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CNS_V_omslag.indd 1CNS_V_omslag.indd 1 10/07/12 15.4810/07/12 15.48

258

1 Robert Simpson, Carl Nielsen: Symphonist, 2nd edn, New York 1979. Later studies

addressing similar topics include: Graham George, Tonality and Musical Structure,

London 1970; Sarah J. Reid, Tonality’s Changing Role: A Survey of Non-Concentric In-

strumental Works of the Nineteenth Century, PhD diss., University of Texas at Austin,

1980; Tyler G. White, ‘The Music’s Proper Domain’: Form, Motive and Tonality in Carl

Nielsen’s Symphony No. 4, Op. 29 (The Inextinguishable), PhD diss., Cornell University,

1991; Harold Krebs, ‘Tonal structure in Nielsen’s Symphonies: Some Addenda

to Simpson’s Analyses’, in Mina Miller (ed), The Nielsen Companion, Portland

1995, 208-249; David Fanning, Nielsen: Symphony No. 5,Cambridge 1997; Thomas

A. Pankhurst, Desiring Closure, Yearning for Freedom: A Semiotic Study of Tonality in

Three Symphonies by Carl Nielsen, PhD diss., University of Manchester, 2004.

2 Among others, see Mark DeVoto, ‘Non-classical Diatonicism and Polyfocal

Tonality: The Case of Nielsen’s Fifth Symphony, First Movement’, in Miller,

op. cit., 257-288; Michael Fjeldsøe, ‘Organicism and Construction in Nielsen’s

Symphony No. 5’, in Carl Nielsen Studies 1 (2003), 18-26; Richard S. Parks, ‘Pitch

Structure in Carl Nielsen’s Wind Quintet’, in Miller, op. cit., 541-596.

3 David Fanning, ‘Carl Nielsen §9 Orchestral music’, in Grove Music Online. Oxford

Music Online, http://www.oxfordmusiconline.com (accessed February 20, 2012).

F L A T W A R D S B O U N D : D E F I N I N G H A R M O N I C F L A V O U R I N L A T E N I E L S E N

By Robert Rival

Robert Simpson’s Carl Nielsen: Symphonist, fi rst published in 1952, spawned a consider-

able number of studies that focused on large-scale tonal design in Nielsen’s music, es-

pecially in the symphonies, tracking the progression of key areas across large spans of

time.1 With this foundation in place attention has more recently turned to moment-

to-moment qualities in Nielsen’s harmony. The proliferation of methods deployed in

these studies is impressive, symptomatic, no doubt, of the challenges posed by the

subtlety of music that defi es analysis even when aurally making intuitive sense.2 Dav-

id Fanning, after summing up the various approaches to large-scale tonal structure

that have been applied to Nielsen’s work, seems to have anticipated this trend:

Just as important, though hardly acknowledged in musicological studies, is

the interpenetration of modal and tonal elements, which accounts for much

of the characteristic fl avour of Nielsen’s harmony and which reaches a peak of

subtlety in the Fifth Symphony. 3

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259

Flatwards Bound: Defi ning Harmonic Flavour in Late Nielsen

My goal here is to try to defi ne this ‘characteristic fl avour’ by identifying at least some

of its ingredients. As the title of this paper reveals, I conclude that Nielsen has a ten-

dency to modulate fl atwards at the local level; along the way I identify and discuss the

variety of ways and contexts in which these modulations unfold. My analytical angle

is informed by the theoretical work of Dmitri Tymoczko, whose rigorous and sophis-

ticated, yet fl exible, approach sheds light on a wide range of music, from Debussy,

Shostakovich and Stravinsky, to minimalism, pop and jazz.4 Tymoczko views ex-

tended tonality as just that, an extension of functional harmony and late nineteenth-

century chromaticism, a stance appropriate for the study of Nielsen in view of the

origins of his style. Using Tymoczko’s scalar approach as my starting point, I exam-

ine the interaction of chords, scales and voice leading in passages taken principally

from the Fourth and Fifth Symphonies and from the Clarinet Concerto. I identify not

only which scales seem to be operative at any given moment (sometimes more than

one) but how Nielsen moves from one to the next via effi cient chordal or scalar voice

leading, and how these scales relate to one another in tonal space – what Tymoczko

means by ‘geometry’. I shall elaborate upon Tymoczko’s approach, as required, in the

course of my ensuing analytical remarks.

I. Modulation to a Remote Key

The second movement of Nielsen’s Fourth Symphony, The Inextinguishable, opens with

a charming tune for woodwinds accompanied by chords easily analyzable using func-

tional harmonic analysis. The music unfolds with such grace, with such fl uidity, that

hearing the theme’s third statement in D major (b. 451) – the key furthest removed

from G major – catches one by surprise and provides an example of a deftly-executed

modulation to a remote key over a short time span (see Ex. 1). As we shall see, Nielsen

extends this modulatory impulse to non-functional chord progressions as well – and

even to collections.

4 Dmitri Tymoczko, A Geometry of Music: Harmony and Counterpoint in the Extend-

ed Common Practice, New York 2011.

&?

#

#43

4342

42

432 œ œ œ œb œ œ œ œ œ œb œœ œ œœ .

cls.

bns.

G:

b b

V7

œ œ œn œ œb œ œ œb œ œ œ œœ œ œn..

bœ œb œ œ œ# œ œ œ œ œœb Jœ ‰ Œœ jœ ‰ Œœ Jœ ‰ Œ

Ex. 1. Fourth Symphony, second movement, bb. 432-455


260

Robert Rival

Ex. 1 continued

&&?

###

42

42

42

446 œœbb ..œœ œœ œœ œœ œœ œœjœ ‰ jœ n

Jœ ‰ Jœ nœœb . œœ. œœ. œœ> œœn œœ. Œ

cl.

I V

Jœœbb œn œ œb œb œnœ œb Œ Œœ œ

cl.

I

bœb œb œn œb œb œbfl.

bœb œb œ œb œ œb

bœb œn œb œb œb œb

FIG. 1A (continued)

&&

##

42

4243

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435 œ. œ. jœ œœ. œ. Jœ œœ. œ. œœ. œ. Jœ œ

jœ

fls.

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œ œ. jœ œ œ œ œœ œ. Jœ .œ œ

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ii vi6 (viiø4) V3

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DC

nn œœbb

œœn œœ# œœ œœ œœ œœ œœ œœ œœbn œœ# œœ œœœ œ œ œ œ œ œ œ œ œ œ œ

œ jœ ‰ Œ

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###

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(iii7)

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bns.

I VPAC


261


modal mixture, no modulation (bb. 424-34) modulation (bb. 435-45) modulation (bb. 445-51)

CG

D

A

E

BF

D

A

E

B

F

In the theme’s fi rst statement (bb. 424-434, the last few bars of which are

shown), Nielsen fl attens , and ({B, E, F}{B, E, F}), turning the operative scale

from G major to G natural minor. This is modal mixture – the borrowing of pitches

from the parallel minor – pure and simple.

The theme’s second statement (b. 435) cancels these alterations, returning to G

major, as if nothing happened.5 In retrospect, then, we are likely to hear the alterations

in the theme’s fi rst presentation as local colour and having no modulatory signifi cance.

Five bars into the restatement (b. 439), however, Nielsen sends the theme into another

melodic direction – and, as it turns out, one with a harmonic twist. The deceptive ca-

dence at b. 441 abruptly reintroduces and ; follows in the next bar. This time the

lowered pitches initiate a process that dislodges the tonic. Another deceptive cadence,

now in F, follows (b. 442). The harmonies then drift between Dm7 and Cm7 chords, with

particular emphasis on the latter, which ultimately reveals itself as the supertonic in

the new key of B. The stop at B is brief: in bb. 447-448 the clarinet introduces A and

G. The fl ute adds a D (b. 449), completing the transformation of the operative scale to

D major.6 Fig. 1 summarizes the three-stage fl atwards drift on a pitch clock:

Fig. 1. Fourth Symphony, second movement, bb. 432-455

Nielsen uses a similar procedure in the fi nale of the Third Symphony, Espansiva,

whose robust opening theme, fi rmly rooted in D major (D mixolydian, to be precise,

in view of the C (b. 10))7 briefl y drifts fl atwards in its third phrase (bb. 17-20), the al-

tered scale degrees evaporating in the subsequent reprise of the opening phrase (see

Ex. 2). But the fl atwards pull exerts itself again, and more forcefully: the introduction

of a new theme at b. 62 (not shown) is in B minor.

5 The leading tone is restored one bar earlier (b. 434).

6 An F and C are thrown in for good measure, thereby fl attening all seven

diatonic pitches, though these last two function as mere chromatic tones.

7 The fl attened seventh is so common in Nielsen that Fanning has dubbed it

the ‘Nielsenesque mixolydian seventh’. See Fanning, op. cit., 1997, 70.


262

Robert Rival

& # # C œ>vns.

. œ œ œ œ œ œ œ œ œ œ œ œ œ jœ œ> jœ ‰ jœ œ> jœ ‰ jœ œ> jœ ‰ jœ œ> jœ ‰& # #7

jœ œ> œ> œ> œ> œ> . œ> . œ œ œ œ œnb œ œ œ œ œ œ œ œ œ œ. œ> œ> . œ

& # #15 œ œ. œ> œ> . œ> œn œ œb œ>b bœn œb œn œb >bb b

œn œn œ œbn

œn œ œb œ> . œn œ œ œ œ& # #23 œ œ œ œ œ œ œ œ jœ œ> jœ ‰ jœ œ> jœ ‰ jœ œ> jœ ‰ jœ œ> jœ ‰ jœ œ> œ> œ> œ> œ> œ Œ

Ex. 2. Third Symphony, fourth movement, bb. 1-28

Like the passage from the Fourth Symphony (Ex. 1), modal mixture has a dual func-

tion: to provide local colour while foreshadowing an imminent fl atwards modulation.

II. Non-Functional Modulation

These passages from the Third and Fourth Symphonies, while unremarkable in them-

selves, provide useful reference points to which may be compared more unconven-

tional modulatory techniques. Consider the lovely Adagio passage at b. 533ff from

the Clarinet Concerto (see Ex. 3).

Ex. 3. Clarinet Concerto, bb. 533-542

&

&

?

43

43

43

533 œœ œœ## œœ œœ œœ## œœ œœ

œ œ# œn -

œ œ# œ#œ# - œ- œ# -

Adagio33

vn.1

va.

vn.2

vc.

db.

g#o c# G#7

T S T

B dia

x

œœ œœ## œœ œœ œœ# œœ œœ##

œ œ# œ-.#œ œ# - œn -œn - œ# - œn -g#ø7 C# C

‹S

x

œœ œœ œœ## œœnn œœ# œ œ# œ œ

œ- œ# œ œ œœ- œ œ œ œb (D

‹) (e)

T S

D dia

x x

Œœœ œœ œœ œœ œœ œœœ œ œ œœ œ

.œ œ .œ œ .œ œb.œ œ .œ œ .œ# œn

cl. solo

CM7 a7 D bo7

G diax .œ jœ œ œ# œ œœœ œœ œœ œœ œœ-

jœ ‰ ‰ jœ œ

.œ œn .œ œ œ-

.œ œ .œ œ œ-e G7CM7 a11

T S

œ œ œ œ œb œ œ œ œb œ œ œbœ- œ-œb œ

œ- œb - œb -.œ œ# œ œb œn

œ- œ œn œb.œ œ# œ- œn œbva.

vn.2

vn.1

e g Db bbm7

Bb dia Ab dia

&

&

?

c

c

c

539 œb œb œ œ œ œ œ.b

.b .bjœœbb ‰ œœbb > œœbb œœ

cl. solo

eb eb(7)

Db diax

œ# œ# œ œ œ# œ œ## œn

œ# ## œ#œœ œœnn œœ## œœ

d#7 g#11 g#(bb=a#)

T S

F# diax œ œ# œ# œ œ œ œ# œ œ œ œ# œJœ ‰ Œ Œ

jœ ‰ Œ ŒJœ# ‰ Œ Œœœ œœ##

d#o F# ped.

E dia

œ# œ œ# œ# œ œ œ# œ œ# œ# œ œ œ# œ# œ

jœœ ‰ Œ

B dia E dia


263


Though the harmonies consist of triads and seventh chords, the music’s chromatic

nature resists functional harmonic analysis. Resembling free-fl owing Renaissance po-

lyphony, extended by nineteenth-century sonorities, the music seems to follow Max

Reger’s dictum that ‘any chord can follow another chord’.8

Ex. 4 shows that despite intense chromaticism – in just seven bars ten chro-

matic roots occur (all but F and F) – the chordal voice leading is remarkably effi cient:

each voice, if not stationary, only moves by small distances (usually a semitone or

whole-tone).

Ex. 4. Clarinet Concerto, voice leading, bb. 533-542

Although the melody’s falling-third incipit (marked x in Ex. 3), reinforced by plagal

relationships, serves as a rough guide to the changing key areas – G minor, B minor,

G major, E minor, E minor and so on – it seems more productive to describe the

gradual and clearly perceptual fl atwards shift as a modulation among collections.9 In

other words, in the absence of functional harmonic reference points or other means

of establishing centricity, we ought to pay more attention to macroharmony, i.e. to the

pitches emphasized in articulated slices of music.

The chords in the fi rst two bars (bb. 533-534) lean towards the B diatonic

collection (its G mode to be specifi c).10 I say ‘lean’ because D/D (and C/C) is what

Tymoczko calls a ‘mobile pitch.11 In this way, b. 535 leans towards D diatonic

8 Max Reger, cited in Daniel Harrison, Harmonic Function in Chromatic Music,

Chicago 1994, 1.

9 Tymoczko calls music that is readily analyzed this way ‘scale-fi rst’ to distin-

guish it from the other type, ‘chord-fi rst’, in which the vertical element is

primary. See Tymoczko op. cit., 307ff. In both types of music the principles of

effi cient voice leading apply. We can productively speak of voice leading be-

tween collections, a generalization of the process of modulation in common-

practice tonality (e.g. modulating from C to G involves FF).

10 Throughout this paper, following Tymoczko’s practice, a collection labeled

‘diatonic’ does not usually imply a tonal centre. As far as the notes go, C

diatonic is identical to G mixolydian, D diatonic identical to E dorian, and

so on. To put it another way, the collection C diatonic can be described as D

dorian, E phrygian etc. C diatonic thus refers to a non-hierarchical collection

of notes; the tonal centre may not be C.

11 Tymoczko, op. cit., 172ff.

&533 œœœ# œœœ# œœœœ### 534 œœœœnn œœœ## œœœnn 535

# œœœ œœœ536œœœœ œœœœ œœœ# œœœœbn

537œœœ œœœœ œœœœ œœœœ&538 œœœ œœœb œœœbb œœœœ

539

bb540

œœœœ#### œœœœ# œœœ541

œœœn#542


264

Robert Rival

(B minor). Bar 536 moves to G diatonic, fi rst centred on G, then on E. In b. 538, the

journey fl atwards continues with the introduction of B on the second beat, and D

and A, on the third. The downbeat of b. 539 is an E minor chord, whose E and G

complete the emerging D diatonic collection. Fig. 2 summarizes the fl atwards trajec-

tory of the macroharmony.

Fig. 2. Clarinet Concerto, bb. 533-542

Within seven bars (bb. 533-539) Nielsen comes two notches shy of completing a full cir-

cle. In the very next bar (b. 540) he inches closer: with B reinterpreted enharmonically

as A we fi nd ourselves in the world of F diatonic (D minor). Bar 541 closes the loop,

bypassing B diatonic and settling in E diatonic (with a brief allusion to B diatonic).12

One of the compositional challenges of hyperchromatic music based on ter-

tian chords is negotiating harmonic tension and relaxation in a kaleidoscopic sound

world. In this passage Nielsen offers a solution to this problem: the gradual fl attening

of the macroharmony lends the music a sense of direction.

A similar passage occurs earlier in the concerto at b. 296ff (see Ex. 5).


12 Using Fanning’s terminology, the fi nal oscillation between B diatonic and E

diatonic could be described as an ‘arc’ on the pitch clock. See Fanning, op.

cit., 1997, 48ff.

CG

D

A

E

BF

D

A

E

B

F

533

535

536

538

538

539540

541542

542

&&

43

43

296 Œ .œ Jœ

Œ Œ œœb

F dia

cl. solo

vns.

œ œ œ œb œ œ..œœ jœœb œœ

œb œ œ œ œ

œ .œ jœbœ œb œbAb dia

Bb dia

œ œb b.œ jœb œ œb.

Ab dia

jœ œn Jœ# œ œn œ# œn

œœb œœn# œœ##

B dia

œ# œ# œ œ œ œ œ œn œ# œ œ œ# œ œ œn

œœ #G dia

&&

302 œ œ œ œ œn œ œ œ œ œ

..œœ# œœ œœ ..œœn œœ ..œœ œœ

G dia œ œ œ œ œ œ œ œ œ

œœ œœ# œœ œœjœœ ‰ Œ

œ œb œ œn œ œ œ œ œ œn œ.Œ Œ ‰ . Rœœœ##

F dia Ddia

+va.

Œ ‰ . Rœ...œœœ# œœœ œœœn . œœœ œœœnb .

G Fdia dia


265


While the later passage (see Ex. 3) begins in four voices and blossoms to six, this one

unfolds in just three. The harmonies, again, can for the most part be understood

as non-functional progressions of simple triads (e.g. in bb. 297-299: a, E, F, c, D,

A). And again, real harmonic motion occurs at the level of collection, completing

a full circle, in the fl atwards direction, from and to F diatonic. On two occasions,

one or more voices contradicts the governing macroharmony, anticipating the one

that follows: 1) the violins shift to A diatonic (b. 298), ahead of the clarinet (b. 299);

and, 2) the clarinet hints at G diatonic in the middle of its rapid descent (b. 301), a

bar before that new collection is established. Finally, harmonic change at the lev-

el of macroharmony, as measured on a pitch clock, ‘accelerates’ over the course

of this passage due to the increasingly large diatonic skips (see Fig. 3). F to B (b.

297) represents one notch on the pitch clock; B to A (bb. 298-299), two; A to B (b.

300), three; B to G (b. 301), four; and, G to F (bb. 303-304), a slight ‘ritardando’, two

notches. The rapid, fl atwards shift from D to G to F (b. 305) echoes the preceding

fl attening process.

Fig. 3. Clarinet Concerto, bb. 296-305

The opening of the Adagio in the Fifth Symphony’s fi rst movement (see Ex. 6) com-

bines the modulatory approaches observed in the preceding examples: a tonal melo-

dy coloured by modal mixture that anticipates a later modulation (see Ex. 1 and Ex. 2);

and, non-functional collection modulation (see Ex. 3 and Ex. 5).

The fi rst four bars unfold in pure G major over a tonic pedal (bb. 268-271). In

b. 272, however, Nielsen introduces prominently into the melody. Modal mixture

continues with the lowering of other scale degrees: and (b. 275), and (b. 277).

While not all of the lowered scales degrees stick, the tendency is clear, culminating

in the fl attening of all diatonic scale degrees, with the exception of (bb. 281-282),

and coinciding with the end of the fi rst long phrase. In the ensuing bar and a half,

most of the fl attened pitches are raised; the second statement of the theme returns

in pure G major (b. 284).

CG

D

A

E

BF

D

A

E

B

F

+2

+1

+3

+4+2

C


266

Robert Rival

The theme’s reprise, now more polyphonic and lusciously scored, repeats

the same process: nearly four bars of unadorned G major before , once again, is

introduced. This time, however, the fl attening of additional scale degrees leads to a

modulation. The fl attening occurs rapidly along the circle of fi fths: over the course

of just two bars (bb. 293-294), all diatonic pitches are fl attened ( doubly so) with the

exception of G, whose function as tonic becomes that of leading tone in the new key

of A minor (confi rmed by the dominant-tonic relationship in bb. 295-296). The music

Ex. 6. Fifth Symphony, fi rst movement, bb. 268-300

B?

43

43

268 œ œœ œ œœ œ œ œ.

Adagio

db.

va.bn.

va.hn.

vc.bn.hn.

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œ œ# .œ jœœœ œ œ.

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.œb jœ œ œœ œ œ# œœ œ œ œ.

bœ œœ œb œ

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bb nœb >

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bn

B

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278 œ> œ> œ>œ ‰ Jœb<

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jœ œ> œ> jœ>œ> Rœ Jœb

<œ œ

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‰ œ

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b b b

all scale degrees flattened except

.œ œb œ œnœb œb .œ Jœbœœbb œœbb œœ Œœb œb œ Œ

nœ œ .œ jœnb œ œ &

‰ jœb . œ œn œ œ#‰ Jœb . œ œn œ œ#

nn n

œ- œ-œœ œ œ..

vn.2

G restored

&

&

?

285 œœœ- œœœ

-

œ œ# .œ Jœ

œ œ œ..

fl.

ob.

va.

œœœœœœ##

# ...œœœ J

œœœŒ Œ œœ- œ-œ œ œ œ..

vn.1

...œ œ# - œ- œ- œ-œ œ# œ œ

œ œ œ..

œœœœœœ

œœœœœœbb

b

.œ jœ œœ œ œ

.

..

bœœœnn

n œœœœ œ# - œ- œ œœ œ œ œ œ œœ œ œ..

va.

n..œœ

jœœ œ.œ Jœ œ

œ œ- œ- œ œœ œ œ œ œn œœ œ œ

..

fl.ob.b

œ œ# œ œ œœjœ

œ- œ-œ Œ Œœ œ# œ œ jœ ‰œœ Œ Œ

nœ œ Œœ œ- œ- œœ œ .œ# jœœ- œ-Œ Œ œ-

Gdia

&

&?

293 Œ Œ œœ œ œœ- œb -

œ œ œ œ

n œ

b b

C Fdia dia

b œb œb œb - œb -

œ œb œbœb

ab: ivI6

b

Bb Ebdia dia

Abdia

œ œb œb œb œ œbœ œ œ œ œ œœb œ œb œb œ œœ œb œb

.b&

V7

œb bœœb œb œ œb.œ Jœb œb œb

.bi

Ab hm

. Œœb - œb -

œb œ# œ œ

œb œb œb

œb œb œœb œb œœb œ œb œb œ œbœb œb œ

b œbV7

B:

.œ œn œn œ# œ# œ œ# œ#-

œ#-jœn œn jœ# œ# œ-.œ œn œn œ œ# œ

-œ#-

.œn œ# œ œiiøb6 Vb35

.# œ- œ# - œ# - œ# œ

.# œ# œ# - œ- œ# œ#.#

.œ> œ# ># >I

IAC

B dia

hns.

Ex. 6 [***REVISED***]


267


coasts in A harmonic minor (bb. 295-298) before abruptly sinking further fl atwards

with an authentic cadence in B major. Taking the long view, the passage shifts sharp-

wards, from G major (b. 268) to B major (b. 300). But Nielsen chooses the scenic route

by approaching B from the fl atside.

III. Modal Interchange & Polymodality

In the previous examples I have examined voice leading and modulation in textures

that privilege chords, whether through the fl attening of pitches that result in modu-

lation to other keys or by a gradual lowering of scale degrees that move the macro-

harmony fl atwards around the circle of fi fths. I now turn to the more linear-driven,

fugato opening of the Clarinet Concerto.13 The cellos and basses introduce an eight-

bar subject in F major, answered by the fi rst bassoon and violas in the dominant. At b.

17 the clarinet enters with the subject back in F (see Ex. 7).


Although the subject begins unambiguously in F, soon scale degrees , and are

fl attened, darkening the underlying scale to F locrian (bb. 3-4). The immediate resto-

13 For a very different analysis of this passage, see David Grimley, ‘Analytical

and Aesthetic Issues in Carl Nielsen’s Concerto for Clarinet and Orchestra’,

in Carl Nielsen Studies 1 (2003), 29-31.

? 42 œ œ. œ-Allegretto un poco

vc.db.

œb œ. œ-F maj

œ œ. œ. œ. œb .b œb œb . œ-F loc

b b œ œn . œ-F maj

œ œb . .œ- œ. œb . œb . œ. œb . œ.F phryg

œb œb . œ œ. œb .

&?

9

œ œ. œ-œb œ. œ. œ œ

va.bn.(8ba) œ œ. œ-œ œ. œ. œ. œ. œ. œ.

C maj

C maj

œ œ. œ. œ. œb .

œ œ œ. œ. œ.œb œb . œ-

.œ œ œ œb . œ.

C loc

Cm

œ œn . œ-.œb œb œ œb œb œ

C maj

C phryg

œ œ. .œ œ.œb œ œb . œ

Cm

œb . œ. œ. œb . œ.œ œ œ œb . œb . œb .

C phryg

C loc

œb œb . .œ œ.œ œn . œ# . œ. œ. œ.

chrom

&??

17

œ œ. œ-œœ œœ œœb œœ œœ

jœ ‰ ‰ Jœ

1

bns.vns.(8va)

+va.(8va)

cl. œb œ. œ-œœ œœ œœ œœ œœJœ ‰ ‰ JœF maj

œ œb œ œ œ œ œ œb œ

Jœ ‰ ‰ Jœ

b

do

CTo7

(ab=g#)

œ# œ. œ-œ# œ œ œ œ#Jœ ‰ ‰ Jœ

F locb b

F#11

7b9

(d#=eb)

œ œ. œn œ œ œb œ œ

Jœ ‰ ‰ JœFM7

œ œ œ œ œ œ œb œ œ œ œ œ3 3

3 3

.œ œb . jœ. ‰œ Jœ ‰Jœ ‰ ŒF maj


268

Robert Rival

ration of C and A in the next two bars, however, tilts the scale back to major. But the

pendulum swings fl atwards again in bb. 7-8, the A, G and D implying F phrygian

(C is not fl attened). The theme’s modal shading therefore alternates between relative

brightness (major) and two shades of darkness (locrian and phrygian), an example

of what Vincent Persichetti calls ‘modal interchange’: changing modes over a static

tonal centre.14

The real answer, by defi nition a strict transposition, oscillates among the same

modes. The counterpoint, while initially reinforcing the new key of C (bb. 9-11), fails

to darken with the subject at b. 12. The polymodal clash – one tonal centre, two or

more superimposed modes – continues, though reversed, in bb. 13-14. By phrase end,

the two strands settle in darkened, though not exactly corresponding, modes.

The tension created by the sounding of two modes simultaneously takes on

a harmonic, rather than a linear, form in the course of the clarinet’s presentation

of the subject. Like the previous entries, the fi rst three bars (bb. 17-19) remain in the

tonic major. For the fi rst time we hear a complete triad (F major). The clash occurs

in bb. 19-20 as the clarinet outlines the subject’s locrian segment. Ex. 8 isolates the

chord progression, built on an F pedal.

Ex. 8. Clarinet Concerto, bb. 17-22, reduction

There are several ways to interpret the harmony in b. 20. Stacking all the principal

pitches together produces an F7 chord with tertian extensions 9 and 11. Or one

might hear a polychord formed by F major and B major, which is how Nielsen spells

it.15 More interesting, however, is that this sonority, which combines pitches from

two modes – major and locrian – that share the same tonic, is the verticalized equiva-

lent of the juxtaposition of the same two modes in the subject itself. Nielsen thereby

momentarily increases harmonic tension while preserving harmonic consistency, an

economic handling of his basic materials.

IV. Mobile Pitches & Oscillating Macroharmony

One of Nielsen’s great achievements is to have refreshed tonality in such a natural way

that the listener hardly notices its newness. Such is the case with the much-discussed

14 Vincent Persichetti, Twentieth-Century Harmony, New York 1961, 40.

15 And which happens to correspond to a transposition of Stravinsky’s famous

Petrushka chord.

&17 18 19 œœœœ# ( ) 20 bb ( ) œœœ## 21n 22

F CTo7

FB

F#11b9

7FM7 F


269


opening segment of the Fifth Symphony: our ears become mesmerized by the relent-

less pedal over which fl oat clouds of undulating fi gures that come and go (see Ex. 9).


The movement begins with a {C, A} dyad in the violas, a pedal which pervades the

greater part of the symphony’s fi rst 94 bars. The minor third suggests A minor, con-

fi rmed by the bassoons’ entry (b. 5), but before long the introduction of fl ats – and

&?

c

c

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œTempo giusto

va.

{C,A}

Œ œœbns.

C dia (subset)

œœ œœ œœ œœb œœ œœn

E Eb E

Cmm

.. œœC dia

œœ b œœ

E Eb

Cmm

&?

10

œœb œœb œœb œœb

+Bb

bBb dia

œœb œœbb>

D Db

.. œœbb >Bb mm

.. œœbb œœ œœbn œœ œœbn

Db D DbEb E

Bb dia

.. Jœœ ‰Bb lyd dim

b

{C,A}E Eb

Ab dia

chrom#b nb

&?

19

..nb rœœ RœœbbB

œ œ ‰ Œœœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb œœbb

?

Cb dia

Œ œ œ œ œ Œ œ œ œ œjœb ‰ Œ

wb

{C,A} Œ œ œ œ œ œ œ ‰ ‰ œ œ

wbJœ ‰ Œ

œ œ œ œ œ œ œ œ

œ Œ Œœœhns.

&&?

24

#G dia (subset)

Œœœ

..# Œ

fls. .. Œ

Œœœ #

Œœœ

# Œœœ

œœ œœ

#

œœ œœ

# Œœœ

&&?

32 œœ œœ

#

œœ œœ œœ œœ

#

œœ œœ

#

œœ œœ

#

+B

G dia (complete)

œœ b œœ

œœ Œ

B Bb F# F

œœ b œœ œœ b œœ

F dia

œœ b œœ œœ œœ


270

Robert Rival

their cancellation – complicates matters. The key of this passage has thus been the

subject of much debate.16

Enigmatic harmony of this kind often prompts the analyst to quote Nielsen’s

now-famous dictum: ‘we should for once see about getting away from keys and yet

still having a diatonically convincing effect’.17 Why not take the composer literally

and do away with keys in our analysis as well? By focusing on intervallic structures,

Fjeldsøe, for one, has done so.18 For my part I will attempt to describe the perceived

tonal ambiguity by identifying the (mostly) diatonic collections at play and, more

importantly, the voice leading between them.

Fig. 4. Fifth Symphony, fi rst movement, bb. 1-40

Fig. 4 summarizes the changing macroharmony in this opening passage. Each row

lists the pitch classes present starting at the corresponding bar and identifi es the

implied collection. Arrows indicate voice leading, not necessarily between notes in

the same voice, but more generally between the collections in relatively small chunks

of music. In bb. 5-9, E is fl attened then raised, then fl attened again.19 D/D is another

16 Compare, for instance, Simpson, op. cit., 95-96; DeVoto, op. cit., 261-263; and,

Fanning, op. cit., 1997, 18-19.

17 From a letter of 13.8.1931 to Henrik Knudsen, cited in Fanning, op. cit., 1997,

20-21. (Vi skulde paa engang se at komme bort fra Tonearterne og alligevel virke

diatonisk overbevisende).

18 Fjeldsøe, op. cit., 18-26.

19 DeVoto aptly refers to the succession of harmonic intervals – third, fi fth,

sixth – as the ‘horn fi fths’ motif, one that actually sounds in the horns in bb.

23-25. See DeVoto, op. cit., 274-275.

Bar Collection 1 C A 5 C D E F A C diatonic (subset) 7 C D E F G A C melodic minor C D E F G A C diatonic 9 C D E F G A C melodic minor 10 C D E F G A B B diatonic 12 C D E F G A B B melodic minor 15 C D E F G A B B diatonic C D E F G A B B lydian dim C A 17-19 E F F G B chromatic D E A B A diatonic (subset) 20 D E F G A B C C diatonic 21 C A B 23 C D E F G A G diatonic (subset) 35 C D E F G A B G diatonic 36 C D E F G A B F diatonic


271


such mobile pitch (bb. 12-16).20 In both cases, the fl attening of a pitch class temporar-

ily and gently slides the macroharmony out of diatonic space. In other words, tension

and release – or at least, harmonic contrast – is taking place at the level of macrohar-

mony. At just a semitone apart these neighbouring collections could not be nearer to

one another, making for exceptionally effi cient voice leading. The pattern of arrows

in the table also makes plain the quasi-sequential effect: a tugging downwards on E,

echoed by the same on D; then, in both cases, the fl attening sticks.21

Bars 17-19 have a transitional character. The introduction of F (=G) and A

creates a pivot collection that smoothes the way to C diatonic, that blustery fortissimo

descent in b. 20. The violas, abruptly swept away by the bassoons, surface almost im-

mediately, sputtering, before resuming their quiet bobbing on C-A. Two new strands

now enter, fi rst in dialog, then superimposed. While the horns imply D diatonic {D,

E, F, G, A} (b. 23) and the fl utes, C diatonic {C, D, E, G} (b. 25), the two strands com-

bine, with the viola pedal, into a macroharmony one pitch shy of the complete G

diatonic collection (the B arrives at b. 35). While the bassoons shifted the initial mac-

roharmony fl atwards, the horns and fl utes not only restore C diatonic neutrality but

shift it slightly sharpside. By b. 36, however, the fl utes’ resolve weakens: the macro-

harmony slides fl atwards again, now to F diatonic.

20 In passages that gently fl uctuate among different diatonic collections, the

mobile pitch serves as the agent for change. The fl attening or sharpening of

a pitch class shifts the macroharmony from one collection to another. By the

very nature of diatonic harmony this usually means that only one ‘instance’

of a given letter-name pitch is in use at any time, e.g. E or E, but not both. A

useful analogy might be the approach to writing for harp, a diatonic instru-

ment adapted to play chromatic music: any diatonic collection is possible on

the harp (and many non-diatonic collections, too) but shifting from one to

another requires at least one pedal change.

21 Perhaps what motivated Nielsen to introduce the E/E mobile pitch class was a

desire to keep the bassoons’ intervals consonant. Here Nielsen’s own words pro-

vide some context. Writing in 1922 in a critique of Wagner, Nielsen proposed

that, ‘The only cure for this sort of taste lies in studying the basic intervals. The

glutted must be taught to regard a melodic third as a gift of God, a fourth as

an experience, and a fi fth as the supreme bliss. Reckless gorging undermines

the health. We thus see how necessary it is to preserve contact with the simple

original’. See Nielsen, Living Music, trans. Reginald Spink, London 1953, 42.

(Mod denne Smagsretning i Musik er der ingen anden Medicin end Dyrkelsen af de

første grundlæggende Intervaller. Man maa vise de overmætte, at et melodisk Terzspring

bør betragtes som en Guds Gave, en Kvart som en Oplevelse og en Kvint som den højeste

Lykke. Tankeløst Fraadseri undergraver Sundheden. Vi ser altså, at det er er Nødvendigt

at vedligeholde Forbindelsen med det oprindelige. Quoted in John Fellow (ed.), Carl

Nielsen til sin samtid, Copenhagen 1999, 265). An E (instead of an E) in bb. 7-8

avoids a diminished fi fth with the A. Likewise, the B in b. 10 avoids the tritone

– in both instances – with the F. The D in bb. 12-14, forming major ninth and

minor seventh intervals with the E, avoids the harsher intervals that would

result from a D – which Nielsen saves for b. 15 near the phrase’s culmination.


272

Robert Rival

A parallel passage occurs at b. 168ff, the bassoons replaying – at exact pitch,

though with some variation in rhythm and phrasing – their initial entry (c.f. b. 5ff).

The harmonic context, however, is altered: the violas’ pedal has been augmented by

one pitch class, the new {D, C, A} pedal echoed by the fl ute and clarinet. Fig. 5 sum-

marizes the fl uctuating macroharmony by identifying the pitch classes present and

voice leading.22


The table reveals that throughout this passage there are three fi xed pitches {C, D,

A} distributed as follows: a low C bass pedal (cellos); and a {D, C, A} wash in the vio-

las, fl utes and clarinets (the pitches change in the last two bars). The persistent low

C strongly suggests C as tonic. Meanwhile there are three principal vacillating pitch

classes: , and . The voice leading is effi cient throughout. The macroharmonies

change by one, two or three pitches at a time. In a few instances there is an added pitch

(spelled C or D) that does not result from collection voice leading; this pitch clashes

with the prevailing macroharmony. What we have here is a remarkable and rapid oscil-

lation among a range of macroharmonies all centred on C. Many of these are diatonic

collections. But some are not, namely the melodic minor, acoustic, lydian diminished

and dorian .

Bar Collection (tonic=C) 168-9 C D E F G A major (no 7) 170 C D E F G A melodic minor (no 7) 171-6 C D E F G A B dorian 177 C D E F G A B acoustic 178 C D E E (F ) G A B lydian diminished / lydian 179 C D E F G A B melodic minor 180 C D (E ) F G A B lydian diminished 181 C D D E F G A (B) locrian (bns.) + dia 182-3 C D E F G A (B) lydian 184 C D E F G A (B) mel minor? (G passing?) 185 C D E F G A (B) lydian diminished 186 C C D (E ) E F G A (B) ? 187 C D E (F ) G A B lydian diminished 188 C D E (F ) G A B dorian 4

22 There are several challenges in trying to label collections in such contexts.

For how long do we retain a pitch class in our memory once it no longer

regularly sounds? In the table I have marked implied pitches in parentheses.

Another problem is that of segmentation. I have used the bar unit as a mat-

ter of convenience. One could quibble with this choice but I do not think, in

this case at least, that modifying the boundaries somewhat would substan-

tially alter the analysis.


273


V. Superimposed Scales

Beginning in the 1940s Soviet musicologists Lev Mazel’ and Alexander Dolzhansky be-

gan to catalogue the modes used by Shostakovich, including the ‘lowered’ or ‘intensi-

fi ed’ phrygian, a phrygian scale with ,23 later identifi ed as a source of the compos-

er’s musical signature, DSCH.24 Shostakovich was not the only composer of the period

who incorporated such ‘lowered’ scales, however. Consider the fi rst part of Nielsen’s

Fifth Symphony. In bb. 120-123, for instance, immediately after the violins initiate a D

minor melody with a strongly-accented leading tone, the scale modulates to {D, E, F,

G, A, B, C}: D locrian with and (see Ex. 10).


Another such moment occurs at the tail end of the {F, D} pedal section: a melody

in the violins clashes with the background harmony creating a polytonal effect (see

Ex. 11). Initially the violins are restricted to fi ve notes {G, A, B, C, D} (b. 145 until

midway through b. 151), a subset of the G/A octatonic collection. Meanwhile, swirling

fi gures in the clarinet and fl ute augment the {F, D} bass pedal, combining to form

the complete C diatonic collection.

At b. 151 the violins introduce E and F, extending the octatonic scale to one

note shy of complete. We never get the G, however, so we might instead hear the

seven-note scale as G aeolian with and .


Fig. 6 shows the two scales at the core of this passage (enclosed pitches indicate ton-

ics). Taken together they form a dissonant 10-note macroharmony. But the disso-

nance, while contributing to the music’s drama and tension, is mitigated by the seg-

regation of the two governing scales into clearly perceptible layers by register, timbre

23 See Ellon Carpenter, ‘Russian Theorists on Modality in Shostakovich’s Music’,

in David Fanning (ed.) Shostakovich Studies, Cambridge 1995, 76-112.

24 Stephen C. Brown, ‘Tracing the Origins of Shostakovich’s Musical Motto’,

Intégral 20 (2006), 69-103.

&?

cc

119

œ # œœ œ œ œlower str.

vns.

Dm with b

œ œ œ œb œb œb œœ œ œ œ

D 'lowered' locrian

b b b.œ œb œb œb œ Œ

œ œ œ œD 'double-lowered' locrian

b‰ œb œ œ œ œ œ œ œ œ œ œ œ œ œœ œ œ œ

œb œ œ œ œb œ œ> œb œ> œœ œ œ œ

violins: C D E F G A B orchestra: C D E F G A B


274

Robert Rival

and texture. The two scales share fi ve pitches: while very different in character, they

retain much in common.25

The chromatic dissolution of the violins’ melody provides additional insight

into the relationship between the two harmonic planes. The tune in the violins spi-

rals downwards, sounding all chromatic pitches between F (b. 155) and the melody’s

arrival point, B (b. 158). The infi ltration of {F, D, B} – contained in C diatonic but not

in G/A octatonic – begins to erase the tension between the two scales. The B at b. 158

25 Can any further relationship between the scales be ascertained? Perhaps,

if we draw on the perspective of ‘multifaceted diatonicism’, a theoretical

approach developed by the Soviet musicologist Valentin Sereda in the 1970s

to address the music of Shostakovich. Sereda contends that certain analyti-

cally challenging passages can be explained as the superimposition of two

scales, one of which is derived from the tertian, quartal or quintal ‘sup-

port’ of another. If we consider the C diatonic collection – D dorian – as the

primary one due to the relentlessness of the {F, D} pedal, then the G, acting

as quartal ‘support’ of D, underpins the G-centred mode of the violins. For a

summary of Sereda’s approach see Carpenter, op. cit., 104-105.

&&?

ccc

145 Œ œ œ œ

œ œ œ œ{F,D}

G/A octa (subset)vns.

lower str.

œ œ œb œ œ œ œ œ œ œ

œ œ œ œ

6

œ œ œ œ œ œb œ

œ œ œ œ

.œb Jœ œb œ œ œ

œ œ œ œ

œ> œ> œ œ œb œ œ>‰ œ œ œ œ œ œ œ œ œ œ œ. Œ

3 3 3œ œ œ œD dor

cl.

œ> œ œ œb œ .œ jœ‰ œ œn œ œ œ œ ‰

3 3œ œ œ œfl.

&

&?

151 œb œ œb œ œb œb

Œ ‰ œ œ œ3œ œ œ œ

cl.

.œ Jœb œb œ œb œnœ œ œ œ œ œ œ œ.3 3œ œ œ œ

w‰ œ œ œ œ œ œ œ œ œ œ œ. Œ3 3 3

‰ œ œ œ œ œ œ œ œ œ3 3 3œ œ œ œ

fl.

cl.

&

&?

154 œ œ œ œ œb œ œ‰ œ œ œ œ œ œ œ œ œ œ œ. Œ3

3 3

œ œ. Œ ‰ œ œ œ œ œ œ œ œ œ3 3 3œ œ œ œ

œ œ- œ-

œ œ œ œ

chrom

.b œ- œ-

œ œ œ œ

œb œ œ

œ œ œ œ

œn Œ

œ œ œ œD dor



275


completely dissolves the G/A octatonic scale into C diatonic, thereby resolving the

polytonal tension.26

VI. Fluctuating Collection Modulation

The entry of the fi rst violins in b. 44 of the Fifth Symphony has been widely discussed

and from a variety of angles. At the heart of the controversy is the confl icting har-

monic signals suggested by the various layers, especially between the melody (fi rst

violins) and bass (cellos). Simpson claims that the V-I quality of {C, F} in the bass

clearly places the music in F.27 Fanning, on the other hand, maintains that the music

actually sounds like it is in C, an assessment with which I tend to agree – at least at

the start of the passage (see Ex. 12).28

But what to make of the melody in the violins that seems centred on E and

whose diminished fi fth (b. 47) suggests E locrian? The matter is further complicated

by the alteration of certain pitches as the melody rises above the confi nes of a single

octave: E4 becomes E5 (b. 49); A4 becomes A5 (b. 54); D5 becomes D6 (b. 62). If we

consider the melody as a whole (bb. 44-69), we cannot say that it defi nes any one scale

– unless we are prepared to label it as a non-octave-repeating scale.

I wonder, however, if the attempt to fi x a tonic on a passage such as this one

is a vestige of the thinking associated with common-practice tonality. As Tymoczko

observes, ‘it is entirely possible […] to write diatonic music in which no note is heard

as a tonal centre, just as one can write chromatic music with a very clear centre’.29

Perhaps none of C, F or E can claim tonic status because of too many competing in-

terests. Or, to put it another way, centricity may be weak at best. Fjeldsøe seems to

acknowledge as much by persuasively describing the melody as an interval network,

a linear-intervallic process that I here express in terms of shifting macroharmo-

nies (see Fig. 7).30

As the melody in the fi rst violins rises, the operative collection is gradually

fl attened, proceeding fl atwards along the circle of fi fths. Unlike previous examples of

fl attening, however, the process is mirrored in reverse: as the melody descends, the

26 Even the C diatonic collection is rendered more consonant when the fl utes

drop the B (b. 160, not shown): the resulting six-note subset {C, D, E, F, G,

A} lacks the tritone. The {F, D} ostinato itself evaporates (b. 163), replaced

by a new pedal on C. By b. 166 the macroharmony is thinned down to four

pitches {C, D, G, A}.

27 Simpson, op. cit., 96.

28 Fanning, op. cit., 1997, 24. Fanning amusingly reports that three informal

Manchester student referendums ‘unanimously’ determined that the pas-

sage is indeed in C (see footnote 14, 110).

29 Tymoczko, op. cit., 16.

30 Fjeldsøe, op. cit., 23-25.


276

Robert Rival

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49 B diatonic E / E 50-53 F diatonic 54-55 E diatonic E / E, A / A 56-59 F diatonic

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E / E 60-61 E diatonic E / E, A / A 62 A diatonic E / E, A / A 63-65 B diatonic E / E66-69 F diatonic E / E


277


fl attened pitches are restored to their original states. Because we tend to associate

fl attening with falling, this counterintuitive fl attening-while-rising is perhaps what

gives the passage its unique fl avour. Fig. 8 charts the progression in graph form mak-

ing apparent the wave-like progression. Because the fl attening occurs in diatonic

space and along the circle of fi fths, the change in pitch content from one collection

to the next results in effi cient voice leading.


A few remarks now about the bass and inner voices. The {C, F} in the bass (bb. 44-57)

belongs to all collections outlined in the melody (F, B, E diatonic). Meanwhile, the

shift to {E, B} / {G, C} (bb. 57-69), echoes, on the one hand, the fl atwards direction

of collection modulation, while, on the other hand, introduces a clash between the

bass E and melody E when F diatonic is at play. As for the inner voices, the violas’

{C, A} pedal is augmented by {G, E} in the second violins forming an Am7 chord (or,

in bb. 44-57, an FM7/9 chord). While {G, C} belongs to all collections outlined in the fi rst

violins, the E and A occasionally clash with the E and A when the latter are present

in the melody.

VII. Flatwards Bound

By now it will be obvious that all the examples I have discussed involve fl attening,

or lowering, in a variety of contexts. I undertook this study with the view of exam-

ining modulatory processes at the local level. I did not go hunting for those of the

fl atwards kind. But once I spotted the trend I went back into the woods and found it

teeming with game.

44 49 54 59 64 69C

F

B

E

A

D

b.


278

Robert Rival

I am not suggesting, however, that Nielsen exclusively modulates fl atwards.

An example of a sharpwards modulation occurs in the Second Symphony, The Four

Temperaments, at the beginning of the third movement, Andante malincolico (see Ex. 13).

Ex. 13. Second Symphony, third movement, bb. 1-12

The movement opens in E minor, deep in fl at territory, and coasts there for some

time. But rather than confi rming the tonic, the fi rst cadence is in the dominant mi-

nor key of B (b. 13), gently shifting the macroharmony sharpwards. The effect is strik-

ing: by substituting a cadence in the dominant for one in the tonic, the sombre mood

is lightened.31 Another example of sharpwards modulation, this time over a longer

span of music, unfolds in the second movement of the Fifth Symphony, from the

Andante poco tranquillo fugue in the strings (b. 679) until the Allegro (b. 731), the macro-

harmony ascending the circle of fi fths from F to E. At the large-scale level, in particu-

lar, Nielsen frequently modulates sharpwards.32

Intuitively, one might assume, then, that sharpwards modulation would also

dominate at the local level. But as many passages in this paper have shown, one can

start anywhere, including in sharp territory, and return there, by only traveling fl at-

31 A more dramatic sharpwards modulation involves moving to the major

mediant, as in Beethoven’s ‘Waldstein’ sonata, fi rst movement, in which the

fi rst group is in C major while the second, in E.

32 The fi rst movement of the First Symphony dwells in G minor but the fi nale

ends in C major. The outer movements of the Third Symphony both rise a

perfect fi fth in tonality.

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279


wards: it’s a circle after all. So, in principle, it is possible to achieve long-term sharp-

wards motion with fl atwards-only local motion.

A more thorough and systematic investigation would be required in order

to determine whether fl atwards modulation at the local level is indeed the norm in

Nielsen.33 Fanning, for one, in calling it a ‘fi ngerprint’, would seem to think so, as do I.34

Broadening the discussion beyond the scope of Nielsen’s work, I wonder if fl at-

tening is generally more prevalent in twentieth-century extended tonality. Consider

one of the simplest examples, that of the fl atwards shift – and back again – of Peter’s

theme in Prokofi ev’s Peter and the Wolf. Lowered modes are well-documented in Shos-

takovich. Modal fl attening is common in Vaughan Williams. Taking an even broader

view, is it fair to say that composers of the common-practice period favoured borrow-

ing minor elements into major, which leads to lowering, over the reverse? If so, then

Nielsen’s practice may be viewed as a further development and extension of this im-

portant feature of common-practice tonality and a signifi cant contributing factor in

defi ning that ‘characteristic fl avour’ of his harmony.

A B S T R A C T

Early studies of Nielsen’s harmony focused on large-scale tonal design, tracking the

progression of key areas across large spans of time. With this foundation in place

attention has increasingly turned to moment-to-moment qualities in Nielsen’s har-

mony. Fanning, for instance, attributes its ‘characteristic fl avour’ to the ‘interpenetra-

tion of modal and tonal elements’. I attempt to defi ne this ‘fl avour’ by identifying at

least some of its ingredients in passages taken principally from the Fourth and Fifth

Symphonies and from the Clarinet Concerto. After discussing the variety of ways and

contexts in which these modulations unfold – modulation to a remote key; non-func-

tional modulation; modal interchange and polymodality; mobile pitches and oscil-

lating macroharmony; superimposed scales; and, fl uctuating collection modulation

– I conclude that Nielsen has a tendency to modulate fl atwards at the local level. My

approach is informed by Dmitri Tymoczko’s A Geometry of Music: Harmony and Counter-

point in the Extended Common Practice (2011).

33 Throughout his dissertation, Pankhurst discusses fl atwards and sharpwards

progressions in Nielsen using phrases like ‘fl atwards slippage’ and ‘fl atwards

drift’. See Pankhurst, op. cit., 222-223 and 310-315, for instance.

34 Fanning, op. cit., 1997, 36.


Documents

Carl Nielsen Studies V - Robert Rival::Composer€¦ · CARL NIELSEN STUDIES ... Structure in Carl Nielsen’s Wind Quintet’, in Miller, op. cit., 541-596. 3 David Fanning, ‘Carl