Composer and Sequenza 21 loiterer Steve Layton ran across this article pairing the two of us and discussing our gradual divergences from minimalism. It’s the kind of composer-centered thinkpiece that I didn’t think anyone wrote anymore except to praise Ligeti, Boulez, Adès, and that crowd that people praise to look cultured. Seems like old times.

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.

Via Mary Jane Leach, here’s a Honda ad that brings the early ’60s avant-garde into the mainstream at last.

UPDATE: Here’s all the info on the ad, including the composer, Steve Sidwell.

Pianist extraordinaire Sarah Cahill, whose browser somehow won’t let her interact with Arts Journal comments pages, nevertheless chimes in on the dynamics issue:

Leo Ornstein… was an excellent pianist himself, and wrote fabulously for the piano.  But most of his piano scores have absolutely no dynamic markings whatsoever.  He believed that it was the pianist’s responsibility to come up with dynamics in the process of interpretation.  It’s so interesting, because there will be a passage which to one person is a climax, to be played forte, and to another person it will be an opportunity to back off and have it be more powerful as a pianissimo passage.  So his scores can be played in a variety of ways, and it’s fascinating to hear different performances.

…[W]hen a piece leaves dynamics out, it makes us as performers explore it in an entirely different way.  We can’t rely on superficial expression (playing dynamic markings as notated), we have to dig deeper and get to the heart of the piece to figure out what’s going on, how to best interpret it, and how dynamics figure into that interpretation.  It can be a more satisfying experience.

Not that everyone should compose the way Ornstein did – but if someone’s imagination works that way, why shouldn’t he be allowed to do it? How did conformity become such a cherished attribute among composers? And I can’t resist re-quoting the following note that Ellen Zwilich appended to her Lament for piano of 1999, a warning that Chopin would have found ludicrously obvious, but that today’s notation neuroses have made necessary:

Throughout, whether the passage is marked liberamente or not, the performer should feel free to ‘sculpt’ the rhythm and dynamics for expressive purposes in order to give a spontaneous, improvisatory quality to the piece. It would be ideal if no two performances were exactly alike.

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.

The venerable Jerry Bowles of Sequenza 21 reminds me that I should be attending to my own PR, and I need the reminder. It never becomes a reflex, for some reason.

But three members of the Da Capo ensemble, joined by myself and my son Bernard, will perform my new piece The Day Revisited this Tuesday, January 24, at 7:30 PM at the Knitting Factory, 74 Leonard Street. It’s my first NYC gig in a year or two, I guess, and if Stockhausen can perform with his son Markus, I can perform with mine. Flutist Pat Spencer and clarinetist Meighan Stoops had asked me to write them a microtonal piece, and after having their heads examined I complied with a work in a 27-tone, just-intonation scale, for flute, clarinet, two keyboard samplers, and fretless bass, this last played by my son, who’s pretty inured to my tunings by now. Though slow and mellow it’s a damned difficult piece because of the tunings, but I’ll just be sitting there playing chords. Also on the program are works by a bunch of famous people: Eric Moe, Martin Bresnick, Derek Bermel, Michael Gordon, Gene Pritsker, and Philippe Hurel, which I guess means I’m a real composer too. Da Capo’s calling this a world premiere – the only other performance was here at Bard, and we had technical problems then that we’re not going to have this time, knock on wood. Call 212-219-3006 and bother the Knitting Factory about it.

Pianist extraordinaire Sarah Cahill will also play two of my Private Dances at REDCAT in Los Angeles on February 18, but I’ll remind you about that later.

I’ve had a hell of a time with my microtonal music lately. I’ve outgrown the samplers I’ve been using for the last 12 years, and am at the epicenter of a complete technological overhaul. Nowadays everything is software-based, so I’ve acquired Kontakt 2, Max/MSP, and Scala (newly available for the Mac) in an attempt to get better sounds and more feasible playability in my microtonal stuff. For years I’ve taken a lot of crap from people who find my electronic timbres amateurish, which has always seem unfair, since I’m using the most expensive microtonal samplers I can afford. So what if I use the sounds that come with the box? – I make up my own pitches, and everyone else uses the pitches that come with the box, which strikes me as a worse infraction. If I can get Kontakt to work (still touch and go at the moment), I’ll reorchestrate as much of my early music as I can stand to. Suggestions on how to get good sounds with microtonal-friendly software are always welcome. It’s a huge barrier between me and the continuation of my career at the moment. As for The Day Revisited, I usually don’t write microtonal music for acoustic instruments because the performance hurdles are just too great, but I was asked, and they’re working their butts off.

While I’m blowing my own horn here, Christopher DeLaurenti has officially given my book Music Downtown its jaunty first review.

I am hugely chagrined to learn from the latest issue of Signal to Noise that composer Luc Ferrari died last August 22 and I never even heard about it. Along with Henri Pousseur and Bruno Maderna, Ferrari was one of those figures peripheral to Darmstadt serialism who seemed so much more intriguing than the central protagonists. I can’t say I ever quite understood Ferrari’s music – in fact, that was what was so damned interesting about the three of them, whereas what Boulez, Stockhausen, and Nono were doing was so obvious, so minutely explained and explainable. The signal piece for Ferrari was, of course, Presque Rien No. 1, a 1969 piece of musique concrète of which I find this decription at the Other Minds website:

By 1970 he had completed Presque Rien No. 1, a kind of musical photography, in which unassuming ambient sounds of a small village in Yugoslavia, recorded throughout a long day, are telescoped by means of seamless dissolves into a 21-minute narrative in which no apparent “musical” sounds are included.

That’s more detail than I’d ever gotten before, and I had never understood exactly how Ferrari seemed to crowd so many sounds into a 20-minute tone poem. Many of his concrète pieces are similar, but he also wrote strange, more serial-sounding instrumental works, and seemed obsessed with the naked female form, which figured on his CD covers and several titles. I kept thinking something would happen to bring him out into the open, and I was excited when, in 1991, he made a seeming comeback and began to put out CDs after a long absence from public visibility. And now he’s dead at 76, with my having been little wiser about him than I was in 1980. I hope some critical dialogue arises around him, brushing away the unfortunate clouds of serialist mystique that obscured the movement’s less dogmatic masters.

Thousands of people consider Elliott Carter a great composer. He’s won two Pulitzer Prizes, and gets performances and even retrospectives out the wazoo. He is assured his chances with posterity, regardless of what I do, or what any other individual does. Aside from the royalties he’s missed by my not buying all of his recordings, twenty years of my expressing misgivings about Carter’s music has not caused five dollars’ worth of harm to his finances or his career. If I really thought any of my ideas could truly do harm to Carter, I would be more reticent about expressing them. I have nothing personal against the man. In the case of far less well-known composers, however, it is possible that a negative review from me might do real damage.

This is why, as a Village Voice critic, I always maintained an ethical policy of only writing negative reviews in cases in which the support given the composer (or performers) was sufficiently compensatory. I have a vague idea that this reflected Voice policy in general, though I can’t specify how I was aware of that. For instance, if Lincoln Center or BAM presented a concert, all gloves came off. Large-scale institutional support for a composer, together with the attendant publicity machine, requires objective criticism as a counterweight. (As Virgil Thomson said, music criticism “is the only antidote we have to paid publicity.”) Many voices would weigh in in such a case, and it was incumbent on each of us to register our opinion as to whether the composer involved merited such grandiose support. The smaller the venue, the less incentive there was to review a composer who failed to impress me. If I heard a concert I didn’t like at Roulette, or the Performing Garage, or some other small space, I would usually simply not review it. There was no reason I could see to draw only negative attention to an artist who, otherwise, would have received no attention at all.

There were exceptions. Sometimes one artist I didn’t care for would perform on a concert otherwise well worth reviewing. In a couple of cases, artists pestered me so urgently for a review that I had to take them at their word and assume that they would prefer honest disapproval to no public reaction at all. Occasionally I would attend a concert I had expected to like, be very disappointed, and not have time to find another concert before my next column was due – thus the negative review appeared perforce. In general, though, I tried to avoid giving negative reviews to artists who were having a hard time making it and getting very little institutional support; if I couldn’t find anything redeeming to say about their work, I would simply ignore them. I would, however, review artists whose work I didn’t like if they were famous and/or getting programmed at major venues. For one thing, my conscience was always clearer if I wasn’t the only critic commenting. Of course, at the Voice I had a luxury few publications provide, of being able to pick and choose what concerts I wanted to write about.

All this is to explain why I am going to impose on the comments that come in response to this blog the same policy I applied to my career. Most of the composers I write about here are not regularly written about by anyone else. Their music is not well-known even among the rarefied circles of new-music connoisseurs. Some of them have little keeping them in the public eye beyond my enthusiasm and that of their immediate colleagues. My advocacy alone is in little danger of bringing them to an undeserved level of worldly success. All of them have in common that I find their music important or interesting in some way or other, even if the musical examples I cite may sometimes be chosen more to illustrate a technical point rather than to prove their attractiveness. I would be ill serving these composers if, in my advocacy, I peripherally left their music open to harsh criticism by every malcontent who chooses to read my blog. Nor should they be held to account for the way I present their work – they themselves might present it quite differently. If I’m just demonstrating technical features, then whether you like the music or not is truly neither here nor there.

If I provide a musical example that you don’t like, you are perfectly free to express your opinion of it on your own blog, at some other forum, or at any other web site. I will not, however, publish that negative opinion here. Most of the negative opinions of music by my peers that I’ve expressed during my career were elicited by the incentive of money, because criticism was my livelihood. My reputation as a dependable critic required the trust of my readership, which demanded honesty on my part, entailing the occasional negative review. Few who respond to my blog have similar incentives. If for some reason you are particularly desirous that I become aware of your unfavorable reaction to music I post here, feel free to drop me an e-mail. But I will not subject the composers I champion to the sting of harsh comments by the random public of internet passers-by. Besides, I submit that it is rather stupid to sign your name to a public, Google-able, harsh disparagement of the music of a total stranger without having any professional reason to do so. In that sense, I am protecting you from your own baser impulses.

As for the objections that were voiced concerning Mikel Rouse’s Quick Thrust, most of them had to do with the allegedly stiff nature of the drum playing. I simply do not acknowledge this as a deficit. For one thing, the piece dates from 1984, at the very beginning of the classical attempt to incorporate rock materials into a classical structure, and indeed, at the very beginning of Mikel’s career. More generally, new music has been largely an attempt to arrive at a music in between classical music and pop music. This compromise has met with violent resistance on both sides: from the classical musicians who refuse to take music with pop elements seriously, and from the pop fans who refuse to countenance music that uses drum sets but is played from a score, and played faithfully to the notation. Believe me, over a 23-year career as a critic, I have received a couple of billion messages to indicate that most musicians hate the music I advocate for one reason or the other. Most musicians never wanted an in-between music, only more of what they already had, and they will never, ever give the in-betweeners any credit for trying. Many pop fans are especially dogmatic in their unalterable position that a piece that uses trap set MUST HAVE THE LOOSE, DYNAMIC ENERGY OF ROCK or the heavens must fall. For all that Mikel has come a long way since 1984, I, as a classically-trained and -raised musician, prefer the tight drumming-to-structure relationship in Quick Thrust to more typical rock drumming. You do not. Your opinion is noted, once again. Clearly, this music is not for you. I recommend not listening to it. That does not mean, however indignant you are in your opposition and however ardently you feel otherwise, that it is bad music. It simply doesn’t.

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.

The most frequent and bitter complaint I’ve gotten about my book on Nancarrow over the years has been about the price. But I’ve just learned – over the internet, with the rest of the world – that a paperback edition is finally appearing this coming May. No price has been set yet, but I figure this should bring it down to no more than £150,000,000,000, or, in US dollars, approximately the monthly salary of an Exxon/Mobil CEO. So hold on a few more months and you’ll save.

I wish I could also correct a few of the errors in the book, most of which have been helpfully dredged up for me by subsequent Nancarrow scholar Margaret Thomas. The most egregious is that, in the charts that show the structure of Nancarrow’s canons, Study #43 is inexplicably missing. There are also some pitches wrong in Example 8.33, which analyzes the bass line of Study #41b. Maybe I can put together a list of errata for the web. Even so, there are fewer errors in the book than there were in Thomas Adès’s pissy review of it in the London Times Literary Supplement.

David W. Galenson’s new book Old Masters and Young Geniuses (Princeton University Press) is an apparently unprecedented study of the relationship of age to creativity. Galenson, an economist with a yen for painting, charts out for many famous painters the age at which each one peaked creatively. His method, brilliant in its empirical objectivity if rather obvious in hindsight, is to rate each painting by three criteria: its top selling price, how often it is included in academic art textbooks, and how often it is included in retrospectives of the artist’s work. He then correlates the paintings that rate highest in these regards with the ages at which they were painted. Thus we find that the most valuable and oft-cited of Picasso’s paintings were executed between the ages of 20 and 29, and the most valuable of Cezanne’s between 60 and 69. We even find that entire movements were populated by painters who tended to do their best work at certain ages. For instance, the abstract expressionists tended to peak later in life:

Mark Rothko, age 54

Arshile Gorky, 41

Willem de Kooning, 43

Barnett Newman, 40

Jackson Pollock, 38

than the pop artists:

Roy Lichtenstein, 35

Robert Rauschenberg, 31

Andy Warhol, 33

Jasper Johns, 27

Frank Stella, 24

Galenson’s next step is to correlate these ages with everything that the artist ever said, or that is known, about his working methods and aesthetic approach. He comes up with an amazing consistency of correlations, and bases on it a theory of two creative types. While one might wish for a less ambiguous terminology, his terms at least possess the virtue of being non-evaluative: the Experimental Artist and the Conceptual Innovator. As detailed in dozens of examples, the Conceptual Innovator:

* tends to peak in his 20s or early 30s;

* produces one or two or three works well-known as his greatest or most influential;

* tends to do a tremendous amount of sketching and planning, finally executing the final work with great speed and a sense of finality;

* relies heavily on research, borrowing, and quotation; and

* achieves a conceptual redefinition of the art form in question without necessarily reaching new depths of expression.

By contrast, the Experimental Artist:

* tends to peak in his 40s or 50s if not later;

* develops steadily throughout his career, producing a consistent body of work in which no particular painting stands out as the greatest;

* figures out what he’s trying to do in the process of painting, without following (at least successfully) a preconceived plan, and often continually revising afterwards;

* takes his material from personal experience or the environment around him; and

* expresses something deeply true about his world without necessarily transforming the genre he works in.

Picasso was the quintessential early-blooming Conceptualist, Cezanne the exemplary Experimentalist. Cezanne said, “I seek in painting”; Picasso replied, “I don’t seek, I find.” Cezanne’s method was described thusly:

the ultimate synthesis of a design was never revealed in a flash; rather he approached it with infinite precautions, stalking it, as it were, now from one point of view, now from another… For him the synthesis was an asymptote toward which he was forever approaching without ever quite reaching it…

Picasso’s career, by contrast, was a series of discrete discoveries; he made over 400 preparatory sketches for Les Demoiselles d’Avignon, quickly brought the final painting to his image of perfection, and it became his most famous work.

Galenson has no expertise in music, he tells me, but he applies the archetypes as well to poets, novelists, and film directors. Conceptual Innovation can be seen in the reliance on quotation of T.S. Eliot in The Wasteland (his most influential work by far), Ezra Pound in his Cantos, Andy Warhol in his famous prints, and (my example) the collages of John Zorn. By contrast, Charles Dickens, Mark Twain, and Robert Frost drew heavily on their environments and continued to develop their technique until the end. The Experimentalist Twain often found that his books would not progress with the plots he had planned, and he would have to take time away from them until they worked themselves out. Conceptualist E.E. Cummings was criticized for never having gone beyond the brilliant innovations of his earliest poems. Dickens, an Experimentalist, gave us pictures of life in Victorian England that are truer than history; Melville, relying on books on whaling rather than personal experience, turned our conception of the novel upside-down with Moby Dick at the age of 31. Conceptualists do not always receive early acclaim – Moby Dick was a financial disaster, not appreciated until after Melville’s death. The two types need not lack affinity. The poet Robert Lowell, who did his greatest work in his last years, was a signal influence on Sylvia Plath, who pre-empted her own late period by committing suicide at 30. And so on and so on, with a wealth of well-chosen personal statements of artistic process.

I suggest applying this typology to composers with some caution. The issues may be different, who knows? But certain examples will spring to mind. We have some Conceptual Innovator composers with explosive early careers, forever best known for one or a handful of precocious early works: Stravinsky, Antheil, Cowell, Messiaen. Easier to call to mind are those Experimentalists who developed their music later in life, with no particular work standing out: Shostakovich, Sessions, Partch, Carter, Feldman. I’m tempted to type Ives and Copland as conceptualists, but the later date of some of their best works militates against it. Perhaps music has some aspects of technical acquisition and performance vicissitudes that require some alteration of the time line. It’ll be fun to do some study and find out.

In any case, Galenson’s book has achieved three objectives. It has created a new form of the always-appreciated parlor game of dividing artists into two types; it has drawn, with the most incisively empirical methods, two contrasted views of the creative process, with surprisingly bundled groups of attributes, deserving of voluminous further study; and it has proven irrefutably that the curve of creative potency over a lifetime differs tremendously for different individuals, with certain pattern types evident. We have new grounds for believing it naive to assume that the later work of a famous young artist will continue to be as profound, and likewise, to believe that an artist who hasn’t evinced signs of greatness by age 40 may well still do so. Galenson has established, with an economist’s objectivity, that these patterns vary with creative type; the evidence his fine book provides will help us gauge our expectations and perceptions accordingly.

Just heard a conductor from the Wichita Symphony (whether the conductor, I didn’t catch) participate in the NPR word puzzle show. The host asked him what Wichita was playing this season. His reply: “Oh, everything from Mozart and Beethoven up through Verdi and the Alpine Symphony. Something for everyone.” No, Maestro, not quite for everyone.

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.