Archives for April 2012

Centennial of a True Original

I’m on my way to London this week to give one of the keynote addresses (Charles Amirkhanian is giving the other) at the Nancarrow in the 21st Century conference at the Southbank Centre, organized by Dominic Murcott of the Trinity Laban Conservatoire of Music and Dance. My talk is at 11:15 AM Sunday, April 22. Trimpin will be there, and composer Nic Collins is giving a paper on computer analysis of Conlon’s music, and Conlon’s widow Yoko Segiura Nancarrow, whom I haven’t seen in some 17 years, is making a rare public appearance. And there will be a bunch of concerts, and papers by young composers carrying on Conlon’s polytempo work. I’m planning to present a dozen of Conlon’s “unknown” player-piano rolls, some of them just interesting sketches, others seemingly complete pieces that I think are well worth adding to his canon (pun unavoidable in this instance). I’m playing them on my computer via Pianoteq software, which allows me to harden the virtual piano keys until they sound remarkably like Conlon’s pianos (he put shellac and strips of metal on the hammers to make a more bristling noise).

Over the succeeding couple of weeks I’ll be lecturing at theÂ Orpheus Instituut in Ghent, Belgium, and at Brunel University back in London, though I don’t think those are public venues. The rest of the time will be pretty much vacation, seeing old friends, and hopefully drinking wine in a slew of outdoor cafÃ©s. Conlon would have approved.

The Progressive Conservative

At the recommendation of our viola professor Marka Gustavsson, I just finished reading Ian McEwan’s 1998 novel Amsterdam, which she urged on me because the main character is a composer. It’s a brief book and an enjoyable read, but what impressed me most was the insightful realism with which McEwan describes, at considerable length, the composer’s thought process. Here’s his description of the composer, the Englishman Clive Linley, early in the book:

For Clive Linley the matter was simple. He regarded himself as Vaughan Williams’s heir, and considered terms like “conservative” irrelevant, a mistaken borrowing from the political vocabulary. Besides, during the seventies, when he was starting to be noticed, atonal and aleatoric music, tone rows, electronics, the disintegration of pitch into sound, in fact the whole modernist project, had become an orthodoxy taught in the colleges. Surely its advocates, rather than he himself, were the reactionaries. In 1975 he published a hundred-page book which, like all good manifestos, was both attack and apologia. The old guard of modernism had imprisoned music in the academy, where it was jealously professionalized, isolated, and rendered sterile, its vital covenant with a general public arrogantly broken… In the small minds of the zealots, Clive insisted, any form of success, however limited, any public appreciation whatsoever, was a sure sign of aesthetic compromise and failure. When the definitive histories of twentieth-century music in the West came to be written, the triumphs would be seen to belong to blues, jazz, rock, and the continually evolving traditions of folk music. These forms amply demonstrated that melody, harmony, and rhythm were not incompatible with innovation. In art music, only the first half of the century would figure significantly, and then only certain composers, among whom Clive did not number the later Schoenberg and his “like.”

So much for the attack. The apologia borrowed and distorted the well-worn device from Ecclesiastes. It was time to recapture music from the commissars, and it was time to reassert music’s essential communicativeness, for it was forged, in Europe, in a humanistic tradition that had always acknowledged the enigma of human nature; it was time to accept that a public performance was “a secular communion,” and it was time to recognize the primacy of rhythm and pitch and the elemental nature of melody. For this to happen without merely repeating the music of the past, we had to evolve a contemporary definition of beauty…. [emphasis mine]

I am surprised to see how much the opinions of this fictional disciple of Vaughan Williams overlap with my own. I have written myself about the primacy of rhythm and pitch, along with my own apologia for being something of a melodist. Of course I grew up making a sharp distinction between conservative and avant-garde, a distinction that has become harder and harder to define with the passing decades, perhaps to the point of total irrelevance. Even today, though, I would bristle at being called “conservative,” though I fully recognize that some of my ensemble works, those in which, for the sake of performer limitations, I have to restrain my microtonality and ferocious polyrhythms – since I am a pitch-and-rhythm composer – probably seem conservative within the definitions of most working composers. In this respect I feel myself an heir to Henry Cowell and Lou Harrison, two composers who endlessly championed progressive musical ideas, but who also sometimes wrote tuneful, texturally commonplace works under commission. In fact, I once submitted my Transcendental Sonnets for a choral competition, and while I didn’t win, the director sent me a complimentary letter calling the piece reminiscent of choral works by Herbert Howells, Hubert Parry, and other great British conservatives, and said he would look into programming it. I was happy to get a compliment from any direction. And I certainly agree with Clive Linley that academia has trapped music in a barren modernist purgatory, though I don’t think I quite agree with him on the most profitable escape route. (And needless to say, I strongly demur concerning the bankruptcy of late 20th-century postclassical, if not classical, music.) It’s funny, as I sit here working with 37 pitches to the octave and seven tempos running simultaneously, to see my opinions reflected back to me from a 1990s British musical arch-conservative.

Second-Guessing Satie

If you sense I’m in microtonal heaven lately, that’s pretty much true. Except for a six-minute piano piece, I haven’t written one of the normal pitches since December. One event that I would have highlighted in advance, but somehow I didn’t have the final information for, was a microtonal performance of Satie’s Vexations that took place last Sunday at the Against the Stream Buddhist Meditation Center in Los Angeles. Pianist Aron Kallay and guitarist John Schneider asked seventeen microtonalists, myself included, to come up with a microtonal tuning for Vexations that would take into account Satie’s peculiar notation, which spells the same piano notes differently in exasperating ways. You probably know the original version:

As written, there are 21 different pitches, D coming back as E-double-flat, C differentiated from B-sharp, and so on. Most of the chords are diminished triads. At first I spelled them all in regular minor thirds of 6/5, for groups of 1/1, 6/5, 36/25. That was logical and pretty but not terribly interesting, so I pushed to differentiate some of the diminished triads a little more. The problem is, sometimes Satie overlaps his diminished triads notationally, the longest chain of them beingÂ A#-C#-E-G-Bb-Db. I felt I had to distinguish A# from Bb and C# from Db. So I kept going up higher in the harmonic series, using harmonics I’d never played with before, and for those six pitches, I ended up with diminished-triad ratios of 5:6:7, 12:14:17, 28:34:41, and 34:41:49. So it turned into my first venture into 41-limit tuning (my teacher Ben Johnston has gone higher), and every chord in my retuned version is a part of a harmonic series, sort of the way I’m thinking lately. You can hear my results, and those of several of the other microtonalists, here.

From the Morass of My Subconscious

I dreamed this morning that Morton Feldman was still alive, that he had made a string quartet arrangement of Ives’s Fourth Symphony that the Arditti had recorded, and that he was advertising to make a string quartet arrangement of any piece for an appropriate fee.

A Scriabinesque Geometry

A new, brief piece, a rhythm study: Mystic Chords, 6:20. It’s the most austere thing I’ve written in decades. The main idea of the piece is an attempt to determine rhythms not by duration, but via tempo, thus creating rhythms incapable of metric notation. Here’s an excerpt from the score:

These aren’t the actual pitches. The piece uses a rather wonderful symmetrical pitch set I discovered, 27 harmonics above an extremely low F#, specifically harmonics nos.Â 1, 3, 5, 7, 9, 11, 13, 15, 21, 25, 27, 33, 35, 39, 45, 49, 55, 63, 65, 77, 81, 91, 99, 117, 121, 143, 169 – or rather, octave transpositions of those harmonics. I’m not much into symmetry; I usually prefer quirky pitch constructions with a scattering of elements that only appear once or twice. But this set creates seven identical chords based on the 1st, 3rd, 5th, 7th, 9th, 11th, and 13th harmonics, containing those same harmonics in each chord.

I called the piece Mystic Chords because I spaced all the chords in fourths after the manner of Scriabin’s famous “mystic chord” – C F# Bb E A D, and I added a G on top. The actual harmonics, then, are stacked as follows, with each chord running vertically:

768Â Â Â Â Â 768Â Â Â Â Â Â Â Â Â Â Â 800Â Â Â Â Â Â Â Â Â Â Â 728Â Â Â Â Â Â Â Â Â Â Â 792Â Â Â Â Â Â Â Â Â Â Â 792Â Â Â Â Â Â Â Â Â Â Â 728

576Â Â Â Â Â 576Â Â Â Â Â Â Â Â Â Â Â 560Â Â Â Â Â Â Â Â Â Â Â 560Â Â Â Â Â Â Â Â Â Â Â 576Â Â Â Â Â Â Â Â Â Â Â 572Â Â Â Â Â Â Â Â Â Â Â 572

416Â Â Â Â Â 432Â Â Â Â Â Â Â Â Â Â Â 440Â Â Â Â Â Â Â Â Â Â Â 392Â Â Â Â Â Â Â Â Â Â Â 432Â Â Â Â Â Â Â Â Â Â Â 440Â Â Â Â Â Â Â Â Â Â Â 416

320Â Â Â Â Â 312Â Â Â Â Â Â Â Â Â Â Â 320Â Â Â Â Â Â Â Â Â Â Â 308Â Â Â Â Â Â Â Â Â Â Â 324Â Â Â Â Â Â Â Â Â Â Â 308Â Â Â Â Â Â Â Â Â Â Â 312

224Â Â Â Â Â 240Â Â Â Â Â Â Â Â Â Â Â 240Â Â Â Â Â Â Â Â Â Â Â 224Â Â Â Â Â Â Â Â Â Â Â 234Â Â Â Â Â Â Â Â Â Â Â 242Â Â Â Â Â Â Â Â Â Â Â 234

176Â Â Â Â Â 168Â Â Â Â Â Â Â Â Â Â Â 180Â Â Â Â Â Â Â Â Â Â Â 168Â Â Â Â Â Â Â Â Â Â Â 180Â Â Â Â Â Â Â Â Â Â Â 176Â Â Â Â Â Â Â Â Â Â Â 169

128Â Â Â Â Â 132Â Â Â Â Â Â Â Â Â Â Â 130Â Â Â Â Â Â Â Â Â Â Â 126Â Â Â Â Â Â Â Â Â Â Â 126Â Â Â Â Â Â Â Â Â Â Â 132Â Â Â Â Â Â Â Â Â Â Â 130

The preceding won’t mean anything to non-math geniuses, but dividing each number by the largest possible power of two gives the octave equivalents:

3Â Â Â Â Â Â Â Â Â 3Â Â Â Â Â Â Â Â Â Â Â 25Â Â Â Â Â Â Â Â Â Â Â 91Â Â Â Â Â Â Â Â Â Â Â 99Â Â Â Â Â Â Â Â Â Â Â 99Â Â Â Â Â Â Â Â Â Â Â 91

9Â Â Â Â Â Â Â Â Â 9Â Â Â Â Â Â Â Â Â Â Â 35Â Â Â Â Â Â Â Â Â Â Â 35Â Â Â Â Â Â Â Â Â Â Â 9Â Â Â Â Â Â Â Â Â Â Â 143Â Â Â Â Â Â Â Â Â Â Â 143

13Â Â Â Â Â Â Â 27Â Â Â Â Â Â Â Â Â Â Â 55 Â Â Â Â Â 49Â Â Â Â Â Â Â Â Â Â Â 27Â Â Â Â Â Â Â Â Â Â Â 55Â Â Â Â Â Â Â Â Â Â Â 13

5Â Â Â Â Â Â Â Â Â 39Â Â Â Â Â Â Â Â Â Â Â 5Â Â Â Â Â Â Â Â Â Â Â 77Â Â Â Â Â Â Â Â Â Â Â 81 Â Â Â Â Â Â 77Â Â Â Â Â Â Â Â Â Â Â 39

7Â Â Â Â Â Â Â Â Â 15Â Â Â Â Â Â Â Â Â Â Â 15Â Â Â Â Â Â Â Â Â Â Â 7Â Â Â Â Â Â Â Â Â Â Â 117 Â Â Â Â Â 121 Â Â Â Â 117

11Â Â Â Â Â Â Â 21Â Â Â Â Â Â Â Â Â Â Â 45Â Â Â Â Â Â Â Â Â Â Â 21Â Â Â Â Â Â Â Â Â Â Â 45Â Â Â Â Â Â Â Â Â Â Â 11 Â Â Â Â Â 169

1Â Â Â Â Â Â Â Â Â 33Â Â Â Â Â Â Â Â Â Â Â 65Â Â Â Â Â Â Â Â Â Â Â 63Â Â Â Â Â Â Â Â Â Â Â 63Â Â Â Â Â Â Â Â Â Â Â 33Â Â Â Â Â Â Â Â Â Â Â 65

Now it’s easier to see that the first column is all divisible by 1 (of course), the second by 3, the third by 5, the fourth by 7, the fifth by 9, the sixth by 11, and the last by 13. Each column contains that number multiplied by 1, 3, 5, 7, 9, 11, and 13, and thus the entire pitch set is all seven numbers multiplied by each other. It’s such an elegant construction, so simple in principle, that I fully expect to be told that someone else has already come up with it. Its benefit for me is that each horizontal line is made of of pitches close together, ranging no further than a whole step and in some cases a half-step. The following chart, showing the same pitches given as cents above the tonic F#, makes this clearer:

702Â Â Â Â Â 702Â Â Â Â Â Â Â Â Â Â Â 773Â Â Â Â Â Â Â Â Â Â Â 609Â Â Â Â Â Â Â Â Â Â Â 755Â Â Â Â Â Â Â Â Â Â Â 755Â Â Â Â Â Â Â Â Â Â Â 609

204Â Â Â Â Â 204Â Â Â Â Â Â Â Â Â Â Â 155 Â Â Â Â Â 155 Â Â Â Â Â Â 204Â Â Â Â Â Â Â Â Â Â Â 192Â Â Â Â Â Â Â Â Â Â Â 192

804Â Â Â Â Â 906Â Â Â Â Â Â Â Â Â Â Â 938 Â Â Â Â Â 738 Â Â Â Â Â Â 906Â Â Â Â Â Â Â Â Â Â Â 938Â Â Â Â Â Â Â Â Â Â Â 840

386Â Â Â Â Â 342Â Â Â Â Â Â Â Â Â Â Â 386 Â Â Â Â Â 320Â Â Â Â Â Â Â Â Â Â Â 408Â Â Â Â Â Â Â Â Â Â Â 320Â Â Â Â Â Â Â Â Â Â Â 342

969Â Â Â Â Â 1088 Â Â Â Â 1088 Â Â Â Â Â 969 Â Â Â Â Â 1044 Â Â Â Â Â 1103 Â Â Â Â Â 1044

551Â Â Â Â Â 471Â Â Â Â Â Â Â Â Â Â Â 590Â Â Â Â Â Â Â Â Â Â Â 471Â Â Â Â Â Â Â Â Â Â Â 590Â Â Â Â Â Â Â Â Â Â Â 551Â Â Â Â Â Â Â Â Â Â Â 481

0 Â Â Â Â Â 53 Â Â Â Â Â Â Â 27 Â Â Â Â Â 1173 Â Â Â Â Â 1173 Â Â Â Â Â Â 53 Â Â Â Â Â Â Â 27

And so I have seven tonalities, all related to the central tonality, each chord equivalent in content, with the horizontal lines moving in very small increments and pivot notes among any two chords. It’s a closed, fully transposable just-intonation system. And since harmonics 1, 9, 5, 11, 3, 13, 7 make up an overtone scale (easier to see renumbered 8, 9, 10, 11, 12, 13, 14), there’s the possibility of deriving a thick web of melodic connections from these 27 pitches. (I could add in the 15th harmonic with only six more pitches, and might, since Harold Budd’s music made me so fond of major seventh chords.) In fact, this is almost the pitch set I used in my recent piece The Unnameable (of which I played the world premiere at the University of Northern Colorado last thursday, at a lovely festival of my music organized by composer Paul Elwood), except that there I used 15/14 instead of the 9th harmonic. Here I use those chords in an extremely minimalist way, but I think I’m going to have to explore them further.

I guess this will be mumbo-jumbo to most readers, but I’m excited about it as extending tonal harmony into new vistas in a surprisingly efficient manner. It took Partch 43 pitches to do what he wanted in 11-limit tuning, and I’ve got 13-limit with only 27. Of course, he used subharmonics and I don’t.