Infinite Pitch Possibilities and Exponential Structure
Frank J. Oteri: If we wanted to try to describe what your music sounds like to somebody who’d never heard it, a very salient feature is your use of glissandos. It’s an infinite approach to pitch, which interestingly is antithetical to the paradigm of the keyboard you grew up playing. It does relate specifically to gagaku, but it’s also obviously a sound that’s all around us: police sirens, the cries of a young child.
Lois V Vierk: What you say about the glissando being all around, I think that’s very interesting. I remember being in my co-op room—I lived in a woman’s co-op when I was in college—and the cars would be going by back and forth, so you had that Doppler effect all night and all day. I constantly heard the glissando in the traffic, as well as in the wind outside, flowing water, all of those natural sounds. To me glissando includes all kinds of continuous smoothly changing sound, be it of pitch, timbre, intensity, or volume.
Keep in mind that I went to Cal Arts for my master’s degree, where we kind of studied John Cage like other schools might study Bach. So, studying Cage rigorously—I know that sounds kind of odd, but that’s what we did—that idea of “all sounds are great” was really in my mind. And then in gagaku, this idea is right in front of you: that continuously changing sound, the glissando. It sounded great to me. But also in gagaku the glissando always has a musical function. It isn’t a decoration. There’s always a musical phrase that’s going from one point to the other point, and the glissando gets you there. Or sometimes the glisses surround the main pitch, emphasizing it. In any case, the gliss has a meaning in the phrase.
It just sounds so beautiful to me, to have that glissando happening and also to have it make sense musically. I think that’s the way I got started into glissandos.
FJO: Now in terms of getting musicians to play this, to get precisely what you’re hearing and what you want your audience to hear, how do you notate that?
LVV: It’s a very tricky proposition to get players who are trained to avoid the sounds that I like, to really play them and bring them out. To do a bend in a pitch, I’m constantly revising the way I notate based on what players tell me. I hear something, I write something, but then the players tell me what they understand when they see my notation, and it may be quite different. The easiest way to think of notating a glissando is to make a picture of it, so of course I use lines, like traditional string notation uses. That’s the main thing that I use, but then I realize sometimes that what I’m hearing in my head is a glissando that speeds up or slows down. So then I have to figure out how to get that across. If it’s a long enough pitch duration, I’ll indicate midpoints. Suppose the gliss goes from E up to G, but I want to have an accelerating glissando. I would write a gliss up to, say, an F in the first two beats, and put the F in parentheses. Then in one beat it would gliss up to the G. The timing and speed of the gliss is written into the notation.
I’ve also noticed that the way I hear things usually has a very clear dynamic shape, so that all has to be notated very clearly, in as normal a notation as possible. I learned how important it is to use standard notation from one of my teachers, Mel Powell. He told me this in the 1970s (and I paraphrase): “All this graphic notation that people are experimenting with, it’s great. But rehearsals are expensive. You’ve got maybe an hour or two to rehearse with your players. There’s no time to discuss anything. Use as traditional notation as you can get away with and you save time and get more rehearsing in.” That’s what I’m constantly striving for, clear notation that gets my point across. And then if at all possible, I’m there for at least one rehearsal with the player. No matter how understandable I think the notation is, there always are things to point out.
FJO: Now it’s interesting that you talked about doing this intense study of John Cage, from everything you’re saying in this conversation, this music leaves nothing to chance.
LVV: You’re right, but what I do love about Cage is the idea that any sound is great. To me it just rings true. It’s real. It’s life. It’s earthy.
FJO: Having a pitch continuum based on glissandos, which is an infinite pitch continuum, is a very different way of thinking about pitch than the way microtonalists look at pitch. Because they’re systematizing it in some way—whether it’s having 24, 31, or even 72 equal steps, or some form of open-ended just intonation where pitches still relate to one another—even those systems are limited compared to what you’re doing. You’re saying it’s all available.
LVV: Yes, but I always have some kind of a pitch center, so maybe this part of the piece is based on D and then maybe this part on G—there’s always a pitch center. In other words, it’s nothing like the twelve-tone system, where there’s no pitch center or anything like that.
FJO: Now when you’re working with, say, bowed strings or slide trombones; your glissandos are relatively easy for a player to do. But what about that amazing piece of yours for trumpets? How do you get a brass player with a valve instrument to do that? I guess it’s all lipping to some extent.
LVV: First of all, I worked extensively with a friend and colleague of mine, Gary Trosclair, who wanted to experiment like this. He uses his tuning slide for a lot of what I have written. Some of it is lipped, but a lot of it uses the tuning slide. So he and I had sessions together where we went through, pitch by pitch, every half-step on the trumpet: “What gliss can you do at this pitch? How come this one is good? How come this one is bad?” We just went through the whole trumpet range. I think I have one recording that we made, and it’s just every pitch on the trumpet—what slides you can do around each and every pitch. And I’ll tell you, once one player has done it; it’s proven it can be done. So there’s a lot of pressure on the next person to really do it.
FJO: Would you say the way you use pitch is more intuitive than systemic, since it’s all these options, or is there a system to how you use the glissandos? How do you think of it?
LVV: Well, I have pitch centers in every piece, and it’s very systematized, but the glissando itself really depends on the instrument. Whatever exists on a particular instrument, I’ll incorporate into my system for that piece. So, if you have an instrument like a trumpet, where a half-step is about it, that’s what I use. A glissando typically will be a structural element in my pieces, as well as just being a sound I like. If I’m writing for strings, for example, if the piece begins quietly, the glissandos may be slow and covering a short interval. At the climax of the piece, the glissandos may be rhythmically fast, articulated, and covering a large interval, say an octave or more. The direction of the gliss, up or down or mixed, will also be significant structurally in the work.
FJO: I was reading an essay where you were talking about exponential structure, and I thought it would be interesting to get into that a little bit.
LVV: When I was a grad student a Cal Arts, I read some literature about how the body perceives sensory stimulation of all sorts. All sensory phenomena in the body are measured in exponential terms, not in linear terms. The one exception is the length of a line. If you look at two lines, you can judge pretty much if one is, say, twice as long as another. You perceive it as twice as long, and it is, in fact, twice as long. But other examples are not so straight forward. A sound that subjectively sounds “twice as loud” as another does not have twice the amount of energy. A light that looks “twice as bright” as another doesn’t have twice the amount of energy. The same applies to touch stimulation and perception of pain. It has been shown that every kind of stimulus yields a different equation. The perceived and the actual amounts of stimuli is an exponential relationship, not an arithmetic one. What sounds, looks, or feels like “twice as much”, “three times as much”, “four times as much” as the first stimulus, is not 2 or 3 or 4 times the first stimulus. It is actually some number to the 2nd, 3rd, 4th, etc. power.
So just as an experiment, I thought, “Well, let me work with time like this.” And that’s when I started composing pieces using what I came to call “exponential structure.”
When I compose a piece of music, supposing I want it to start with longer sections and work down gradually into shorter sections to end. I would not start with say, five minutes and then four minutes and then three minutes, two minutes, one minute. That would be an additive or subtractive process, a linear process. Instead I’ll take a section of music; we’ll say it was x number of seconds. The second section would be, say, .9 times x, the next section would be .9 squared (or .81) times x, the next would be .9 cubed (or .73) times x, the next .9 to the fourth power (or .66) and so on. The sections of this piece would always be getting shorter and shorter, and the pitch centers would be changing faster and faster. If you do that and you also compose your musical materials in the same way, what I just described will be music that seems to be getting faster and faster. I don’t mean tempo here, but since more and more information and more and more energy are being added to the sounds, the musical material is moving past you in time quicker and quicker.
FJO: As I hear you talking about this, I’m thinking of two very completely different things. I’m thinking of how very highly structured Cage’s pre-indeterminate music was, the kind of grids he came up with to structure his percussion ensemble pieces, which was a very individualistic application of Schoenbergian-type theory which led to a very unique approach to rhythm. I’m thinking of Elliott Carter’s use of metrical modulation. Neither of these approaches leads to music that sounds anything like your work, but there’s a similar philosophical orientation to it. And this makes me wonder what your attitude is about how listeners perceive your music. Is this something you would want a listener to hear? Is this an attempt to have a process that’s perceptible?
LVV: I’m interested in listeners hearing the energy of the piece. I don’t care if they’re aware of a process. I want the energy of my music to come through. I can’t tell you that someone’s going to hear .9 or .81; I hope they don’t. But I think they can hear something that’s an increase in energy. Along with musical materials that start out, say, calmer and get more and more exciting and then have more and more information packed into shorter and shorter amounts of time, there’s an energy sweep there. I certainly would not be interested in somebody—other than a music student with a score—sitting and hearing numbers. I think there’s a sweep, and I think the numbers are a part of the sweep.