Three Generations of Teaching Music Composition

4. 12-Tone Tonality

GEORGE PERLE: Let me talk about the mistake I made in connection with Schoenberg. I just mentioned it in this review of a biography of Schoenberg that just appeared. I don’t know how many people are going to realize how important it is?

PAUL LANSKY: The new biography or what you are going to say?

GEORGE PERLE: Let me go and get that review… This was in the Wall Street Journal.

These are two paragraphs. “It was Schoenberg’s hope that his 12-tone method would lay ‘the foundations for a new procedure in musical construction.’ He saw the role ‘invented to substitute some of the unifying and formative advantages of scale and tonality.’ And he also saw it as functioning ‘in the manner of a motive which must be invented anew for each piece.’ This is the point at which in 1937, maybe 1938, I came upon the Lyric Suite and figured out a lot of what happens in 12-tone tonality from there. Then I tried to find out something about Schoenberg and this is what I found out, that the tone row was supposed to function as a scale and a motive at the same time. And this is the conclusion I came to at that time. ‘There was an intolerable contradiction in the dual nature of the tone row. In tonal music the scale and its harmonic component defined the language, whereas motives are what a piece is about; a way of saying something about language. Schoenberg does not resolve this contradiction. Neither understandably does Mr. Shawm.’ That’s the author of this book. That’s something very important there and if I had studied with Schoenberg the way that you have studied with me, I would’ve pointed this out to him. That the scale and the motive aren’t the same thing, that they can’t be the same thing. They’re not supposed to be the same thing and particularly if you’re conceiving the tone row as “‘invented to substitute some of the unifying and formative advantages of scale and tonality.” And what I realized is that the 12-tone system as I had come to it was way ahead of what Schoenberg had come up with. Schoenberg’s idea was impossible. It wasn’t what he wanted and there are places where he practically says that, you know? Anyway, what I came up with way back in 1937, I began to study Berg; I began to study the Lyric Suite. By 1939, I looked at Schoenberg, I thought about Schoenberg and came up with my own notion about what a tone row is supposed to be. It had to do with my own insight, which was correct about what Schoenberg was looking for.

PAUL LANSKY: I’ve always meant to ask you this, if you’re looking at the Berg Lyric Suite, it’s a sort of skewed example because the set in the Berg Lyric Suite was also congenial with your approach because of the axis of symmetry, so maybe that was a bad piece to start with. That totally confused you. Turns out that the set of the Berg Lyric Suite has interlocking dyads that form the same interval.

GEORGE PERLE: Yeah, yeah. If you start the Berg set of the first movement in the second half and then move on to the first half, you have the basic symmetry.

PAUL LANSKY: So then you came across the chart that Berg made years later.

GEORGE PERLE: Yeah, but that was a long, long time later.

PAUL LANSKY: Yeah, but that shows sort of you probably weren’t that far off the mark when you were looking at Berg and you were probably further off the mark when you were looking at Schoenberg.

GEORGE PERLE: I think the basic criticism I had at that time was completely valid. You either have a scale or you have a motive. A scale can serve as a motive sometimes, but it’s a secondary use that it has in that case.

PAUL LANSKY: It can only be referential. It can’t be both.

GEORGE PERLE: Right. And Schoenberg was looking for a scale. He was wondering about the problem of what you do with the twelve notes. How do you make a scale out of all the notes? And the scale, the diatonic scale takes some notes. If you transpose a perfect 5th up, you lose one note, you get one new one, but it’s the same structure. Now we’ve only got all twelve notes, so we’ve got only one mode, nothing but half-steps instead of all the different modes we had before. And you only have one scale; you can’t have any transposition. It’s like having the piano with all the keys white. So, instead of jumping into it and doing what Schoenberg was doing, I did something that made more sense. I remember something that you said to me. You came to visit us in the country…

PAUL LANSKY: Was it Maine or Woodstock?

GEORGE PERLE: Woodstock. To talk to me about what I was doing. You wanted details and you asked questions. Do you remember that?

PAUL LANSKY: Yeah, I remember.

GEORGE PERLE: And then you had your insight and wrote me about it. And I wrote back to you that you’d come upon something that had been puzzling me for 22 years by then and that’s exactly vis-à-vis what I was doing. It was exactly the thing that I had done in relation to Schoenberg. But it all comes from looking at something from the outside.

PAUL LANSKY: With some sort of objectivity.

GEORGE PERLE: I’m trying to think about how I can present it here.

PAUL LANSKY: Well I can help…

GEORGE PERLE: Do you want me to tell them what my idea of a tone row is? Symmetrical sums and so on?

PAUL LANSKY: Well, maybe, you can talk about sums and differences.

GEORGE PERLE: That would be even worse.

PAUL LANSKY: More confusing?

GEORGE PERLE: I’ll dump it in your lap [laughs].

PAUL LANSKY: Gosh, I think I forget at this point! [laughs]

GEORGE PERLE: Well, in Schoenberg’s systems you have a set and you also have a retrograde and an inverted retrograde. Did you see that cartoon in The New Yorker about this? [laughs]

PAUL LANSKY: No.

GEORGE PERLE: It’s worth finding… I had a sonata for unaccompanied cello—this goes way back—and I temporarily withdrew it; I felt there was something wrong with it. And somebody I’d never met wrote to me a number of times and wanted to see it. And I said, “Well, it needs revision, I can’t show it to you right now.” And then a publisher wanted it and so I looked at it again. There was something wrong with it. It needed a crescendo in the first three bars and that’s all it needed. [laughs] So that was what was wrong with it!

PAUL LANSKY: Yeah, you’d be surprised!

GEORGE PERLE: So maybe there’s nothing seriously wrong with what we did.

PAUL LANSKY: Well, I think I can explain the contribution of your system in simple terms, which don’t require a sort of, too many technical terms.

GEORGE PERLE: Yeah. Don’t call it my system.

PAUL LANSKY: Our system or the system?

GEORGE PERLE: After all, there’s so much that Bartók did and so much that Berg did—

PAUL LANSKY: This “way of looking at things” then.

GEORGE PERLE: There was already a very solid basis. There’s some pretty significant music that’s involved with exactly this by a composer named Bartók and a composer named Berg and some other composers too.

PAUL LANSKY: Well, I think an important distinction is that it actually creates a sort of coherent harmonic language which is consistent across all pieces that use this kind of system and that’s based on the notion of symmetry. And an important thing to think about is that a pair of notes—I mean, this is true in the 12-tone system too, but it has a different complexion in this approach—that a pair of notes is typically thought of as an interval and thinking of symmetry as an important aspect of this way of doing things, that pair of notes also has got a significant membership in a different way of looking at things which is instead of thinking of it in terms of difference, you’re thinking of it in terms of sum. So that C and D are typically thought of as being a pair of notes that have an interval of two semi-tones and that’s a difference of two, but B and D-sharp, B-flat and E natural are considered members of the same class of things that C and D are. So interval and sum are considered equal and this of course occurs in the 12-tone system by definition.

GEORGE PERLE: Yeah, by definition. If you want to think about it at the piano, you can play a chromatic scale with your left hand and your right hand going in the same direction, and you’re keeping the same difference when you do that. You can also play it with the left hand ascending and the right hand descending and when you’re doing that your are keeping the same sum.Anything which is on that scale, let’s say you start with two C’s go down a half step and go up a half step and you get B and C-sharp. Go down another half step and go up another half-step and you get B-flat and D, it’s the same sum. Now both of those ways of evaluating an interval are of primary structural importance in a lot of Bartók and in Berg’s use of the 12-tone system in the first movement of the Lyric Suite. A lot of Berg’s music, no matter what kind of 12-tone music he’s writing, symmetrical rhythm. You see, there are two ways of looking at an interval. C and D are the same as C-flat and C-sharp.

PAUL LANSKY: Yeah, but the interesting thing about it is that the intervals, the dyads are then embedded into tetrachords and trichords which sort of look at this in a more complicated way so you get a kind of sense of harmony which is—in the 12-tone system, the sense of harmony is essentially aggregates because there’s the sense that there are always 12 tones circulating, in this system, in this way of looking at things, I don’t like to call it a system—this way of looking at things, you also—

GEORGE PERLE: What’s wrong with having a system? Beethoven had a system. Bach had a system. Why can’t we have a system?

PAUL LANSKY: Well…

GEORGE PERLE: I know it’s a shame to say Beethoven had a system.

PAUL LANSKY: I just don’t like the word system.

GEORGE PERLE: Why not? It’s a good word. Don’t let people who don’t know any better steal the vocabulary from you. Didn’t Bach and Beethoven have a system? They had the same system. They had the diatonic tonal system.

PAUL LANSKY: The point is that any collection of four pitches, any collection of four notes, even if several of them were the same has got a sort of metric in this system. So that if you take a C, a C-sharp, and a D-sharp and an A-natural, let’s say, then there’s a way of looking at that which brings in a set of relations to a lot of other tetrachords that is external to any specific piece so it’s kind of a generalized sense.

GEORGE PERLE: That’s exactly what Schoenberg was looking for. I mean, he didn’t have this solution to it, but it’s the kind of thing he wanted to have.

PAUL LANSKY: Well, it’s hard to say. I mean, that’s your idea…

GEORGE PERLE: That’s what he said.

PAUL LANSKY: But it’s a very interesting way of doing things and I just felt that I wanted to explore different directions and different ways to go about things, but in a way, maybe you need to go through a lot to get to that point. This is interesting.

GEORGE PERLE: I think other things have come into music as a result of not having a scale. As a result of the irrational part of what happens in music, which is also a constant reminder of the Schoenbergian revolution, what Schoenberg called the emancipation of the dissonance. There was a whole universe of musical possibilities just in terms of quantities. It’s really overwhelming that nobody was using them and there were ways to use it. Starting with Opus 11, No. 1.

PAUL LANSKY: Opus 16. No. 1… A lot of the pre-12-tone things Schoenberg was doing…

GEORGE PERLE: The thing I was doing was trying to work with this in a systematic way. I said something about combining two chromatic scales moving in parallel motion or moving in opposite motion. And I’m getting into the business of four notes, which you were talking about before. I saw these harmonic possibilities falling out of this and because, in the 12-tone system you have these two aspects, prime and inversion—we don’t care about these because we’re not dealing with a motive, you’re not concerned with retrogrades.

PAUL LANSKY: In this system.

GEORGE PERLE: Right. You’re dealing with these entities that are created by this material. So I would combine two sets, one of which was the inversion of the other and get my material that way.

PAUL LANSKY: I should say before you go on that the important distinction between what you are talking about and the ways in which the 12-tone system functions is that there is no pre-defined sense of order; there’s no pre-defined sense that you have to go from this note to this note. In other words there was sort of a free-floating harmonic language.

GEORGE PERLE: Like tonality.

PAUL LANSKY: Yeah.

GEORGE PERLE: You know, when you write tonal music, nobody tells you that every time you get to that note, you have to go to that note, you know? I mean, even if you’re dealing with notes that have a harmonic function, like the leading tone, you don’t have to go to the tonic.

PAUL LANSKY: Right.

GEORGE PERLE: There’s some kind of defined way not to go to the tonic that’s interesting.

PAUL LANSKY: True.

GEORGE PERLE: I didn’t like the notion of being told what the next note is going to be.

PAUL LANSKY: But it’s a different way of looking at things. I mean, in the 12-tone system, that is the relevant structure.

GEORGE PERLE: Yeah. You suggested that something interesting would happen if we could combine two sets that were transpositions from another instead of inversions. And the reason I didn’t do that is that I thought I had to do something that was complete. And, well you can see why I thought that. And it didn’t even occur to me to try the other. But you get the same kind of completion when you get the two sets that are moving in the same direction because then you can also have two sets that are moving in the opposite direction to the first—so that there are two sets moving in the same direction in the opposite way.

PAUL LANSKY: What I think had emerged was that the way you had been thinking about it had been in a two-dimensional sense that sort of everything goes like this. And…

GEORGE PERLE: Any idiot could have thought what you thought!

PAUL LANSKY: Yeah, any idiot could’ve thought of what I thought of.

GEORGE PERLE: This idiot didn’t!

PAUL LANSKY: No, that’s O.K. But then what we came up with, which I think is really quite beautiful, is that things didn’t just go this way and this way but they also went this way, so this is where we actually diverged—I started to think of it in terms of four dimensions, as sort of a four-dimensional array: X, Y, Z, and then transpositions of the whole thing and you had all these little slips of paper—you probably still do! The slide rules?

GEORGE PERLE: I threw them all away.

PAUL LANSKY: You threw all the slide rules away?

GEORGE PERLE: I think I threw them all away. Of course, every now and then I think I threw everything away.

PAUL LANSKY: Because I would come to your studio and there’d be all these slips of paper.

GEORGE PERLE: And we don’t need that anymore.

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