A Procession of Earth Pigs

Thumbnail image for aardvark.jpgWith some slight hesitation I post a new and rather comical work to the internet. It was supposed to be titled Triskaidekaphonia 2 because it uses the same tuning as my piece Triskaidekaphonia, but it turned out so programmatic that I couldn’t leave it with such an abstract title. So it’s The Aardvarks’ Parade (click to listen, just over ten minutes), in honor of an animal with which I had a childhood fascination. For the first time ever I’ve written a microtonal piece in a scale I’d already used before, and it’s the simplest one I’ve ever used: all the ratios of the whole numbers 1 through 13 multiplied by a fundamental, yielding 29 pitches. The form is AAAA: I was musing about a melody repeated over and over, in simple quarter-notes and 8th-notes, but so intricate in its tuning that several repetitions wouldn’t be enough to make it predictable. If I Am Sitting in a Room is the conceptualist Bolero, maybe this is microtonality’s Bolero. I tend to repeat things four times in my pieces: partly because it’s an American Indian tradition, paying homage to the East, West, North, and South, and partly because my first college composition teacher, Joseph Wood, told me that you could only get away with repeating something three times in a piece, instantly stirring my innate rebelliousness.

It was a luxury not having to spend the first week working out the scale, and also returning to a scale whose properties I’m beginning to know pretty well. The scale’s only limitation is that it tends toward tonal immobility, and I succumbed to a drone in this case, as I did in Triskaidekaphonia. I’ve already started two more pieces on the same scale, though, that move it around to different tonics a little. I’ve fallen in love with a couple of new intervals: one is 13/10 (454 cents), on which a phrase ends unexpectedly at 1:06; another is 13/9 (636), which ends a phrase at 1:15 and almost sounds like a slightly sour dominant; and I’m appreciating the double leading-tone pairs of 13/9 with either 13/7 or 13/12, for a deliciously out-of-tune yet consonant medievalism (heard in the resolution of the opening sonority). Part of the point, after all, is to train myself (and perhaps others) to hear and recognize the whole new color that 13 provides. Perhaps The Aardvarks’ Parade will never be as popular as Bolero became after the movie 10, but when they finally make the movie 13, I’ve got the soundtrack ready.
In retrospect, it’s occurred to me that there was a model for the piece in one of my favorite memories as a music reviewer: One year Skip LaPlante’s microtonal group in New York, Music for Homemade Instruments, played a melody over and over in 13-tone equal temperament, and then at the end everyone sang it, a thrillingly simple yet ungodly weird achievement. Sometimes I feel like my music is a deliberate caricature of new music, all the expected subtleties quantized, pixelated, and translated into quarter-notes and 8th-notes. I like hard, clean lines and bright colors. I hate vagueness and violence, am sick of emotive gesturalism, and only like ambiguity if it’s sharply drawn and unmistakable. I warn my students that subtleties tend to get lost in performance, and that the reason Beethoven was so successful is that there are no subtleties in his music. Thus the naivete is intentional. Composers hate naivete, but most other people like it. 


  1. says

    Honestly, I love the piece. My ears like it better then Triskaidekaphonia, though I need to listen to the latter again.
    As a “coincidence”, I was thinking about asking you if you had ever reused a tuning (I thought you actually hadn’t).
    I love the Bolero, I think it’s a great piece of music, no matter what many people say, even its composer… thought of course I understand you comparison, I really think your piece has its own charm as to the repetition of the melody. And I loved to learn about the North-South-East-West idea of repetitions.

  2. says

    I imagine a performance by the Sun Ra Arkestra in full Hopi ceremonial garb.
    KG replies: I saw Sun Ra and his band live once, he wore a pyramid on his head and it was a cosmic experience. But he’d need a very special piano for this.

  3. says

    Looking forward to the Parade, as is friend of mine who looks for the beasts in every zoo she passes. (I listen to just about everything you post.)
    That you “only like ambiguity if it’s sharply drawn and unmistakable” is charmingly close to a Wildean paradox, and I will pass it along to my friends.
    I’m intrigued by your response to Lisa, since the Grosse Fuga contains a notoriously problematic ‘subtlety’ on the very first page: what does he mean by the tied eighths of the Allegro? (No two violinists seem to agree.)
    Coincidence? An example of “sharply drawn and unmistakeable” ambiguity? Or am I overthinking, again?

  4. peter says

    At last, someone who talks sense about Beethoven! I have long wondered why the music world so idolizes his music, when most of it is as subtle as a house-brick. Not for him, the sudden changes of mood – from one bar to the next, like a sudden cloud in the sky – one finds in Mozart. Not for him, the musical representation of separate foreground and background one finds in Mendelssohn, two ideas being expressed at once. No, Mr B. grabs hold of your collar and shouts in your ear, rudely and loudly, to tell you of his personal problems, like some drunken, uncouth stranger.

  5. mclaren says

    Beethoven can blow me. The hell with Beethoven. I’m a lot more interested in the fact that you said it takes you a week to work out a tuning. Yowie zowie! A week??!?!??
    Man oh man. Longest I ever took to work out a tuning is a couple of hours. In a JI tuning, the main things I worry about are if there are any really small intervals — like, say, less than 12 cents. 16 cents, 18 cents, you can hear that, 23.4 cent Pythgaorean comma, no problemo, 21 cent syntonic comma, that’s easily audible. But below about 12 cents it gets dicey. I can’t reliably produce successive notes on the violin below about 12 cents, so it’s up tails all if the JI intervals get below 12 cents. That means going in and ripping ’em out of the tuning, which requires deciding which JI scale steps to deep six. That can take some time, ’cause you don’t want to jettison the wrong scale steps, it limits your harmonic options too much.
    Another big concern (for me) is if the JI tuning is symmetrical. From lowest to highest do all the pitches reflect around the tritone? Some JI tunings do, some don’t. It’s important for me to know because if the tuning isn’t symmetrical around the middle, it means you’re going to run into complications when you transpose intervals up or down. More than usual complications, that is. Transposing intervals or chords up or down in JI is always more complicated than in equal tempered tunings.
    And the last thing that’s important for me to know is whether there are recognizable perfect fifths in the JI tuning, and if so, how many. (Some JI tunings have more than one. Others, especially non-octave JI tunings, have none.) Without recognizable perfect fifths you have to use a different style of composition — you can’t just bang away with triads and do chord progressions, you have to move to quartal harmony, or tone clusters, or a pointillistic style a la Xenakis’ Kraanerg or gorgeous dense washes of orchestration like Dutilleux’s Mystere de l’instant.
    Do you worry about that stuff? Do you care if a JI tuning is symemtrical? Are the relative sizes of the smallest and largest intervals a concern? If there are especially big melodic gaps in the JI tuning, do you try to fill ’em in, or just leave ’em there and work around them?
    You mentioned earlier that you start by setting up harmonic areas and sticking to ’em in a JI composition. Do you start with a harmonic progression? (Easley Blackwood started that way with his 15 equal piece and Wendy Carlos also started that way with her track Beauty In the Beast in the Carlos Alpha tuning.) Or do you start with a melody and choose the harmonies from the available gamut? (I think Erling Wold tends to work this way.) Or do you assemble counterpoint and erase and re-write the contrapuntal lines depending on the location of the harmonic areas? (David Doty seems to work that way.) Or do you instead think in terms of modulating into and out of the various harmonic areas you’ve previously mapped out but not worry too much about sounding those particular harmonies or outlining ’em in melodies, Alberti bass, etc? (David Behrman worked that way on his JI piece On the Other Ocean from 1977.)
    You also mentioned you’re using ratios of 13. The ones you discussed, like 13/10, are primary ratios. How often do you get into secondary ratios (13*13, or 13*13*13, etc. In 7-limit JI tunings these tend to crop up a lot, as in the 49/35, also in 3-limit, as in the 9/8 = 3*3)? Is it easier for you to start out with primary ratios and then work up to secondary ratios because the secondary ratios are harder to hear? Or, like Partch, do you start with a JI tuning and then modulate part of it up or down and fold it back into the rest of the tuning so you have more useable harmonic areas? (This always gives you secondary ratios because you’ve modulated some parts of your scale up or down by other ratios.)
    Enquiring minds want to know.
    KG replies: Assuming you’ve come up with all possibilities, is this multiple choice? :^D I usually start out with harmonies, and the melodies result from the way the harmonies interact (even in 12tet, actually). What’s happened in the past – in The Day Revisited, in fact – was that sometimes I end up with harmonies that are a little too parallel, and so with each new piece I learn pitfalls that I try to avoid in the next one. In other words, I choose the harmonies to facilitate good counterpoint, because I was weaned on Renaissance counterpoint and consider it the most divine of all arts. Hey, choosing a tuning to spend a few weeks composing in is like choosing a wife (a temporary one, of course) – I don’t want to rush into it and then find there are things I can’t live with.
    I’m not a big fan of symmetry, and one thing I didn’t inherit from Ben is the subharmonic series. I speculate that it’s because I’m working on synthesizers, and the subharmonic series just sounds awful on them. I’m half-convinced it sounds much better on acoustic instruments. So for me minor isn’t the inversion of major, it’s just another chord color, and a variety of chord types facilitates counterpoint. Normally my roots are all simple ratios (or else the main melodic notes are), but I get into higher secondary ratios by building seventh and ninth chords. (I kind of feel like I’m explaining my medical history to a doctor.) Harmonically I’m more conservative than a lot of you wild and crazy guys, but the Triskaidekaphonia tuning is getting me out of that, and I’m learning to use 7:9:11 and 8:11:13 triads. I haven’t even checked whether the tuning is symmetrical, but I suppose not.
    Thanks for responding to the subject of the post.

  6. mta says

    Very fun and sinuous — with just the right amount of processional pomp for an aardvark. Thank you for posting it!
    KG replies: Exactly what I thought, thanks.