‘Chaconne principle’ and form in the music of Magnus Lindberg

ABSTRACT: In the mid-1980s, Magnus Lindberg began to use pitch-class set theory in designing the harmonic reservoir of his compositions. In UR (1986), the pool consists of twelve symmetrical 12-note chords made of a hexachord and its transposed inversion. The form of the piece develops as a sequence of sections based either on a single chord or a process leading from one chord to another. Processes of this kind also define the form in the orchestral trilogy Kinetics (1989), Marea (1990) and Joy (1990). In Corrente (1992) Lindberg adopts a new method that he calls the ‘chaconne principle.’ It consists of continuously recycling a set of chords throughout the piece with a strong connection to spectral writing. Lindberg uses the same method in most of his later works. In some of them, there is only one chaconne, while some others (such as Aura, 1994) make use of several. Sometimes, the form is based on this principle alone. At times, other kinds of situations and processes are interpolated between the chaconnes. The purpose of this paper is to examine the set-up and use of the ‘chaconne principle’ in Corrente, which is its first and purest implementation.

* * * * *

For the first performance of Corrente II (1992) Magnus Lindberg wrote a programme note in which he says that after the piano concerto (1991) and the orchestral trilogy (KineticsMarea, and Joy, 1989–90) he felt that he had come to the end with a certain musical expression and compositional technique and that he couldn’t continue the same way. ‘All these works,’ he wrote, ‘were based upon an extended chaconne principle, with chord chains cycling around, undergoing constant transformation and being articulated in a very gestural way.’ He then goes on by saying that in Corrente (1992) he ‘abandoned the chaconne principle and based the harmony on different scale aggregates.’[1]

The problem with this statement is that it is not quite accurate. Lindberg did not abandon the chaconne principle. On the contrary, in Corrente, he uses it in a more consistent way than before, and he has continued to use it in most of his compositions ever since, the only major exception being Engine for chamber orchestra (1996), based on an entirely different concept.

According to a handbook-definition chaconne is a ‘continuous variation form of the Baroque, similar to the *passacaglia, based on the chord progression of a late 16th-century dance imported into Spain and Italy from Latin America.’[2] In Lindberg’s music chaconne is a continuous variation form based on a series of 12-note chords. As every chord, the number of which varies between 6 and 13 in different works, contains all 12 pitch classes of the tempered scale, the chords only differ from each other in the distribution of the pitches in the pitch space. In other words: the pitches of the chords are fixed in the register.

The warehouse from which Lindberg fetches his chords is the cardinality-class 6. Of all chords of this class he normally uses only 13. All these 13 chords have two forms, A and B, which are inversions of each other. In the composer’s chart of cardinality-class 6 they are marked in gray, blue and green (Ex. 1).

In Lindberg’s view, the chords can be arranged in five groups on account of their characteristic properties (interval array, interval vector, etc.):

1) 6-2, 6-5 and 6-9, generous in seconds, the ‘chromatic group’;
2) 6-15, 6-16 and 6-18, rich in minor triads, the ‘minor group’;
3) 6-21 and 6-34 (the ‘Promethean chord’), whole-tone oriented;
4) 6-22 and 6-33, containing a pentatonic array of pitches;
5) 6-27, 6-30 and 6-31, with diminished fourth chords, the ‘ethnic group.’

Ex. 1. The cardinality-class 6 (table annotated by ML)

In Corrente, Lindberg uses seven chords (labeled A, B, C, D, E, and F), composed out of one hexachord and its complement. The first chord (the A chord), for instance, is 6–30B/A (Ex. 2).

Ex. 2. 6-30B/A [224223]

Here, the pitches of the hexachords are arranged in such a way that their ambitus exceeds one octave. In the ‘normal order’ they are, of course, within an octave. How did Lindberg arrive at this particular ordering of the pitches? The six modes of the hexachord 6–30B, the lower hexachord of the A chord, are given in Ex. 3, numbered from 0 to 5.

Ex. 3. Modes of 6-30B

The lower hexachord of the A chord in Corrente is the mode no. 1. But Lindberg has done a slight permutation to it. He has transposed the second pitch, e1, one octave higher. One possible reason for this permutation is that the composer wanted to avoid the minor second relationship between E flat and E natural, the first pitch being a kind of ‘tonic’ of the composition. Or else, he may have wanted to spread out the pitches into a wider space. Whatever the reason, the permutation is automatically reflected in the A form of the hexachord. Combined, the two forms yield a ‘wide-scale’ — a term used by Marcus Castrén in an article on Lindberg’s Gran Duo[3] — that encompasses two octaves plus a minor third, as shown in the composer’s handwritten sketch (Ex. 4).

Ex. 4. The A chord of Corrente in Lindberg’s handwritten chart or chords.

All seven ‘wide scales’ that make up the chaconne in Corrente are similarly formed (Ex. 5). They are not randomly chosen but follow a carefully designed plan. All groups except the ‘chromatic’ group in the composer’s typology are represented. The ‘wide scales’ A (6-30), E (6-27) and F (6-31) are ‘ethnic,’ B (6-34) and C (6-21) are ‘whole-tone oriented’ while D (6-22) is ‘pentatonic’ and G (6-15) is ‘minor’.

Ex. 5. Corrente: the chords

The distribution of the chords in the pitch space also follows a definite pattern. The bass line E flat – B flat – F sharp – B flat – G sharp – D – E flat establishes a sort of tonal plan of the composition, although chaconne — unlike passacaglia — does not recycle the bass line.

One of the main characteristics of Lindberg’s technique of composition is the way he uses the ‘wide scales.’ He treats them in the manner of modes. As each pitch class is available only in given registers within the mode, each mode has a certain number of typical melodic figures and harmonies that different from those of the other modes. The E flat of the chord A, for instance, is not available one octave higher or lower but is again available two octaves higher or lower. In some situations, though, a case of a pitch class may appear in a ‘wrong’ register. These cases are exceptions and they usually occur when transposing the scale by an octave.

To illustrate the use of modal ‘wide scales’ in Corrente, I have chosen a passage in which the harmony changes rapidly (Ex. 6).

Ex. 8. Corrente, mm. 33–34.

Ex. 6. Corrente, mm. 33–34

In measure 32 — one measure before the beginning of Ex. 6  — we are in the area of the ‘wide-scale’ E. It seems that, on the first beat of measure 33, that we still are there. But suddenly a ‘foreign body,’ an E flat (indicated with an exclamation mark) appears. It shouldn’t be there, because, in the ‘wide-scale’ E, an E flat is not available in this register. Milliseconds later the same ‘foreign body’ appears in the percussion, harp and piano parts. And then, in the middle of the final sextuplet of the English horn’s descending figure, an E flat is missing between the pitches f1 and d1, where it should be.

Ex. 7. Corrente, m. 33 (reduced)

Now we realize that we are not in the area of the ‘wide-scale’ E anymore, but have proceeded to the realm of the ‘wide-scale’ F that is almost identical. There are two differences only: the pitches G sharp and B (8 and B) are two octaves higher and the pitch E flat one octave higher. This instance is an example of a very smooth, almost unnoticeable change of mode. On the third beat of measure 33, the bassoon takes over the descending figure of the English horn and continues descending on the pitches of the ‘wide-scale’ F. On the fourth beat, the clarinet, and the cello join the bassoon in contrary motion to each other. The clarinet uses the pitches of the ‘wide-scale’ G (6–15) in descending order from pitch 8 to pitch 4, which means that all the pitches of 6–15A plus the highest pitch of 6–15B, the e1, are present. The cello starts ascending from E flat, the lowest pitch of the mode, up to the pitch 4, the e1, on which it arrives one unit of a seventuplet before the clarinet (Ex. 8). Then it moves out of the system, or so it seems since the pitch no. 5 (F) is not available in that register.

Ex. 8. Corrente, m. 33 (reduced)

This f1 (indicated with an exclamation mark) is a sign of change; it marks the beginning of a new chaconne cycle where the modal ‘wide-scale’ A is the first harmony. The pitches 4 and 5 (e1 and f1), played by the clarinet and the cello as a shake, and supported by horns, percussion, harp and piano on the first beat of measure 34, make up a dyad on which the two forms (A and B) of the wide-scale A are symmetric (see Ex. 6). This powerful statement of the nucleus of the A chord is then supplemented by descending scale fragments in parallel motion, first of the English horn and the second violin and then of the bassoon and the viola (Ex. 9).

Ex. 9. Corrente, m. 34 (reduced)

On the last beat of the measure, the pitches F sharp and E flat in the bassoon part (see the exclamation marks) seem to be in wrong order. But they are not, since the highest note of 6–30A (F sharp) in that register is higher than the lowest note of 6–30B (E flat) on the primary level of the ‘wide-scale’  (see Ex. 2). The first beat of the next measure nails down the change of mode by letting all the pitches of the chord 6–30B sound at the same time (Ex. 10).

Ex. 10. Corrente, m. 35: 6-30B as a chord on the piano

Corrente is a work in three broad sections that I’m tempted to call movements (Ex. 11). They proceed without a break. Each movement is further divided into sections characterized by a particular type of texture. The main texture types are loops, chorales, and canons. Besides, there is a ‘slow movement’ and a ‘macchina’, common in several of Lindberg’s compositions.

  • 1st movement Measures Tempo
    Introduction 1 11 63
    Loops I 12 34 63
    Loops II 35 52 96
    Chorale I Clockwork Orange 53 60 72
    2nd movement
    Canon I 61 73 72
    Canon II 74 84 108
    Canon III 85 88
    Canon IV 89 92 168
    Chorale II 93 118 108
    Chorale III Background harmony 119 134 72
    Slow movement 135 149 54
    3rd movement
    Canon V 152 165 72
    Canon VI Unisono 165 172
    Macchina Loops III 184 210
    Chorale IV 211 222
    Chorale V Clockwork Orange 223 230

Ex. 11. Corrente: the form.

All 16 sections contain at least one full cycle of the chaconne. The larger ones may contain several. We may conclude that instead of abandoning the chaconne principle in Corrente, Lindberg created what seems to be the most straightforward implementation of it in his entire output. In this sense, Corrente is one of the milestones in the development of his compositional technique and a key work in understanding his later compositions.

[1] Magnus Lindberg, Corrente II. See http://www.chestermusic.com/work/8447/main.html.

[2] The New Harvard Dictionary of Music, Cambridge, MA & London, England: The Belknap Press of Harvard University Press, 1986, p. 145.

[3] Marcus Castrén, ‘Aspects of pitch organization in Magnus Lindberg’s Gran duo for 24 wind instruments’, A Composition as a Problem IV (Proceedings of the Fourth International Conference on Music Theory, Tallin, April 3–5, 2003), ed. Mart Humal, Tallinn: Eesti Muusikaakadeemia: Scripta Musicalia, 2004, pp. 61–74.

Paper presented at the 14th Nordic Musicological Congress, 11–14 August 2004, Helsinki, Finland. A version in Finnish is published in Sävellys ja musiikinteoria no. 11/2004. Last updated on Sep 18, 2017.

About Ilkka Oramo

Professor of Music Theory, emeritus
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