Harmonic Unity in Magnus Lindberg’s Cantigas

By Ilari Kaila

A doctoral essay, submitted in partial fulfillment of the requirements

for the degree of Ph.D. in Music Composition,

Stony Brook University, Department of Music

Stony Brook, New York

April 2008

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1. Introduction

Ever since the late 1980s, beginning with compositions such as Kinetics and Corrente I

and II, harmony has become an increasingly important parameter in the orchestral music

of Magnus Lindberg.1 While the harmonic language in his earlier orchestral works, such

as Kraft (1983-85), was already very strictly defined and systematically used – often

based on computer-generated pitch materials – there was no focus, as yet, on the use of

harmony as an expressive tool. On the contrary, an important function of Lindberg's pre-

calculated lexicons of interrelated chords was to reduce the time spent on constructing

harmony, so as to focus on elements such as orchestration, form, rhythm, and even

theatrical gestures.2

This shift in creative attention has occurred together with a gradual transition

towards an increasingly consonant harmonic language, reaching its extreme in the

Clarinet Concerto (2002), with its pentatonic melodies and triadic harmonies. The

stylistic change between this and Lindberg's earlier works such as Kraft and Ur (1986) –

written in what the composer has termed his 'brutist-structuralist idiom' – is radical, to say

the least (Anderson 1992, p. 566). Cantigas, written in 1998-99, chronologically halfway

between the first spectral explorations of Kinetics and the unabashedly tonal Clarinet

Concerto, displays the varied influences behind Lindberg's harmonic language – most

1 Long, Stephen. "Magnus Lindberg's Recent Orchestral Music". Tempo, New Series, No. 208, 1999: p. 2.

Anderson, Julian. "The Spectral Sounds of Magnus Lindberg". The Musical Times, Vol. 133, No. 1797,

1992: p. 566. 2 Anderson, Julian. "The Spectral Sounds of Magnus Lindberg". The Musical Times, Vol. 133, No. 1797,

1992: pp. 565-6.

Warnaby, John. "The Music of Magnus Lindberg". Tempo, New Series, No. 181, 1992: p. 25.

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notably, the serial tradition and the French spectralists. Its harmonic vocabulary spans

from the sharply dissonant to the quasi-tonal.

Describing his compositional process, Lindberg often refers to the use of

interrelated and repeated harmonies, sometimes calling the use of such cycles his

'chaconne-technique.' While the term is derived from the Baroque-era compositional

form, no stylistic kinship to functional tonality is implied. The name Cantigas, however,

refers to an even earlier stylistic period, in the composer’s words,

… to the melodic artistry of the medieval troubado[u]r tradition, particularly that of the

Cantigas de Santa Maria … the interval of the perfect fifth, frequently heard in medieval

music, is used as a point of departure for much of the melodic and harmonic material and

is proliferated throughout the work …3

Cantigas spans twenty minutes, and while all of the music is derived from closely

interrelated harmonies, the piece is strikingly multifaceted, with a wide spectrum of

heterogeneous textures, colors, and sonorities. Despite the underlying harmonic unity, the

degree of dissonance or consonance varies dramatically. The tour de force of the piece

lies, therefore, in the seemingly endless forms into which the same basic material is

molded. This is also the subject of my paper: I will compare three sections of the

composition with very differing characters, and will attempt to inspect, on the one hand,

how they are harmonically related to each other, and on the other hand, what makes them

so starkly contrasting. The first passage I will look at is the opening, mm. 1-29; the

second at mm. 193-198; and finally, the dramatic climax at mm. 505-513.

3 Lindberg, Magnus. Cantigas. London: Boosey & Hawkes, 1999.

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2. Opening

The first minute sets the outlook of the entire work. It begins with static open-chord

sonorities, the initial tonal plan is very straightforward and simple, and the overall mood

is almost introspective. Even within the first thirty seconds, the music quickly ‘grows in

momentum and density,’ a process which, in the composer’s words, continues through

the whole work. 4

In addition to setting the overall character of the whole composition, the opening

music has other introductory qualities. The very first phrase (mm. 1-7) spells out the core

harmonies of the work, and also introduces the oboe, whose role in the piece is very

soloistic. As the oboe arpeggiates two trichords of superimposed fifths, the strings sustain

the pitches, resulting in a stack of thirds (see Example 1). A build-up of momentum and a

process of transformation has already begun: the latter arpeggiated trichord is an

inversion and a rhythmic diminution of the first.

Example 1. Harmonic reduction of the first phrase.

The following phrase (mm. 8-15) is a development of the first one: the same notes

are outlined by the solo oboe (now joined by the second oboe), and the same harmonies

are sustained, but new gestural elements are used to embellish the melodic line, dissonant

4 Lindberg, Magnus. Cantigas. London: Boosey & Hawkes, 1999.

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notes are added to the harmonies, and the orchestral pedal is enforced with clarinets and

flutes. Despite the shared structure of the two phrases, the latter is also slightly longer, as

the last sustained harmony has been stretched by one measure.

Paradoxically, the harmonic process that takes place in the second phrase can best

be described as an elevation in the level of dissonance, whose end goal is a chord that is

derived from the overtone series. This is only a seeming paradox, as will soon become

evident.

As shown in Example 2a, the same stacks of fifths that were used in the first

phrase are gradually built into the orchestral pedal, but an additional, dissonant B-F#

open chord is added after the Ab, while the bass line moves down to E. The chord in its

entirety can be seen at the end of Example 2a. Example 2b is the acoustic scale on Gb,

with the seventh and eleventh ‘out-of-tune partials’ (diatonically, the sharp fourth degree

and the flat seventh degree) represented by two chromatically adjacent pitches in the

proximity of the actual frequency. (The acoustic scale, which can be produced, for

example, with natural wind instruments such as the willow flute or fujara, is a melodic

manifestation of the first partials in the overtone series.) Example 2c demonstrates how

the pitches of the chord in question can be traced back to this scale.

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Example 2. Harmony in the second phrase and the acoustic scale

Here, the composer plays with the kinship between his fifth-based harmonies and

the overtone series. Stacks of fifths are, of course, directly related to the diatonic scale

and thus also to the harmonic series. But in addition to the interval matrix, the

consonance or dissonance of any harmony depends on its voicing; the pitches of a triad

form a dissonance when the chord is in second inversion. Similarly, while the pitch

classes here can be traced back to a spectral collection of notes, the octave placements

make the harmony extremely dissonant. The chromatically adjacent notes that represent

the seventh and eleventh partials add to the degree of dissonance. In this setting, the

spectral quality of the harmony in general, and the chromatic representations of the

aforementioned two partials in particular, might seem theoretical to say the least. Yet, it

is worth noting that spectral chords with similar chromatic approximations take center

stage towards the end of the piece, in a more obviously acoustic voicing (in other words,

as consonant sonorities). This way of representing the out-of-tune partials is also

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consistent with Lindberg’s musical language, which is based entirely on the equal-

tempered twelve-tone system. I will discuss this in more detail in connection with the

final climax (m. 505).

A sense of growing momentum throughout the second phrase is heightened by the

more animated rhythmic and melodic movement on the surface level, where some of the

key motives of the piece are introduced. These include the perfect fifth as a rapid,

fanfare-like gesture (Example 3a), and the repetition of a single note (Example 3b). At

first, these two motives are, in effect, one and the same. What in the score, at first glance,

looks like a pair of fanfare-motives on two instruments actually produces the repeated

attacks on single notes shown in Example 3c. These are doubled by the harp, with the

open chord written out in two different enharmonic forms; in addition to making the

motive easier to play on the instrument, this brings about a similar, subtle color change

between the fifths.

A development on these motives links this phrase to the following, where the

implicit perfect fifth gesture (as seen in Example 3c) is separated, as it were, into an

independent motivic entity.

Example 3. Motives

In addition to the hybrid forms of these two gestures in the third phrase, they are

also present in their original form. The repetitive motive is played by the strings (mm. 16-

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20), while the motive seen in Example 3a gradually expands into a melodic cell of three

superimposed fifths. This expanded motive is played in imitation between the horns,

emphasizing its fanfare-like character, and echoed in the clarinets. In the previous

phrases, the melodic lines have been sustained in the orchestral pedal, and as a result, the

fifths placed at a distance of a major third have resulted in stacks of thirds (with

additional, dissonant notes added in the second phrase). Here, however, the chord is

anticipated in the string pedal, and the horn imitation, followed by a similar duet on the

clarinets, ‘picks out’ the perfect fifths inherent in the harmony.

Both this harmony and the one that concludes the first phrase are symmetrical,

composed of consecutive interval classes 4 and 3 (major thirds and minor thirds). The

latter expands on the first one, adding notes below it, as shown in Example 4.

Example 4. Stacks of thirds

Unlike the previous two phrases, the third phrase does not end here, but lunges

into a rapid-paced development. There is a clear reference to the classical Satz-form here,

with two almost identical statements, followed by a third, more long-winded and

developmental conclusion based on the original statements. This contributes to the

overall structural clarity and straightforwardness of the opening. Unlike in a strict

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Beethovenian Satz-form, however, the development already begins in the second phrase,

and in place of a conclusive cadence, there is a transition to a new section.

Dissonant notes are added to this stack of thirds, quite like at the end of the

second phrase, but this time through a more expansive process where the pitch-class set is

used both as a scale and as a harmony. Runs in the oboes and strings in measure 24 end

on a chord whose pitches are all members of the preceding scale (m. 25), though not all

the notes are used. Not only is the process of adding more notes to the core harmony

directly related to the conclusion of the second phrase, so is the pitch-class set itself

(comparison in Example 5). Only the D in measure 25 is a ‘new’ pitch class. A

particularly conspicuous element in this chord is the two-line A (coupled with its lower

tritone Eb) as its highest note, which is held from the end of the second phrase, creating a

connection on a structural voice leading level.

Example 5. Related sets in the second and third phrases

The runs are executed in parallel motion from a D-G perfect fourth up to the

structural Eb-A tritone, with only the soloistic first oboe playing the upper line, and the

second oboe playing the line from D to Eb together with the strings. In addition to the

verbatim doubling of the second oboe in sixteenth-note triplets by the first violins, the

rest of the strings have three different augmentations of the same line – the second violins

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play the scale run in straight sixteenth notes, the violas in eighth notes that speed up to

eighth-note triplets, and the cellos in dotted eighth notes. The newly introduced pitch

class D, and a seeming D diminished triad on top of it, are held as a pedal underneath the

runs. Thus, not only are the notes of the harmony all derived from the scale, but these

three notes are already anticipated in the preceding measures, further diminishing the

sense of harmonic movement.

This is followed by a similar process (mm. 26-29); the same scale, this time

played by the clarinets in parallel thirds with the strings doubling the lower line, leads to

a held harmony in measure 27. Unlike the soloistic first oboe, the upper clarinet line is

doubled by the first violins, and this time both lines are coupled with slower-paced

augmentations. This chord is related to the previous one, with one pitch class

chromatically altered, just like that harmony was, in turn, related to the preceding one at

the end of the second phrase. This time the chromatic change that occurs is in the

structural upper line, with the Eb-A tritone ‘resolving,’ as it were, to an Eb-Ab perfect

fourth. Voice leading on a larger scale is depicted in Example 6.

Example 6. Structural voice leading in the first section

This final sonority is held for the remainder of the section, up to the tempo change

in measure 30, embellished with motivic figurations. The transition to the following

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section happens via a smooth tempo modulation, where the sixteenth note triplets in the

new tempo (168 eighth notes per minute) equal the dotted thirty-second notes in the

conclusion of the first section.5

3. Measures 193 to 198

The section with the most stark contrast to the bright open chord sonorities of the

beginning, as well as to the triadic harmonies of the final climax, begins in measure 193.

Although the shift in tempo that leads to this section has already been reached in measure

189, there is a very clear formal conclusion at measure 192; a tutti chord ends with a rest

and is then followed by music that is strikingly different from the previous materials,

both in terms of its orchestration and its harmonic outlook.

On a larger scale, measure 193 begins a phase which can be described as

transitional in character; it sounds as if the music is constantly on its way somewhere,

continuing all the way to measure 233. Measures 193-233 are composed of short cycles,

each of them beginning in a low register, then gradually climbing upwards while the

tempo increases, and finally ending with an interruption, only to begin the same climbing

motion again. A large-scale tempo shift takes place by a process of “two steps forward,

one step back": the passage in mm. 193-198 begins at 63 quarter notes to a minute, and

accelerates to 94 beats, only to drop back to 63; mm. 199-202 accelerates to 72 beats per

minute, which this time begins the following section; mm. 203-207 accelerates to 94

beats per minute, and drops to another new and increased tempo, 84 beats per minute. In

5 The modulations are not immediately apparent in the score, as the composer has chosen only to mark the

new tempo, rather than to indicate the corresponding note values between the two tempi.

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measure 216, the last accelerando reaches the fastest tempo in the section, which also

seems like the goal of all of the preceding shifts. Instead of an interruption, a longer,

developmental section follows, ending the transitional process at the downbeat of

measure 233, where yet another tempo modulation takes place.

The first phrase of this section (mm. 193-198) is related to the beginning of the

piece, despite their very differing characters. The atmosphere of the latter section is

murky and dark; low bassoons and the bass clarinet, together with the low strings, take

center stage. The 3/4 meter that dominates the section gives it the feel of a macabre and

ever-quickening dance, perhaps ironically referencing The Hall of the Mountain King by

Edvard Grieg, another Nordic composer. While the overall sonority of the section is

harsh, the core harmonies are not considerably more dissonant than those already used

throughout the piece. Rather, the effect is achieved through the use of dissonant passing

harmonies and, of course, by means of orchestration.

As the phrase begins, it seems that the first beat of each 3/4 measure contains a

dissonant harmony which then ‘resolves,’ as it were, to a more stable sonority that is

sustained for the second and third beats of the measure. These last two beats are further

accentuated by the low percussion instruments. The sustained harmonies are embellished

with the motive that was introduced in the first section (the ‘hybrid’ motive of Example

3c). A reduction of the harmonic progression between mm. 193-196 is depicted in

Example 7.

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Example 7. Mm. 193-196

The melodic motive introduced in measure 193 (in the double bassoon and the

contrabasses) outlines the tritone E-Bb, which then shifts at the second beat to a Bb-F

perfect fifth. This can be seen as small-scale intervallic diminution, where one of the

arpeggiated fifths from the opening of the piece has been reduced to a diminished fifth.

However, much more emphasis is placed on the last two beats of the measure – the dyad

here is amplified with the addition of two bassoons, the bass clarinet, and the low

percussion. Thus, the first beat can be perceived as a passing harmony, whose

contribution to the overall murky sonority is more important than its role in the

underlying harmonic structure.

The following measure has a similar construction; the same melodic motive,

consisting of a whole step, a minor third, and a half step, outlines a tritone before moving

on to a perfect fifth. This time the motive and its retrograde are superimposed, further

emphasizing the underlying tritone. The relationship between this C#-G diminished fifth

and the C#-G# perfect fifth resembles a traditional resolution – also in terms of medieval

counterpoint, to which the composer refers to in his preface – much more than the tritone

and perfect fifth in the previous measure, and makes the first beat sound even more like a

passing sonority.

Although the harmonic progression of the section at hand unfolds much faster

than that of the beginning, these same two dyads are found in the opening phrase of

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Cantigas; the first four measures outlined a Bb-F open chord, with one more

superimposed fifth on top of the F, which was followed by a C#-G# open chord (spelled

Db-Ab) and its upper fifth. As in the opening, the minor third relationship between these

chords results in an implicit stack of thirds (or interval classes 3-4-3-4).

Quite like the opening, measure 104 is followed by a repetition and development

of the same harmonies, though this time transposed, and the progression becoming even

further condensed in time. Measure 195 begins like the previous two 3/4 bars, with a

passing chord introduced in the first measure, followed by a perfect fifth. The rhythms

are becoming faster; instead of the previously used sixteenth notes, this measure begins

with a sixteenth note quintuplet. As there are now five notes during the first beat, the

initial melodic motive is also expanded and compacted. All the same interval classes are

used in the melody (minor and major seconds, minor third), but it now spans a minor

sixth (A-F#). As in the previous measure, the ascending line is coupled with its inversion.

Within this minor sixth motive, there is an implicit C-F# tritone, which resolves – in the

same way as the preceding C#-G tritone – to a C open chord (as shown in Example 7).

Instead of continuing in the same pace, the measure is stretched by a quarter note, which

already introduces the open chord a minor third above, after adding another fifth (the D

on top of the G), creating an explicit, rather than implicit stack of thirds (3-4-3-4).

Measure 196 roughly corresponds to mm. 8-15 of the opening, where a higher

level of dissonance was achieved by adding another perfect fifth (B-F#) a half step below

the upper voice of the structural open chord (F-C). In m. 196, followed by the expanded

melodic motive introduced in the previous measure, a dissonant combination of two

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perfect fifths (G-D and Db-Ab) is reached. The sextuplets introduced here are carried

through to the end of the phrase, further condensing the rhythm.

In measure 197, the highest level of dissonance is reached, while the underlying

harmonic structure is still derived from the stacks of fifths. Even though each beat in this

measure has a chromatic cluster, these clusters and the sextuplet figurations are merely

embellishing the arpeggiation (by the trumpets) of a Bb-F-C stack of fifths – the initial

harmony of the entire piece, which was also implicitly present in the first measure of this

phrase. The line ends on G in measure 198, adding one more fifth to the arpeggio. The

concluding harmony is essentially a G major triad, coupled with an Ab-Eb perfect fifth in

the high register. This harmony is arpeggiated in the solo of the D-trumpet, with the

dissonant Ab-Eb being present on the weak beats. These two pitch classes make the final

connection to the opening of the piece, where they served an important function in the

large-scale voice leading structure (as shown at the end of Example 6).

4. The final climax

Like the opening, the triumphant, climactic section between mm. 505-513 is very

consonant. But while the consonance in the first bars of Cantigas does not revolve around

any tonal center or centers, and is aurally more akin to the archaic sounds of medieval

music, the ending has a more triadic and tonal quality. In place of the stacks of

superimposed fifths of the beginning, the final climax is essentially composed of a

progression of three massively orchestrated triads, embellished with a Lydian scale, in an

almost John Williamsian spirit. Though these harmonies turn out to be, upon closer

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examination, derived from the overtone series, their spectral quality seems to merely

contribute a kind of orchestrational edge to this basically tonal passage.

At the beginning of the section, a new tempo has been reached through a gradual

shift rather than a modulation. The bass line begins on Db, a note which in the first

phrase of the first section was also an important bass note (see Example 1). Due to the

triadic quality of the harmony here, Db sounds more obviously like a tonal center, unlike

in the opening. Crotales take center stage with their ostinato, which repeats the scale

degrees 5, 4, 2, and 1 on top of Db, along the Lydian mode. The woodwinds have faster

ostinati, based on different combinations of fifths and fourths picked out from the scale –

ostensibly arpeggiating different sus4-chords. A process that binds the following simple

progression of three triads is a shift towards a more spectral sonority. This happens

through a gradual addition of notes from outside the Lydian scale, finally resulting in an

acoustic scale whose fourth and seventh scale degrees (representing the eleventh and

seventh partials, respectively) consist of two chromatically adjacent notes. This scale was

introduced in the second phrase of the first section (as illustrated in Example 2), though

in an intentionally dissonant setting, which is in stark contrast to this section.

The string and brass pedal emphasizes the Db major chord, while the sixth scale

degree is also present, even if not as strongly orchestrated. The sharp fourth degree – a

conspicuous sonority within both the Lydian and the acoustic scales – is, together with

the second degree, very audible in the crotale ostinato. Lastly, the seventh degree (C) is

present in the woodwind ostinati, along with the other notes of the Lydian scale.

After the harmonic and melodic material has been established in the first measure,

the first shift towards a more spectral sonority happens in measure 506. While the oboes

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do not have a soloistic role in this section, the central role they have had throughout the

composition emphasizes the significance of their entrance here, as they introduce the first

chromatic pitch, F#. The addition of this pitch class builds another ostensible sus4-chord

(C#-F#-G#) into the underlying pitch-class set, which is arpeggiated in the ostinato taken

up by the oboes. More importantly, we now have both the sharp and natural fourth

degrees from the tonic note, constituting the aforementioned chromatic approximation of

the eleventh partial.

The second of the three chords is an A major triad. It is orchestrated similarly to

the preceding Db major, but the crotale line is merely transposed down by a half step. As

a result, it now repeats the scale degrees 1, 7, 5, and 4, the last one being, as a result of

this transposition, the perfect fourth. Both the major scale and the Lydian scale are

present on top of this chord right away, maintaining the acoustic quality reached in the

previous measure. The crotales are then joined by the oboes, whose ostinato lines also

contain the perfect fourth, as they did on top of the Db major chord.

The A major chord is followed by a C major in measure 511. The interval of

modulation between all these chords is a third (first a major third, then a minor third).

This same interval was used to shift the stacks of fifths in the opening of the piece, as

well as in the section between mm. 193-198, where the results were symmetrical stacks

of thirds. (A transposition by either a major third or a minor third of a stack of fifths will

result in the same symmetrical harmony, with consecutive interval classes 4 and 3.)

Though the transposed harmonies in this section do not overlap, and though the fifths are

only implicitly within the ostinati but not arranged in symmetrical stacks, the

transpositional relationship is still fresh in the listener’s ear.

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As the C major triad is introduced, the crotale line shifts down by a major third

and falls, as a result, back to the degrees 5, 4, 2, and 1 of the Lydian scale. As one would

expect, the oboes add the F natural, after which the final shift towards the acoustic scale

happens: Simultaneously with the entrance of the oboes (m. 512), the second horn

descends from C to Bb, adding the last note of the chromatically approximated acoustic

scale.

Thus, after molding the same harmonic materials into seemingly infinite forms,

the piece has arrived at the polar opposite state from the opening. This same set class was

introduced only a few seconds into the piece as the peak of dissonance, and right before

the composition dies down, it is shown in a completely new light, as the triumphant

consonance of the dramatic climax.

The climax is followed by a brief coda, where the music breaks free from the

preceding chains of consonant sonorities, and gradually dies away. Static cluster on the

wind instruments, composed of dissonant fragments of fifth-related harmonies, float on a

slowly transforming string pedal. Underneath, the strings gradually find their way to their

final sonority – an open chord, the defining interval of the entire work.