This is a work of art as abstract as Mondrian’s Composition No. 2, as Milton Babbitt’s Three Compositions for Piano or Webern’s Op. 24 Concerto. It is music about the logic of music – but its logic is perhaps easier to process audibly than Babbitt’s or Webern’s, and more playful. His interest sparked decades ago by Steve Reich’s early music and the logical processes of Tom Johnson, Paul Epstein has long nurtured an interest in attractive surfaces generated by tight, self-replicating melodies. 57:4/5/7 is spun from a 57-note series structured in such as way as to replicate itself every 4, 5, and 7 notes, as can be seen in this breakdown whose lower three lines correspond to the opening measures above:

However, Paul’s music is never as mechanical as this correspondence suggests. Like many of his pieces, 57:4/5/7 is kind of a theme and variations on a logical concept. As you’ve heard or will hear, it changes key, it goes through a series of different textures, sprouts melodies, and its 16th-note momentum speeds up to various densities. Rarely does Paul simply set a process in motion and let it run. I sometimes call him “the postminimalist Babbitt” because of the ingenuity he expends twisting these logical constructs into an obvious-sounding but elusive series of processes. (And contrary to what you may assume, Babbitt is the composer of many pieces I have long been fond of.)

What I get from Paul’s music is a pleasurable but slightly exasperating feeling that I could figure out what the music’s doing if I could just listen a little harder. Motives repeat, tunes emerge, voices echo in canon, and I keep thinking that the piece will resolve into something obvious any minute now. This is a common experience for postminimalist music, which, more than totalism, has often become a strategy for setting up cognitive dissonances. In its most intricate form (of which Esptein is the extreme and William Duckworth another strong example), it tends to create structures that sound consistent and logical, but in such a way that the ear can’t quite tease out where the logic comes from.

It seems to me that postminimalism, and to a lesser extent totalism, have suffered in the public ear from having flourished at a time when formalism had acquired a sour reputation, following the long-awaited demise of 12-tone music. After I wrote the article “Downtown Beats for the 1990s” that sparked recognition of totalism, one of my Midtownish composer friends (Scott Wheeler) remarked with surprise, edged with disapproval, that “the Downtowners seemed to pick up where the Darmstadt composers had left off.” It’s true that postminimalism and totalism were united by the exploration of technical devices, as a way of creating a new musical language. Outsiders to the style have not had much patience for this particular aesthetic goal over the last 25 years. Even though serialism’s strictly formalist period was the 1950s, and it had evolved into something else by the 1970s, it created an understandable public perception that to “merely” play with formal structures was an intellectual self-indulgence, an elitist retreat into professional concerns. Minimalism was sometimes formalist too, of course, but its processes were so perceptually obvious as to be self-effacing – so exaggeratedly foregrounded, one might say, that you forgot about them. Postminimalism certainly attracted some composers – Janice Giteck, Elodie Lauten, Daniel Lentz – whose music dealt with political issues and diverse cultural influences. But the emphasis of the music, and its most original features, were on aspects of musical material, process, and syntax.

The 1980s – decade of performance art and world music – were all about teasing out music’s political significance, under a deconstructionist-driven assumption that one could read a person’s politics, conscious and unconscious, in the structure of a work. Abstraction seemed exposed as the irrelevant mind-game of privileged white males. It has certainly been that, at times. But one of the pendulums that swings back and forth in the history of art is that between society’s claim on artistic meaning and art’s own need to define its inner principles. Perhaps postminimalism picked an inauspicious cultural moment to develop a new musical language of auditory illusions based on minimalism. But at some point people will once again become fascinated by music’s inner workings, and when this happens, I hope there will be some recognition of all the wonderful territory postminimalism has explored.

The rhythm in question, perhaps totalism’s second-favorite rhythm after 8-against-9, is an interference of two periodicities, one five units long against another 4 units long. It is given here with its standard American mnemonic device, and also with the one I learned in England:

Several of Mikel Rouse’s pieces for his totalist rock quartet Broken Consort from the mid-1980s revolved around this rhythm. One that did so entirely was High Frontier. In High Frontier Mikel applied a Schillinger technique to this rhythm that was interestingly close to one of Stravinsky’s 12-tone usages. Stravinsky would sometimes rotate through the 12-tone row, moving the first note to the end of the row and then the second note, and so on; likewise, Mikel would take two notes off the front of the rhythm and place them at the end, then do the same with the next two notes, and so on, resulting in the following rhythmic patterns:

Every rhythm in High Frontier, except for the steady 8th-note pattern in the keyboard and drums, is either one of these rhythms or a 2X or 4X augmentation of it. Through these he runs a permutation pattern of six pitches: low F, A-flat, B-flat, B, D-flat, and high F. As I once wrote about the work,

High Frontier sometimes sounds like it is in 5/4 meter, at other times like 4/4 with quintuplets; at other times the listener can perceptually move back and forth at will between these meters, as in an optical illusion. The various rhythms are predetermined numerically to support each other; a slower-rhythm bass line, for example, may coincide with a quicker saxophone melody on every fifth beat, outlining a subtle secondary accent. The surface of Rouse’s music is lively and varied, while the background exerts a consistent, unifying structural influence. The listener can rarely identify by ear what process is going on, but gets a strong sense of an unfolding, internal logic. [“Downtown Beats for the 1990s: Rhys Chatham, Mikel Rouse, Michael Gordon, Larry Polansky, Ben Neill,” in Contemporary Music Review, 1994]

You can listen to High Frontier here.

In my own music based on moving among various pulses, inspired by Hopi and Pueblo rhythms, I often used a quarter-note tied to a 16th as a basic pulse, along with quarter-notes, dotted 8ths, and so on. In “Venus” (1994) from my multi-movement work The Planets, I decided to divide the ensemble in half, one half playing a 5/16ths pulse against the others playing a quarter-note pulse – much like the middle movement of Ives’s Three Places in New England, only 5:4 instead of 4:3. “Venus,” couched in 3/4 meter with a running 16th-note arpeggio in the synthesizer, is filled with durations and phrase lengths of five 16th-notes, five 8th-notes, and/or five quarter-notes. These durations pile up subtly in the beginning, and then when the main theme begins, the eight-member ensemble begins to split in two, the synthesizer and lower winds marking the 3/4 meter as the flute, oboe, and bass play a beat only 4/5 as fast:

The theme, moreover, is in five-beat groupings, a kind of virtual 5/4 meter that imposes a 25/16 meter over the notated 3/4 meter. As the two tempos thicken and continue, it can be difficult, as in High Frontier, to tell whether you’re listening to 3/4 with a 5/16 beat superimposed over it, or 5/4 with quintuplets. At the end of the piece, however, the four and five trade roles, so that the woodwinds are now playing the quarter-notes, and the synth is grouping 16th-notes into fives:

You can hear “Venus,” from The Planets, here, played by the Relache ensemble.

Both of these pieces represent totalism’s earlier, “heroic” phase, in which we were willing to go to great lengths of ensemble difficulty to achieve sonic illusions from polyrhythms. The next two works, though, relax into a milder polyrhythmic usage.

Rouse’s 1995 opera Failing Kansas, based on the murders of Truman Capote’s In Cold Blood, returned to the 4-against-5 rhythm on a less virtuosic level. A five-beat isorhythm, divided 3+3+1+3 in 8th-notes, is a recurring idea in the work:

The middle of the second scene, “The Last to See Them Alive,” is based on five- and ten-beat cycles over which a more “normal-sounding” 4/4 sometimes asserts itself. The effect is less illusionistic than in High Frontier, but you still have a continual choice as to which meter to tap your foot to (notice the 5/4 ostinato in the bass, reinforced by the harmonica):

You can listen to the two-and-a-half minute excerpt of Failing Kansas that illustrates this tempo effect here. Or, you can listen to the entire ten-minute scene, “The Last to See Them Alive,” here. If you listen to the whole scene, you’ll hear a different, equally elegant effect at the beginning. The opening lyrics are from a hymn favored by Perry Smith, one of the murderers:

I come to the garden alone

Where the dew is still on the roses

And the voice I hear

Falling on my ear

The Son of God discloses

This hymn is in 12/8 meter and spoken that way, though the instrumental music is in 4/4 (the 8th-note equal between the two), creating a subtle out-of-phase relationship of 3+3+3+3 against 3+3+2 patterns. It’s so simple one could easily miss it – in 1995 it took me several listenings to analyze why the rhythm of this passage is so charmingly off-kilter.

Several years later, in 2004, I came back to the 5:4 idea in the “Saintly” dance for the Private Dances I wrote for pianist Sarah Cahill. Since one player needed to play both rhythms, this was a simple matter of placing 4/4 phrases (marked with accents only for illustration) above a 5/4 ostinato:

You can listen to “Saintly” here. Once again, at the end, I couldn’t resist switching the rhythmic roles as I had in “Venus,” changing to a 4/4 ostinato in the left hand with five-beat phrases in the right.

And, as a bonus track, here’s a four-minute percussion work by John Luther Adams, Always Coming Home, which will give you your fill of five-against-four tempos if you hadn’t had it already. It’s from a larger work called Coyote Builds North America, from 1990, the great heyday of 5:4.

Now that I’ve got more than 7500 mp3s on each of two external hard drives, one for home and one for school, my attention has turned to PDF scores. I’m collecting a lot of Beethoven from the Sheet Music Archive, and I recently wrote an article about Melissa Hui entirely from PDFs she sent me. Now I’ve found out, through a post at Sequenza 21, that Leo Ornstein’s son is inputting Ornstein’s music and offering it to the public through Other Minds, so in a few minutes yesterday I went from years of wishing I had scores of Ornstein’s early piano music to carrying around more than I could possibly need of it on my computer. And from a comment on the tuning groups, I chanced to learn that the manuscript scores of Tui St. George Tucker – a quarter-tone pioneer who, it turns out, died in 2004 without my being informed – are available at her web site. Of course, a dozen or so of my scores have long been available as PDFs, although if I’ve received a single performance from the fact, no one’s ever apprised me. I love having hard copy, which is indispensible for certain purposes. But I also waste a tremendous amount of student time, and mine, looking for scores that I know are in my library somewhere, that somehow never manage to get placed back where I think they live. With my PDF scores, it’s a problem I’ll never have. (Though I’ve also run into the difficulty that my own PDF scores don’t seem to print out correctly on certain computers. I’ll be glad when all this gets standardized.)

Probably no one but me gives a damn whether John Luther Adams’s music is postminimalist or totalist. As far as the specific terms go, I don’t give a damn either. But when I started surveying, in the 1980s, all the music that passed through New York (and, via recording, the rest of the country as well), I couldn’t help but notice that, among composers who were continuing and developing the minimalist aesthetic, there were two groups of qualities that almost always went together. The composers whose music was based on a steady beat virtually throughout, usually an 8th- or 16-th note pulse, also tended to use diatonic tonality, quasi-minimalist structures like additive process or permutation, mostly quiet dynamics, and acoustic timbres augmented by the occasional synthesizer. Those who used competing tempos, either simultaneously or interlocked somehow, tended to use more dissonant sonorities, more global large-scale rhythmic structures, mostly loud dynamics, and amplified or electric instruments such as guitars. For the former I appropriated the already-current but undefined word postminimalism; for the other the word totalism was provided. The distinction between the two styles was so striking and consistent that it would have seemed capriciously anti-intellectual, an act of scholarly irresponsibility, to have neglected to articulate my observations. Yet, judging from the comments I’ve received in subsequent years, the vast majority of musicians wish I had done exactly that: leave my musicological data on the ground where I found it.

Very few composers wrote music that combined different qualities from those two styles, but one major one who did was John Luther Adams. More often than not his tonality is diatonic, using a seven-note scale (often the “white” notes) with no pitch ever given precedence. Yet some of his pieces, like Clouds of Forgetting, Clouds of Unknowing and his piano cluster piece Among Red Mountains, have proved that he is just as happy to use the entire chromatic spectrum and a maximum of dissonance. His music for pitched instruments is almost always soft; his percussion music is mostly fortissimo. Nominally, his music falls square in the totalist camp because it almost always layers different tempos together. But some of John’s implied tempos are very slow, giving a new pulse only every 10 or 15 seconds, so that the effect seems more postminimalist, without the gear-shifting surface complexity you find in much totalist music. Even when he has 4-against-5-against-6-against-7 in each measure, the effect – achieved pianissimo with mallet percussion, celeste, and harp – is not so much one of tempo contrasts as of indistinct clouds of notes. No other composer from the minimalist tradition so resists being pulled into one definition or the other.

Dream in White on White (1992) has been surpassed in its ambitions by many of John’s works, but it became a prototype for one side of his ouput, and was a watershed in his development. Scored for string quartet, harp, and string orchestra, the piece opens with the string orchestra playing seven-note chords, changing to a new one every 2 and 2/3 measures. The solo quartet enters with chords changing every two measures, for a slow 3:4 rhythm. The harp then enters in four-note phrases in quintuplets, a new phrase every 1 and 3/5 measures. Thus the phrase rhythm is 20:15:12 by duration, or 3:4:5 by tempo, coming back in phase every 8 measures. At measure 53, the string quartet launches into what is marked as the “Lost Chorales,” outlining out-of-phase 4- and 5-beat loops between the two violins versus viola and cello. You can see those relationships, against the recurring harp and string orchestra pulses, in this example:

The next section has plucked notes in the quartet and harp outlining faster 3:4:5 rhythms in each measure, over a chord periodicity of 1 and 1/3 measures in the orchestra:

The chorales return, the string orchestra’s tempo increases, but in a final section the original tempo relationships resume.

You can hear Dream in White on White here. The work’s template has become the basis for at least two much larger works by Adams (and two of my favorites), Clouds of Forgetting, Clouds of Unknowing and In the White Silence. In the White Silence is in fact a magnificent expansion of Dream in White on White, stretched out to 75 minutes and with lovely solo lines for the quartet members. Clouds of Forgetting, Clouds of Unknowing achieves much denser clouds using mallet percussion and the entire chromatic scale. In each of these a large-scale process, implicit in Dream in White on White, is carried out more rigorously: an slow, stepped expansion of melodic intervals from 2nds through 3rds, 4ths, and on up to 7ths. (I kid John that when I start hearing tritones in his music, I know the piece is half over.) More aggressive aspects of totalism appear in John’s drum music, which hammers out more obvious intricacies at a more virtuoso tempo; but that’s for another day.

We have an MFA program in conducting, and I teach a course for it in 20th-century Orchestral Repertoire. I used to start chronologically with Busoni, Reger, and Holst, and work my way through the decades, but the class always broke down at some point into a discussion of the problems of programming 20th-century music for orchestra. The usual objections would arise: 20th-century music is more complicated than most orchestra subscribers can understand. It’s more anxious and dissonant than they like. You have to have followed the course of 20th-century music to understand the recent stuff.

So now I teach the course backwards, 2005 to 1900, and I start with Sara’s Grace by San Francisco composer Belinda Reynolds, which you can hear here. The performance is by Dogs of Desire, an orchestra that is a subset of the Albany Symphony, and that doesn’t market itself as an orchestra. The piece sets the whole discussion on a different footing. Turns out, some 20th-century music is difficult to figure out. Some of it depends on a familiarity with old styles. And some orchestra subscribers will reject Sara’s Grace just because the composer has the effrontery to not be dead yet – but then it becomes the audience’s problem, not the music’s. After all, anybody who can’t “get” what’s going on in Sara’s Grace might as well realize that music isn’t their thing.

Speaking of totalists, John Luther Adams turned 53 Monday; Mikel Rouse turned 49 today; Art Jarvinen turns 50 tomorrow (January 27). Had Mozart gotten a little more daring with his cross-rhythms, I might have noted his 250th as well. Those are the breaks.

Come to think of it, though, the party scene from Act I of Don Giovanni, with dances going in three meters at once, is quite audibly metametric. Consider him celebrated.

For whatever reason, I was never much drawn to the type of nested 3:2 and 4:3 crossrhythms that I described in my last metametrics post, but I did use it once, and could have mentioned it. In 1985, on the verge of turning 30, I was under some psychological pressure to write something ambitous. I decided on a big set of variations for two pianos, somewhat inspired by the two-piano tradition of Busoni’s Fantasia Contrappuntistica, Wallingford Riegger’s Variations, The Art of Fugue, and such huge solo piano variations as the Diabelli and Brahms’s Handel. (This was before Larry Polansky wrote his Lonesome Road Variations, which dwarfed mine.) My I’itoi Variations was a set of eleven variations on the “Black Mountain” song from the I’itoi cycle of the Papago Indians. I was very involved in collecting, transcribing, and analyzing American Indian music in those days, because I was attracted to its, um, proto-totalist rhythmic character – specifically the way it shifted back and forth among tempos.

Another influence on I’itoi Variations (and on much of my music) was Beethoven’s Op. 111 Sonata – variations 1 through 6 were stormy and tense like Beethoven’s first movement, variations 7 through 10 were impersonal and calm like the second movement, and no. 11, in an attempted tour de force, went back through the first ten variations in reverse order. Variation 8 was based on a nested 3:2. The idea was simple. (I try to make all my ideas simple). There were two foreground lines, the bass line in piano 2 and the right-hand melody of piano 1, plus a line of quarter-note chords shared by both pianos. The bass was in dotted quarters, the treble in triplet quarters, for a 4:6:9 tempo resultant. I hoped the treble and bass would float in seeming unrelatedness to each other, though subtly mediated by the chords in between. Here’s a passage from the beginning of the variation:

and another from the end, where the treble and bass lines have doubled in tempo:

The bass line is the inversion of the theme, with the intervals doubled in size (a trick I picked up from Messiaen’s bird song music). I suppose it won’t much harm my reputation to admit that the changes of key are timed according to a descending sequence of Fibonacci numbers. Everyone who studied Bartok’s music had to try them once. This was back in 1985 when I had not yet heard of Mikel Rouse, Michael Gordon, or Art Jarvinen, and was blissfully unaware that they were using the same ideas.

Here’s the recording of Variation 8 from I’itoi Variations, played by the Double Edge duo – Nurit Tilles and Edmund Niemann, who premiered it at Cooper Union in New York circa 1990.

As a performer – and I was a pretty good pianist in college, it’s the regret of my life that I didn’t keep it up – I never liked the feeling of complicated tuplets that couldn’t be expected to be played exactly right. I imagine you know what I mean: septuplet quarter-notes over a 4/4 measure, or an 11-tuplet with a couple of notes missing, and the composer says, “It doesn’t have to be exact, just make sure you end the phrase on the downbeat.” I never liked cheating, and I was so obsessed with polyrhythms that I didn’t want to fudge them, I wanted to feel them and feel secure playing them. Even with an ornamental quintuplet in Chopin, I worked to get it mathematically right. I had fallen in love with the three-against-four, two-bands-at-two-tempos section of the “Putnam’s Camp” movement of Three Places in New England, and at age 14 I said to the Universe, “Sir, it will be an honor to devote my life to replicating this effect.” So the fake polyrhythms, the little flurries that didn’t need to be accurate to achieve their goal, bothered me.

Judging from the music of my contemporaries, I wasn’t alone. The evolution of multitempo music in the wake of minimalism during the 1980s was an exploration of playable tempo relationships. When Conlon Nancarrow went this route, not relying on performers, he followed the arithmetical logic of numbers, going from tempo contrasts like 14:15:16 to 17:18:19:20 to 60:61. Those were impractical for the guys of my generation who wanted their bands to play multitempo music. Instead, they started out with simple relationships anyone could play, like 3-against-2 and 4-against-3, and then nested them. For example, take four drummers:

No. 1 plays a steady beat.

No. 2 plays a triplet against every two beats of 1.

No. 3 plays a triplet against every two beats of 2.

No. 4 plays a triplet against every two beats of 3.

This triply-nested 3:2 yields a pretty complex tempo resultant of 8:12:18:27, Drummer 4 playing 27 beats to every 8 by Drummer 1. This is exactly what Art Jarvinen does in one section of his Ghatam for sculptural percussion (1997), as you can hear here. He builds up the rhythm slowly, as a process, and doesn’t try to notate it, just gives instructions, because the notation would be needlessly complex.

This is also the same rhythm, though, that Ben Johnston used in the first variation of his “Amazing Grace” Quartet, No. 4 (1973). Going up one more 3:2, to 16:24:36:54:81, Ben did notate it, using different simultaneous meters to handle the overload. (You can hear that variation here, in the brand new recording by the Kepler Quartet.) Two variations later, Ben achieves (with great difficulty for the performers) a large-scale rhythm of 35:36, the same way one arrives at it in tuning pure pitch intervals: as the difference between a 9:5 and a 7:4 (or, rhythmically, 9 in the space of 5 and 7 in the space of 4). For Ben, as for Cowell in New Musical Resources, the methods of extending rhythm flowed by analogy from traditional ways of handling pitch, which was one of the core meanings of the word totalism in the first place.

In fact, Ben (who was my postgraduate composition teacher) could be taken as one of the leading and underacknowledged pre-totalist composers, perhaps even the most influential one. It was he, after all, who, in 1967, translated a 12-tone song in pure tuning into analogous rhythmic ratios, and those ratios into a rhythm-only piece of conceptual theater that was to be beaten on the outside of a piano with any available mallet-like objects. Titled Knocking Piece, the work was played all over the Midwest in the ‘70s, and was an obligatory virtuoso showpiece for young percussionists. It always had two tempos going at once, in ever-changing ratios determined by the 12-tone row the song had been based on:

The equal signs between measures indicate that the same pulse continues across the barline at that point. (No recording I know of available, unfortunately. If you know something about tuning, you can figure out the original pitches from these rhythms: taking the first as C, it continues G, E, B, D#, A#, F#…) Ben’s reputation never took off on the East Coast to nearly the same extent. But insofar as some of the totalists had been educated in the Midwest, Knocking Piece may well have been a seed that quietly (or rather, noisily) blossomed in the music of 1980s New York.

The piece that went furthest in exploring this kind of performable tempo layering, as far as I know, was Michael Gordon’s Four Kings Fight Five of 1988. Scored for three winds, three strings, percussion, electric guitar, and synthesizer, the work starts out with a melody that pits quarter-notes against dotted quarters in 6/4-slash-12/8, because the other rhythms (the four kings who fight against five) are going to be drawn from this concurrent contrast. The pounding opening, with much unison, is the part most relevant to the piece’s dedication, which is to Glenn Branca – of interest to those of you who may doubt whether the Branca/Chatham artrock of the time had any immediate connection to totalism. (Branca produced Gordon’s first record, as well.)

At 3:08 (three minutes, 8 seconds) into the recording of Four Kings Fight Five, the music pauses, and a rhythmic continuum starts to build up that will proceed through eleven different tempos, as many as seven of them at a time. The tempos are represented by the following note values, repetitively articulated:

quintuplet 16th-notes in the space of 6 (a dotted quarter)

triplet 8th-notes

dotted 16th-notes

8th-notes

triplet quarter-notes

dotted 8th-notes

quarter-notes

quarter-notes tied to 32nd notes*

dotted quarter-notes

half-notes

half-notes tied to 16th-notes

*(Gordon notates the quarter-notes tied to 32nd notes as dotted 8ths in a tuplet over the three 8ths of a dotted quarter beat, but it works out the same. Don’t worry about it.)

The eleven available pulses are given here with the ratios of their relative tempos and durations:

These ratios can be seen as analogous to pitch. If we take the quarter-note as C and the triplet quarter as G, we get the following “harmony” of tempos:

A – 60 tempo – quintuplet 16th-notes in the space of 6

G – 54-tempo – triplet 8th-notes

F – 48-tempo – dotted 16th-notes

C – 36-tempo – 8th-notes

G – 27 tempo – triplet quarter-notes

F – 24-tempo – dotted 8th-notes

C – 18 tempo – quarter-notes

Bb – 16-tempo – quarter-notes tied to 32nd notes

F – 12-tempo – dotted quarter-notes

C – 9-tempo – half-notes

Bb – 8-tempo – half-notes tied to 16th-notes

Note the self-inversional character of this harmony, except for the fastest A-tempo. At the work’s most complex point (long before the halfway point, at about 5:47), there are seven tempos going at once:

You can sort of see that everyone else is playing off either the quarter-note beat or the dotted-quarter beat, which are unified in the keyboard part. The viola and bass clarinet play triplets off the quarter-note beat. The violin, less obviously, is playing 2 beats to every 3 dotted-quarter beats. The oboist, poor dear, is having to play 4-against-3 to the dotted-quarter beat, or 16 even pulses over three measures; actually twice the tempo of the violin, but not lined up in rhythmic unison with it. Here six of the lines are cued to the dotted quarter beat and three to the quarter-note beat, but one assumes that elsewhere the ratio is four lines against five, as per the title.

From here on, the piece gradually floats into a more static continuum, which became typical of Michael’s music about this time. At 19:22 a viola starts up in free rhythm over the throbbing G major continuum underneath, and at 20:56 a snare drum rhythm in military time joins it, and the piece dies away. You can hear Four Kings Fight Five in its 23-minute entirety here; the rhythmic points I’ve been making are all illustrated within the first seven minutes.

Please don’t get too exercised over whether you “like” the piece or not. Frankly, I don’t find it, overall, one of Michael’s most compelling works, though I certainly love parts of it – I somewhat prefer Thou Shalt!/Thou Shalt Not!, Yo Shakespeare, Trance, and the Van Gogh Video Opera, among others. The question is not whether you “like” it, but whether you understand what it offered in terms of multitempo composition. In that respect it was not only remarkable for 1988, but offered possibilities that have still not been fully explored since.

What’s common to all three pieces, by Jarvinen, Johnston, and Gordon, is that the performers achieve a remarkable degree of rhythmic complexity – a true “harmony of rhythms” in Cowell’s sense – by selectively listening to some performers within the ensemble whose pulses they play off of, and having to ignore others. The ability to maintain a 4-against-3 rhythm over a steady-beat reference point, and the relative impossibility of securely maintaining a more difficult 27-against-16, is the same in rhythm as it is in pitch: a perfect fourth (4:3 pitch ratio) is easy to tune, a Pythagorean major sixth (27:16) extremely difficult. Gordon could still have gone a little farther than he did by factoring in more 5-against-4 rhythms, both as quintuplets and as quarter-notes tied to 16th-notes. I have sometimes succeeded in getting a class of students to clap 25-against-16 by conducting a quarter-note beat and having half clap quintuplet quarters while the other half clap quarter-notes tied to 16ths. Gordon goes only so far as a quintuplet over the dotted-quarter beat. I don’t know of a piece that went further in drawing so many competing rhythmic layers at the same time in a large, live-ensemble texture. It wouldn’t surprise me if Gordon’s Trance does, but I haven’t seen the score.

For years I have fought within musical academia for the right (for myself and students) to minimally notate dynamics, to not use dynamic contrast as one of the ways of structurally articulating a piece if you don’t want to do so. I have seen student works cancelled or excluded because they were soft (or loud) throughout, or because within a certain range they wanted to leave dynamic nuances to the performer. I have paraded around with copies of manuscripts by Bach and Rzewski that are devoid of dynamic markings, to prove that their absence does not indicate musical idiocy, and I have argued myself blue in the face to composers adamant that dynamic particularity is synonymous with “professionalism.” But such a discussion came up on Sequenza 21, and Peter Gordon, of Love of Life Orchestra fame back in the ’80s, gave an eloquent rationale for dynamic reticence that had never occurred to me:

I don’t know whether dynamics is so much about compositional contrast, but more how much you want to signal for the listener within the composition. More static dynamics allow the listener more freedom and offer a contemplative space to explore other parameters, often at the listener’s own pace. More active and extreme dynamics can involve the listener on a more physiological level, which can be good or bad. Overactive and domineering dynamics can, if cynically used, run the danger of becoming – like the work of Steven Spielberg – emotionally pornographic.

UPDATE: One more point in response to some comments, because I hadn’t planned on getting into another notation argument – the whole issue has come to disgust me because of the neurotic, historically myopic concensus that has come to exist among 95 percent of today’s composers.

I have found a tremendous difference in responses to notation between performers who specialize in 20th-century music and those who play mostly Classical/Romantic repertoire, and far prefer the latter. One of my colleagues intimidates students who hand her music that is “deficient” in dynamic markings by saying, “This is the way they’ll play it:” – and then she plows through the music at the piano with the most unimaginative uniformity. In my experience, that can indeed be true with 20th-century specialists, who have been trained to react to the printed page with the literalness of a computer; but hand the same music to a Beethoven specialist, and they’ll do what they do with Beethoven, interpret it and invest it with feeling, coming up with the most delightfully varied and creative responses.

Whenever possible I prefer to work with conventional classical musicians. If I know in advance I’m writing for 20th-century specialists, I try to dutifully nail down every tiny nuance, as if I were making electronic music, because I know they’re not bringing any creativity to the table. The process is so much nicer, though, when the performer comes with her own human and musical instincts. Pianist Sarah Cahill is such a creative performer, even if she does specialize in 20th-century (but recent, not the academic stuff) – and the way she plays my Private Dances is more beautiful than I imagined them, and surprising in some cases. Thank goodness I didn’t load the pages down with hairpins, slurs, accents, and precisely calibrated tempo changes that would have kept her from following her muse.

For the other 31 reasons why I think most composers have their heads up their asses where notation is concerned, I once again refer the reader to my article The Case Against Over-Notation.

I thought I’d put up a more detailed example of an early totalist piece, to show precisely how composers started breaking away from minimalism in the early 1980s. Mikel Rouse’s Quick Thrust of 1984 is a work that both reaches back into minimalism’s most formalist concerns and also forecasts ideas that would later become widespread. For one thing, it was one of the first fully notated pieces for a pop instrumentation, written as it was, like most of his music of the ‘80s, for his rock-instrumentation quartet Broken Consort, consisting of soprano sax, electric keyboard, electric bass, and drum set. Secondly – it’s a 12-tone work. The composers whose work would later be called totalist loved minimalism’s formalism, hard-edged textures, reduced range of materials, impersonality, and amplified ensemble concept, but were not much enamored of its pretty, diatonic tonality (at least as manifested in the work of Reich and Glass). Few turned to 12-tone technique, nor did Mikel ever repeat the experiment as far as I know, but Quick Thrust is a bona fide piece of 12-tone totalist rock – perhaps the only one.

Thirdly, Quick Thrust is an example of music drawn from Schillinger technique, for Mikel studied with a Schillinger specialist when he came to New York in the early 1980s. Today Joseph Schillinger’s technique is more widely known by reputation than example, but in the 1930s and ‘40s, it was particularly picked up by Tin Pan Alley composers as an aid to churning out music in a hurry. Gershwin studied it; so did, later, Earle Brown. (Schillinger’s hefty two-volume exegesis of his methods is forbidding, but quite clear if you persevere. It tends to introduce a new principle and work its way up to a musical example, and is actually easier to follow if you kind of start with each musical example and work your way backward to the principle.) The technique is based in a faith in the ability of number systems and arithmetical techniques to generate musical forms of innate aesthetic attractiveness, and some of its devices had been presaged in Henry Cowell’s precocious book New Musical Resources.

One technique in particular resonated with Cowell: generating rhythms via what Schillinger called the interference of periodicities. This meant repeating several rhythms of different lengths, and using the sum of their resultant attacks as a melodic rhythm. For instance, the pattern made by the simultaneous repetitions of a dotted 8th-note at the same time as a repeated quarter gives the resultant 3-against-4, the rhythm known by the mnemonic device “PASS the GOD-damned BUTter.” Since only one rhythmic value is used for each rhythm, this is an interference of monomial periodicities. In Schillinger technique, one could also have a rhythm of two notes (say, quarter + 8th) against another two note rhythm, creating a binomial periodicity. The song “Fascinatin’ Rhythm,” in fact, starts with an interference of a sexonomial periodicity (8th, 8th, 8th, 8th, 8th, quarter, totaling 7 8th-notes in duration) against a 4/4 meter. (That Gershwin wrote the song long before studying Schillinger suggests why he was drawn to the technique.)

Quick Thrust is entirely a product of interferences of monomial periodicities. Mikel rather fanatically derived all of his rhythms based on periodicities of the Fibonacci numbers 2, 3, 5, and 8. Every rhythm was either the result of the sum attacks of repeated notes of these durations, or else of a larger rhythmic unit divided into 2, 3, 5, and 8 parts. For instance, the bass line was frequently the result of dividing a duration of 30 8th-notes into 2, 3, and 5 equal parts:

Note that the 12-tone row is run through the eight-note rhythm in a phasing relationship, the pitch row and rhythm row returning to their original relationship every 24 notes. This is, of course, a recurrence of medieval isorhythmic technique, in which a pitch row (called a color) and a rhythm (called a talea) go out of phase with each other. The practice was the structural basis of the 14th-century motet, died out around 1450, and was resurrected again by Messiaen in the first movement of his Quartet for the End of Time (1941) and Study No. 7 by Conlon Nancarrow (early 1950s). It has appeared in several totalist works, my own Desert Sonata (1994) included.

The upper lines of Quick Thrust, also treated isorhythmically, tend to be drawn from patterns of recurring small durations, such as this line made up from the summed attacks of notes 3, 5, and 8 8th-notes long:

At the beginning of the piece the entire 12-tone row is heard as an introduction, upon which the bass line enters, and then the keyboard and saxophone, creating a texture of three Schillinger rhythms at once, the same tone-row cycling through all three:

Notice that the high hat rhythm follows that of the keyboard, basically doubling it, and that the drums follow the bass line. Mikel never used any other transposition or form of the row (no retrogrades or inversions), for an effect that has always reminded me of the second movement of Stravinsky’s Threni, where he does something very similar. Others will be reminded of the young Steve Reich in the ‘60s, using the same row form over and over until his teacher Luciano Berio finally asked, “Steve, if you want to write tonal music, why not just write tonal music?”

And now, ladies and gentleman, you can hear Quick Thrust in its five-minute entirety here. (By the way, there has never been a score to Quick Thrust – Mikel gave me the individual instrumental parts for his music from those years, and I’ve had to assemble the scores myself.)

I emphasize that this piece represents one of the initial starting points of what has been called the totalist, or metametric, movement. Like so much postminimalist music of the early ‘80s, it is minimalist compositionally, but not perceptually. Its repetitiveness is intricately disguised. Its strict processes are not linear but global, real to the composer but not heard by the listener. (Many movements of Bill Duckworth’s earlier Time Curve Preludes are similar in this respect.) Quick Thrust is a fantastically clear example of a certain kind of rhythmic and structuralist thinking that was pervasive, “in the air,” in the mid-1980s among a certain kind of minimalism-impressed-but-not-quite-impressed-enough composer – not characteristic of the totalist movement as a whole, but quite typical of several months in 1983/84.

This kind of intense structural fanaticism was soon left behind. Number patterns remained in use in the works of many composers, such as Michael Gordon, Art Jarvinen, Rhys Chatham, Glenn Branca, Ben Neill, Evan Ziporyn, Diana Meckley – but usually in textures of more intuitive freedom. The interference of periodicities became the basis of the fifth movement of Chatham’s An Angel Moves Too Fast to See, at least part of Branca’s Sixth Symphony “Devil Choirs at the Gates of Heaven,” and several pieces of my own in the ‘80s, most concentratedly my 1987 piano piece Windows on Infinity – though my interest was always in longer time stretches and larger prime numbers, with events occurring every 53 8th-notes, every 71, every 103, and so on. When Mikel heard a concert of my music by Essential Music in 1989, and I heard his Quick Thrust and other Broken Consort works soon afterward in 1990, we got together, started talking, and realized that we had been on the same track. You could look it up.

Subsequently I wrote about Quick Thrust and other works with similar rhythmic tendencies in an article in a 1994 issue of the academic journal Contemporary Music Review. Possessing entire file cabinets full of unpublished scores by composers of my generation, I could write another article like this every month. But very few people have seen that article, and articles in academic journals pretty much disappear into libraries, to be scoured at rare intervals by the occasional researcher. I’ve got tenure, I don’t need any more resumé lines, thanks. Now that I can put both score examples and recordings on the internet, I would far rather publish here, where I am am actually read. And since few people who weren’t immediately involved in the scene were aware of techniques used by the music I’ve spent my life writing about, I hope that with this method of presentation I can bring the underground history of the 1980s and ‘90s out into the open and help the world catch up. Does it sound like I’ve finally begun that book on Music After Minimalism that I’ve been threatening for years? I guess I have.

Composer Art Jarvinen, known as “the West-Coast totalist” (poor guy, he never got to come to any of the parties), writes to remind me, in detailing qualities of totalist music, that there was a characteristic totalist instrumentation as well as rhythmic style:

For totalist music to really work requires an edge. A lot of totalist composers have guitar or saxophone or electric keyboards (Rhodes, Hammond, Mini-Moog), or drum set, as their main instrument. I wrote for chromatic harmonica and baritone sax. I don’t want to hear a totalist piece for the Berlin Philharmonic, I want to hear Icebreaker, or the Berlin Phil-Harmonica Band! That’s why the Bang on a Can All Stars have an electric guitar. And Evan Ziporyn plays bass clarinet as if it were a Stratocaster! My totalist rhythmic/contrapuntal ideas and techniques might work with a string quartet, more or less. But my “totalist” pieces, if we are to call them that, work best with more vernacular (less standard/classical) instrumental combinations, that provide a certain edge not available in the standard instrumental groupings that are all about blend and balance. Balance? That’s why we have a guy at the mixing board!

When we recorded [Art’s piece] Clean Your Gun, I could hardly get the engineer to do what I wanted, which was, run the harmonica, cello, violin, and baritone sax through guitar amps, crank ’em up, and mic the amps. He didn’t want to do it, even though I was paying him to. I had to tell him, it’s my piece, we’re going to take a bit of paint off the walls, and you just get it on tape! There is a clarity in amplification, vernacular instrumentation, and players who play like rock musicians – i.e. with a soloistic attitude and stage presence – that I would consider a vital and indispensable factor in the development and successful delivery of the totalist style. I would probably not have written any of my totalist pieces if I didn’t have access to the instrumental doublings of the E.A.R. Unit. They just wouldn’t sound right.

It’s true, there was generally a kind of mixed, all-or-partly amplified ensemble sound that made those pieces come off. Just as Nancarrow had to harden his piano hammers to keep his counterpoint masses from softening into mush, totalist music needed amplification and instruments with percussive attacks to bring off the gear-shifting tempo contrasts.

Although I might also mention that one of Art’s most rhythmically inventive works, The Paces of Yu (1990), was scored for solo berimbau (a simple Brazilian stringed instrument) accompanied by pencil sharpeners, window shutters, plucked wooden rulers, wooden boxes, mousetraps, and fishing reels. Here’s a small excerpt from the score, showing a section for flicked and jiggled window shutters. It employs a fairly common totalist or metametric rhythm, triplets in odd-numbered meters, so that downbeats contradict the momentum set up by the triplets, and also a gradual rhythmic process, showing the inheritance from minimalism:

And here’s a recording, courtesy of the California Ear Unit and O.O. Discs. (Warning, the opening is very soft for a few minutes.) It’s hardly a sonically typical totalist example, but a suitably whacky bit of pure Jarvinen.