Jan Herman sent me this link, and I absolutely laughed my ass off. It would be churlish not to share such effective medicine with the world. (If the link doesn’t still take you to Ten Worst Album Covers, try this: http://salamitsunami.com/archives/91.)

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.)

Had my G4 Mac laptop in my lap. Smelled smoke. Felt hot place on my knee. Sparks flew. Screen went blank. Please expect communications to be on special schedule for a few days.

Art Jarvinen weighs in on the relation between totalism and dance:

I just watched Blow Up again. Had not seen it in a long time. There is a slightly interesting moment around 50 minutes in, where the bored photographer guy and the scrawny uninteresting woman are smoking and listening to groovy music. She’s trying to move to it, and she’s really lame. He gets her to move slooowly, "against the beat." She starts to get it, and it’s a totally Totalist moment….

I always wondered why I couldn’t dance. I couldn’t dance to The Twist, or "I Wanna Make It With You." But I could not NOT dance to Captain Beefheart. "Lick My Decals Off Baby" is my disco record. I have to move when I hear it, both knees going in different rhythms, one arm not knowing what the other one is doing – until it all comes around after…a while – or not.

We understand difference tones. You talk about ratios all the time. Totalist rhythmic structures usually add up to something – a big honkin’ downbeat that is so satisfying, and that you feel coming for a long time before it hits.

Composer Paul Epstein told me the other day that the only thing wrong with my Disklavier disc was that he couldn’t exercise to it – the different tempos kept throwing him off. I had had the same experience. When working out on a treadmill I often listen to Postclassic Radio. One day Michael Gordon’s Trance was on. I almost fell off. I could not keep moving in tempo to the jerking around of all those dotted quarters and triplets fighting with each other. Wherever we totalists make our money, it’s not going to be through the sale of totalist exercise videos.

 

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.

Lovely article, painstakingly accurate in its description, about Meredith Monk by Ann Midgette in today’s Times. It is overdue compensation for Ed Rothstein’s scandalously contemptuous dismissal of a great artist in those pages after the premiere of Monk’s Atlas in the mid-’90s.

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.

Next Monday night in New York my friend, classroom nemesis, and jazz harmony teacher John Esposito is involved in a concert in which will be premiered a couple of 1960 tunes by John Coltrane, recently discovered, that had never been recorded. The titles are “Out of a Dream” and “The Backbeat,” the handwriting on the manuscript John recognized as Coltrane’s, and since John is amazingly adept at historical styles (or so he keeps telling me), he was asked to harmonize and arrange them. He’s playing with the Eric Person Quartet, of which he is a regular, but he’s not sure where the gig is (jazz musician, you know…). Something to do with the Public Library, he thinks. I’ll find out and give an update here. They look like really nice bebop tunes.

UPDATE: Oops, turns out the concert by Eric Person and Meta-Four is a private affair. My announcement has news value only. But you can get info at their website.

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.