Dallapiccola Analysis Essay 2 - Alex Aitkenalexaitken.co.uk/assets/Metrical and Rhythmic Analysis...

SYMMETRY, DISRUPTION, AND MISMATCH IN

DALLAPICCOLA’S TRE EPISODI:

A METRICAL AND RHYTHMIC ANALYSIS

ABSTRACT

This second essay will present a rhythmic and metrical analysis of Dallapiccola’s Tre Episodi,

and will explore a number of readings for the metrical schemes and organisational principles

underlying the music. The final part of the analysis will draw together conclusions from both

this and the first essay, assembling a framework around which the compositional processes in

the Episodi can be understood.

This essay further investigates the organisational role of the number 5, and the interaction of

symmetry and disruption, instead focussing on rhythmic and metrical parameters. It will be

demonstrated that symmetry and disruption permeate the rhythmic and metric levels of the

Episodes, in addition to the pitch-class elements, and that the number 5 is still a controlling

force. A final section investigating the level of structural mismatch of rhythmic parameters

will conclude that the rhythmic profile largely aligns with structural divisions, with any

anomalous points contributing the symmetry on another level.

There is a clear symmetry to the metrical scheme in Episode 1.1

SYMMETRY DISRUPTED

BAR

1 3 5 20 28 29 30 32 33 35 37 38 43 47 49 51 59 60

3 4 3 2 4 3 4 2 4 3 5 3 2 4 2 3 4 3

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

FIGURE 52: SYMMETRY IN THE METRICAL SCHEME OF EPISODE 1

1 This essay uses both motivic and bar-by-bar divisions, since this will be an effective analytical tool. Symmetry is again

indicated with black lines and disruptions are highlighted in red.

TIME SIGNATURE

SYMMETRY, DISRUPTION, AND MISMATCH IN DALLAPICCOLA’S TRE EPISODI: AN ANALYSIS OF METRIC AND RHYTHMIC PARAMETERS

2

Reading this as a group of eight unsymmetrical time-signatures flanked by groups of five

yields uninterrupted symmetry:

NUMBER OF BARS

28 18 18

5 8 5

FIGURE 53: ALTERNATIVE ‘BLOCK’ READING OF METRICAL SCHEME IN EPISODE 1

The number 5 here continues its demarcative function. The middle block of eight time

signatures consists of two mirror image blocks of three:

BAR

29 30 32 33 35 37 38 43

3 4 2 4 3 5 3 2

4 4 4 4 4 4 4 4

FIGURE 54: MIRROR IMAGE BLOCKS IN MIDDLE SECTION OF METRICAL SCHEME IN EPISODE 1

The 3/4 and 2/4 sections separate the outer symmetrical sections and the mirrored inner

blocks. They are therefore functionally equivalent and yield a looser symmetry.2 Note too

that they add to five.

BAR

1 3 5 20 28 29 30 32 33 35 37 38 43 47 49 51 59 60

3 4 3 2 4 3 4 2 4 3 5 3 2 4 2 3 4 3

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

FIGURE 55: SYMMETRY OF THE METRICAL SCHEME OF EPISODE 1

The middle group can also be read as two overlapping blocks of five elements: the first

symmetrical; that of the second being prevented by the last element. In this second block,

the number 5 continues its anchorage function.3

2 This kind of looser symmetry often appears in Messiaen’s music. He calls it ‘inexact’ symmetry. 3 See Essay 1, p.4.

TIME SIGNATURE

TIME SIGNATURE


3

BAR

29 30 32 33 35 37 38 43

3 4 2 4 3 5 3 2

4 4 4 4 4 4 4 4

SYMMETRICAL BLOCK SYMMETRY DISRUPTED

FIGURE 56: MIDDLE GROUP OF METRICAL SCHEME IN EPISODE 1

The first two bars of the 2/4 section disrupting the symmetry (bb.43-44) are shown below.

FIGURE 57: EPISODE 1, BB.43-44

The bars could easily be notated in 4/4 (they contain the same gesture). This would preserve

the symmetry in Figure 56. But bb.45-46 below show that bb.43-44 are two distinct

gestures.


This, along with the shape of the gesture, justifies the 2/4 notation. The potential for

symmetry is subordinated to the gesture. Figure 34 (essay 1) showed that the interaction of

symmetry and disruption within pitch-related elements permeated each level (of surface

TIME SIGNATURE


4

and underlying processes). The interaction occurred relatively independently from each of

the processes (i.e. the process did not often contribute to, or determine, the level of

interaction), and was therefore not itself a controlling force. The notation of this section in

2/4 sees the musical gesture controlling the interaction of symmetry and disruption, and so

it can no longer be thought of as being semi-independent.

Further consideration of the metrical scheme reveals a number of symmetrical subunits.

BAR

1 3 5 20 28 29 30 32 33 35 37 38 43 47 49 51 59 60

3 4 3 2 4 3 4 2 4 3 5 3 2 4 2 3 4 3

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

FIGURE 59: SUBUNITS IN METRICAL SCHEME OF EPISODE 1

These submetrical units (they operate underneath the broader metrical principle in Figure

52) are mostly coterminous, with one unit displaced. The 2/4 section (bb.20-27) should be

in 3/4, but this is prevented by the musical idea (again glissandi).

TIME SIGNATURE


5


2/4 supports the musical idea: both beats provide a goal-orientated closure to each

glissando, strengthening the effect and simultaneously compensating for the induced

weakening of the beat (the physical movement of playing a glissando results in all notes

becoming unaccented). As with bb.43-46 the potential for and expectation of symmetry is

thwarted to strengthen the gesture.


6

Figure 61 reveals a number of mirrored blocks of three:

BAR

1 3 5 20 28 29 30 32 33 35 37 38 43 47 49 51 59 60

3 4 3 2 4 3 4 2 4 3 5 3 2 4 2 3 4 3

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

FIGURE 61: MIRRORED BLOCKS IN METRICAL SCHEME OF EPISODE 1

The displacement of the second block is explained by Figure 56, where the 2/4 section

contributes to the symmetry in the block. As with pitch-related parameters, disruptions on

one level support symmetry on another. Five of these mirrored blocks are symmetrical

through the 5/4 section at bar 37. The number 5 therefore continues its demarcation and

anchoring function. The main weight of the metric scheme acts through the 5/4 bar (bar 37

itself consists of five quintuplets – shown below).

FIGURE 62: EPISODE 1 BAR 37

Whilst there is no similar organisation within the metrical scheme of Episode 2, there are a

number of overlapping submetrical units with symmetry (they are not coterminous as in

Episode 1). Figure 63 shows symmetrical blocks in black and near-symmetrical blocks in

red.4

4 Only the largest symmetrical blocks are shown.

TIME SIGNATURE


7

BAR

1 6 7 9 11 12 13 14 15 16 17 21 22 27 28 34 35 39 40 47 48 50 51 53

5 4 5 4 5 4 5 4 3 2 5 2 5 2 5 2 5 2 5 2 5 4 5 4

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

54 55 56 58 59 61 62 64 65 67 68 72 73 75 76 77 78 83 84 86 87 88 92 93

5 3 5 4 5 4 5 4 5 4 5 2 5 4 5 4 5 2 5 4 3 5 4 3

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

94 108 109 116 117 118 123 124 125 127 128 130 131 132 133 134 137 138 144 145 146 148 150 152

5 4 5 3 2 5 3 6 5 3 5 3 5 3 2 3 4 5 6 5 5 4 3 5

8 8 8 4 4 8 4 8 8 4 8 4 8 4 4 4 4 4 4 4 8 8 8 8

156 157 160 161 166 167 184 186 188 189 191 192 193 194 195 196 201 202 203 204 206 207 210 211

2 5 4 5 2 5 4 5 4 5 3 5 4 5 4 5 3 2 6 5 3 2 3 1

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 8 8 4 4 4 4

212 213 215

3 2 5

4 4 8 FIGURE 63: METRICAL SCHEME FOR EPISODE 2

The blocks (either symmetrical or disruptive) cover over 90% of the Episode. The most

prevalent time signature is 5/8, with each thwarting element (the time signatures in red)

displaying a looser trajectory towards the 5/8 in bar 146. The number 5 continues its

anchoring function in eight blocks and its demarcation function in eight blocks.5 Each

disruptive block (in red) consists of five elements. In this respect the number may be

assigned an additional function – that of being a disruptive agent. The disruption of

symmetry again occurs in the back end of the block, as with Figure 56.

An alternative reading of the metrical scheme sees a process of alternation of two elements,

each time disrupted by blocks of 2.

5 The number 5 sometimes demarcates and anchors within the same block, but the functions mostly operate independently.

TIM

E S

IGN

AT

UR

E


8

BAR

1 6 7 9 11 12 13 14 15 16 17 21 22 27 28 34 35 39 40 47 48 50 51 53

5 4 5 4 5 4 5 4 3 2 5 2 5 2 5 2 5 2 5 2 5 4 5 4

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

54 55 56 58 59 61 62 64 65 67 68 72 73 75 76 77 78 83 84 86 87 88 92 93

5 3 5 4 5 4 5 4 5 4 5 2 5 4 5 4 5 2 5 4 3 5 4 3

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

94 108 109 116 117 118 123 124 125 127 128 130 131 132 133 134 137 138 144 145 146 148 150 152

5 4 5 3 2 5 3 6 5 3 5 3 5 3 2 3 4 5 6 5 5 4 3 5

8 8 8 4 4 8 4 8 8 4 8 4 8 4 4 4 4 4 4 4 8 8 8 8

156 157 160 161 166 167 184 186 188 189 191 192 193 194 195 196 201 202 203 204 206 207 210 211

2 5 4 5 2 5 4 5 4 5 3 5 4 5 4 5 3 2 6 5 3 2 3 1

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 8 8 4 4 4 4

212 213 215

3 2 5

4 4 8 FIGURE 64: TWO-ELEMENT ALTERNATION PROCESS WITHIN THE METRICAL SCHEME FOR EPISODE 2

Extracting the beat elements in the red blocks reveals another looser symmetry, common in

Messiaen’s music.

15 16 54 55 69 72 133 134 191 192 201 202

3 2 5 3 5 2 2 3 3 5 3 2

FIGURE 65: SYMMETRY WITHIN DISRUPTIVE BLOCKS OF FIGURE 12

Note that the pattern begins in bar 15 – a multiple of five.6 Working from the outside in, the

two identical outer blocks are followed by two mirrored blocks and two blocks whose

symmetry is thwarted (as indicated). The number 5 again acts as a disruptive agent, but this

time in the sense that it is expected in bar 134 but does not happen. Figure 63 shows that

again the disruptive element at this level contributes to symmetry at another (in this case it

forms a symmetrical part of another disruptive block). Each block in Figure 65 also either

6 Notice too that adding the totals of each of these disruptive blocks in Figure 65 gives:

5 8 7 5 8 5

Itself another disruptive block where the number 5 continues its demarcative function. An alternative reading is of a

process set up and then broken by the number 5 (587587 would be expected). 5 again acts as a disruptive agent (deep)

within the metrical scheme. Note too that adding each pair yields a symmetry:

5 8 7 5 8 5

13 12 13

TIM

E S

IGN

AT

UR

E


9

contains the number 5 or adds to give five. Reading the metrical scheme as an alternation of

three, rather than two, elements reveals another process.

BAR

1 6 7 9 11 12 13 14 15 16 17 21 22 27 28 34 35 39 40 47 48 50 51 53

5 4 5 4 5 4 5 4 3 2 5 2 5 2 5 2 5 2 5 2 5 4 5 4

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

54 55 56 58 59 61 62 64 65 67 68 72 73 75 76 77 78 83 84 86 87 88 92 93

5 3 5 4 5 4 5 4 5 4 5 2 5 4 5 4 5 2 5 4 3 5 4 3

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

94 108 109 116 117 118 123 124 125 127 128 130 131 132 133 134 137 138 144 145 146 148 150 152

5 4 5 3 2 5 3 6 5 3 5 3 5 3 2 3 4 5 6 5 5 4 3 5

8 8 8 4 4 8 4 8 8 4 8 4 8 4 4 4 4 4 4 4 8 8 8 8

156 157 160 161 166 167 184 186 188 189 191 192 193 194 195 196 201 202 203 204 206 207 210 211

2 5 4 5 2 5 4 5 4 5 3 5 4 5 4 5 3 2 6 5 3 2 3 1

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 8 8 4 4 4 4

212 213 215

3 2 5

4 4 8

FIGURE 66: THREE-ELEMENT ALTERNATION PROCESS WITHIN THE METRICAL SCHEME FOR EPISODE 2

Extracting the three elements which make each block in Figure 66 produces ten blocks

(again a multiple of five) containing an initial pattern which is then abandoned.

PATTERN ABANDONED

345 245 345 245 345 235 345 245 345 235

FIGURE 67: CONSTITUENTS OF THE THREE-ELEMENT ALTERNATION BLOCKS IN FIGURE 65

Each block here also contains the number 5. The block is ‘345’ appears five times; ‘245’

appears three times; and ‘235’ appears twice. (The total appearances for the latter two

blocks making five.)

TIM

E S

IGN

AT

UR

E


10

An alternative reading sees two symmetrical blocks of five elements:

345 245 345 245 345 235 345 245 345 235

FIGURE 68: ALTERNATIVE SYMMETRICAL READING OF THREE-ELEMENT ALTERNATION BLOCKS IN FIGURE 65

The metrical scheme of Episode 2 also displays a process of metrical growth and reduction.7

BAR

1 6 7 9 11 12 13 14 15 16 17 21 22 27 28 34 35 39 40 47 48 50 51 53

5 4 5 4 5 4 5 4 3 2 5 2 5 2 5 2 5 2 5 2 5 4 5 4

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

54 55 56 58 59 61 62 64 65 67 68 72 73 75 76 77 78 83 84 86 87 88 92 93

5 3 5 4 5 4 5 4 5 4 5 2 5 4 5 4 5 2 5 4 3 5 4 3

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

94 108 109 116 117 118 123 124 125 127 128 130 131 132 133 134 137 138 144 145 146 148 150 152

5 4 5 3 2 5 3 6 5 3 5 3 5 3 2 3 4 5 6 5 5 4 3 5

8 8 8 4 4 8 4 8 8 4 8 4 8 4 4 4 4 4 4 4 8 8 8 8

156 157 160 161 166 167 184 186 188 189 191 192 193 194 195 196 201 202 203 204 206 207 210 211

2 5 4 5 2 5 4 5 4 5 3 5 4 5 4 5 3 2 6 5 3 2 3 1

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 8 8 4 4 4 4

212 213 215

3 2 5

4 4 8

FIGURE 69: GROWTH AND REDUCTION PROCESSES WITHIN THE METRICAL SCHEME FOR EPISODE 2

Figure 69 shows five reduction cells and five growth cells. Symmetry within the pitch-related

elements competes against these patterns of growth and decay, giving the music its

propulsive element. There are 99 metrical sections (one would perhaps expect 100, since it

is a multiple of five). The central metrical section is the 4/8 in bar 108. There is a symmetry

orientated around the previous 5/8 section (bar 94), with two mirrored cells either side (of

metrical reduction and then growth). This symmetry is therefore mismatched with the

central element. But centring the metrical scheme on the number five allows a continuation

7 In terms of quaver beats in each bar (the predominant metrical value in Episode 2).

TIM

E S

IGN

AT

UR

E


11

of its anchorage function. Note that the number additionally demarcates the metrical scheme

as a whole, providing the boundaries within which other processes operate. This yields a

looser symmetry, with five on the outside and at the centre. Again, anomalies on one level

often contribute to symmetries on another. This could account for why the central metrical

section at bar 108 is not 5/8 – the 4/8 bar is most likely contributing to a symmetry on

another level. Indeed, Figure 63 reveals bar 108 to be operating within a disruptive block of

five elements, broken by the 3/4 section at bar 116.

In summary, Episode 2’s metrical scheme has a number of interacting processes operating at

different levels:

1) Symmetrical and near-symmetrical blocks (Figure 63). The near-symmetrical blocks

have their potential symmetry thwarted at the end of the block. The number 5

continues its demarcative and anchoring functions in eight blocks each (the functions

do, in some cases, overlap and occur within the same block);

2) A process of alternation of two elements broken by blocks of two elements, which

themselves can be extracted to form a looser symmetry (Figures 64 and 65). Each

block in Figure 65 either contains the number 5, or adds to give five;

3) A process of alternation of three elements (Figure 66). Extracting the three elements

from each block gives three units; ‘345’ (which appears five times), ‘245’, and ‘235’

(appearing thrice and twice respectively, and therefore their combined appearances

total five) (Figure 67);

4) A growth and reduction process (Figure 69), with five reduction cells and five growth

cells;

5) The metrical scheme is orientated around the 5/8 in bar 94, despite the central

element being the 4/8 in bar 108. This mismatch has been shown to be due to the 4/8

bar contributing to the disruption of symmetry on another level. The predominant

meter (proportionally) is 5/8.

Episode 3 has a simpler metrical scheme:

BAR: 1 9 49 57

5 3 5 3

4 4 4 4

FIGURE 70: METRICAL SCHEME FOR EPISODE 3

This can be interpreted as a block of five elements whose symmetry is thwarted by an

invisible 5/4 element (the number 5 is again a disruptive agent):

5 3 5 3 ?

4 4 4 4 ?

FIGURE 71: ALTERNATIVE NEAR-SYMMETRICAL READING OF METRICAL SCHEME IN EPISODE 3


12

Potential symmetry is prevented by the last component of the block.

In each Episode the symmetry of the near-symmetrical blocks is always disrupted in the

back half (most often by the final element), since its maximum effect occurs only once the

expectation of potential symmetry has been generated. This gives the music a sense of

progress, acting as a compensatory mechanism for the stasis risked by using symmetry.

This last proposition is, however, invalid: Episode 1’s symmetry in Figure 52 is disrupted

whilst working inwards from the outside (against the musical direction); the near-

symmetrical blocks in Figure 63 are not evenly distributed amongst Episode 2, and their

location in relation to the symmetrical blocks does not match (which would be expected if

their function was to counteract stasis caused by symmetrical blocks); and in Figure 71 the

symmetry is prevented by an element which does not appear in the music.

The most likely explanation as to why disruption is a key feature within these Episodes is

that Dallapiccola was aware that twentieth-century music was increasingly being composed

for the analyst as well as the musician, and that works were often now designed to be

analysed extensively to reveal compositional processes, as well as being works to be

performed. The metric symmetry explored so far provides the foundation for further

symmetries present in other parameters, and exhibits the same features involving the

interaction of symmetry, disruption, and the number 5, in order to unify the work across

multiple levels.

Patterns within the metric scheme also pervade the rhythmic level. Figure 72 shows a

rhythmic reduction of the left hand of Episode 1 from bar 5.8

BAR: 5 11 14 15 16

RHYTHMIC GROUPING: 2 3 4 3 4

FIGURE 72: RHYTHMIC GROUPING OF LEFT HAND IN EPISODE 1 BARS 5-17

Again the symmetry is broken by the final element. Note that it is another block of five

elements. The left hand motive through these bars consists of symmetric cells (shown

below).

8 This occurs again from bb.53-58.


13

etc.

FIGURE 73: SYMMETRIC CELLS IN LEFT HAND OF EPISODE 1, BB.5-11

Each pitch has five attack points, continuing the number’s organisational function. At the

return of this motive in bar 39, the symmetry is first reproduced, then broken:

FIGURE 74: BROKEN SYMMETRY IN EPISODE 1, BB.39-42

This happens again at the end of Episode 1:

FIGURE 75: BROKEN SYMMETRY IN EPISODE 1, BB.62-65

Figures 74 and 75 show that breaking symmetry at the rhythmic level does give the music a

sense of progress by thwarting an expectation generated by the previous appearance of a

symmetrical motive. In the case of Figure 74, the disruption to the expected symmetry

generates the momentum required to enter a new rhythmic idea at bar 43, as shown below.


14

SYMMETRY EXPECTATION OF FURTHER SYMMETRY

FIGURE 76: BROKEN SYMMETRY AND RESULTING MOMENTUM IN EPISODE 1, BB.42-43

In the case of Figure 75, the thwarting of the symmetry generates momentum into the

second Episode.

The number 5’s importance within the rhythmic scheme is emphasised by the appearance of

two quintuplets within the first two bars of Episode 1.9

FIGURE 77: EPISODE 1 BB.1-2

The quintuplets return at the end of Episode 1:

9 The rhythmic grouping is also loosely symmetrical: 5 3 3 5.


15

FIGURE 78: EPISODE 1 BB.59-60

The number 5 therefore acts as a framing device at the rhythmic as well as metrical level.

Episode 1 is also saturated by a rhythm with five attack points:

FIGURE 79: EPISODE 1 RHYTHMIC FIGURE

which pre-empts the ostinato of the second Episode, created by eliding the tied quavers into

a 5/8 pattern.10 The moment of crisis in Episode 2 occurs as the glissando in bar 134

dissipates into a trill that leads, through a 5/4 (bar 138), into new material (shown below).

10 This rhythmic manipulation centred around the number 5 was common in Dallapiccola’s later works – see Ritmi, where

rhythms are systematically reduced to yield a group with five attack points.


16

FIGURE 80: MOMENT OF CRISIS AND DISSIPATION INTO 5/4 IN EPISODE 2

In Episode 3 the trajectory acts towards the 5/4 at bar 49, approached through a three bar

transition (bb.46-8) with a diminuendo.


17

The 5/4 bars occur at the point where the percentage of bars and beats passed is roughly

equivalent, linking both the metrical and beat levels.

EPISODE 1 EPISODE 2 EPISODE 3

BAR PERCENTAGE 60 56 71

BEAT PERCENTAGE 57 53 67

_________________________________________________________________________________________________________________________

PERCENTAGE DIFFERNCE 3 3 4

FIGURE 81: BAR AND BEAT PERCENTAGE FOR 5/4 TRAJECTORY IN EACH EPISODE

The grouping of five (i.e. into three and two, or two and three) also permeates the rhythmic

organisation of the Episodes. Bar 11 of Episode 1 introduces an idea whose rhythmic drive is

generated by the three-against-two cross-rhythms in bars 14 and 16.

FIGURE 82: CROSS-RHYTHMS IN EPISODE 1, BB.13-16


18

Bars 31-32 of Episode 1 again feature three-against-two cross-rhythms that provide

momentum linking the similar material in bar 30 with that of bb.33-34.

LINKING BARS

FIGURE 83: CROSS-RHYTHMS IN EPISODE 1, BB.30-35

Episode 3 begins with a similar three-against-two idea:

FIGURE 84: CROSS-RHYTHMS AT BEGINNING OF EPISODE 3

Note that the three and two division acts horizontally as well as vertically.


19

The following section looks at the level of mismatch between the rhythmic profile and

structure.11 The graphs trace the predominant rhythmic value in each bar. Again, the black

vertical lines show the segmentation of each Episode into sections with similar motivic

and/or rhythmic features.

BAR

FIGURE 85: PREDOMINANT RHYHTMIC VALUES IN EPISODE 1

Episode 1’s graph shows that change in predominant rhythmic values is mostly aligned to

structure. There are, however, five peaks or troughs which do not align. The two most

significant alignments (bb.14 and 16) are part of the rhythmic pattern shown in Figure 72,

where potential symmetry is thwarted. Bars 14 and 16 generate the expectation of

symmetry in Figure 72, before it is disrupted. As with numerous occasions disruptions on

one level contribute to symmetry, or the expectation of symmetry on another. Figure 86

shows the rhythmic profile for Episode 2. Since the Episode is almost entirely quaver

dominated, only the structural alignments around the changes in the rhythmic profile are

shown.

11

The rhythmic profile is a graphical representation of the predominant metrical value in each bar.

PR

ED

OM

INA

NT

RH

YT

HM

IC V

AL

UE


20

BAR

FIGURE 86: STRUCTURAL ALIGNMENT IN RHYTHMIC PROFILE OF EPISODE 2

Figure 86 shows that the rhythmic profile does align with structure. Figure 87 below shows

the rhythmic profile for Episode 3.

BAR

FIGURE 87: STRUCTURAL ALIGNMENT IN RHYTHMIC PROFILE OF EPISODE 3

The onset of a new predominant rhythmic value again aligns structurally in Episode 3.

Each Episode can be seen to build and build, before a moment of climax releases the tension

and allows for the music to begin building again. In Episode 1 this happens at bar 47; in

Episode 2 in bar 146; and in Episode 3 at bar 49. The table below shows the location of these

PR

ED

OM

INA

NT

RH

YT

HM

IC V

AL

UE

P

RE

DO

MIN

AN

T R

HY

TH

MIC

VA

LU

E


21

moments with percentages in terms of the number of beats and number of bars through the

composition.

EPISODE 1 EPISODE 2 EPISODE 3

BAR % BEAT % BAR % BEAT % BAR % BEAT %

72 72 60 60 71 67

FIGURE 88: BAR/BEAT PERCENTAGES OF MOMENTS OF CLIMAX WITHIN THE EPISODES

Figure 88 shows that the bar and beat percentages align in the first two Episodes, but do not

in the third; probably because it was impossible to get the percentages closer together,

considering that the process of growth immediately after the climax has to begin on the bar-

line. All three do, however, align structurally, and do match to the rhythmic profiles of the

Episodes. The pitch-circulation graphs from the final section of the first essay were also

shown to align structurally in most cases, and so there it can be concluded that rhythm,

pitch-circulation and moments of climax do all align structurally. Any anomalies of pitch-

circulation and structural mismatch were attributed to the beginning of a new aggregate

cycle, which had been shown to not have aligned with the structure in some cases. It

remains, then, to investigate whether these misalignments can be attributed to rhythmic

factors.

In Episode 1 the most noticeable anomalies shown in the pitch-circulation graphs were bb.2-

3, 26-28, and 33-34. In the first of these cases the aggregate is formed within the first two

bars; bb.3-4 function as a linking passage between bb.1-2 and the new idea introduced at bar

5, explaining the structural mismatch. The aggregate formed by bar 26 occurs because this

analysis accounted for the pitch-classes within the glissandi, and is therefore a by-product of

the motive, rather than a deliberate mismatching of aggregates and structure. The aggregate

formed in bb.33-34 again occurs before a two-bar linking passage, leading to the 5/4 bar

through which the main weight of the metrical scheme acts (see Figure 61). The aggregates

in Episode 1 are therefore not structurally misaligned – they occur at the end of the section

and are explained because this analysis demarcates sections according to where new

motives and ideas are introduced (as well as a change in the predominant rhythmic value). It

does not account for linking bars, hence why these aggregates appeared to be structurally

misaligned.12 This is also the case for Episodes 2 and 3: the aggregates appear at the end of

the section, with linking bars following them.

12 The term ‘misaligned’ is not used in a pejorative sense, but to observe how the location of the aggregates differs from the

structural divisions in the score.


22

The number 5 has been shown to play an important organisational role, permeating the

metrical schemes, pitch-class sets, linear progression and set cells, as well as acting as a

disruptive agent on multiple levels. The Episodes feature five of Messiaen’s modes (I, II, III, V,

and VII) as underlying processes, but are controlled by whole-tone processes in the outer

Episodes and by mode III in the case of Episode 2. Each Episode is also concerned with the

use of ten-, eleven- and twelve-note aggregates, with the sets used each being subsets of the

two 10-note sets to which each Episode can be traced. These, together with the controlling

processes outlined above, interact within the pitch-related elements. The interaction of

symmetry and disruption permeates each level (of surface, underlying, and controlling

processes), with deeper levels of symmetry evolving from disruption at surface levels. It has

been demonstrated that disruption at any level arises from the disruptive element (or agent)

contributing to a symmetry on a larger scale, or at a different level.

Similarly, any structural mismatches, between pitch-circulation, consonance, dissonance,

aggregate cycles, or rhythmic profiles have been shown to also be due to the contribution of

the thwarting element to symmetry at another level. It has been shown that the mismatch of

aggregate cycles to structure was not due to rhythmic or motivic factors, but rather because

the segmentation of the Episodes for this analysis was primarily concerned with where new

sections began, and therefore did not take account of any linking passages between sections.

The aggregates appear at the end of the section, before any transition bars, and therefore

appear mismatched within the graphs.

The use of symmetry on multiple levels engenders and necessitates disruption. Dallapiccola,

in recognising the impossibility of having pure symmetry at multiple levels within the music,

uses disruptive agents and elements to also permeate the piece in order to facilitate and

initiate symmetry at deeper levels, whilst maintaining a propulsive element in the music

(necessary because of the stasis risked by purely symmetrical elements). This risk of stasis

explains why deeper symmetry ultimately evolves from disruption at surface levels (see

Figure 43 in essay 1), rather than the other way around. Ultimately, it has been shown that

the disruption and elements of mismatch within these Episodes are both caused by, and

indeed contribute to, symmetry.


23

BIBLIOGRAPHY

Alegant, B. (2010) The Twelve Tone Music of Luigi Dallapiccola. Rochester: University of Rochester Press.

Alegant, B. (2006) Octatonicism in Luigi Dallapiccola’s Twelve-Note Music, in Music Analysis 25/1: 39-87.

Cook, N. (1987) A Guide to Musical Analysis. Oxford: Oxford University Press.

Dunsby, J. and Whittall, A. (1988) Music Analysis in Theory and Practice. London: Faber.

Eckert, M. (1985) Octatonic Elements in the Music of Luigi Dallapiccola, Music Review 46: 35-48.

Fearn, R. (2003) The Music of Dallapiccola. Rochester: University of Rochester Press.

Forte, A. (1973) The Structure of Atonal Music. Yale: Yale University Press.

Forte, A. (1986) Liszt’s Experimental Idiom in 19th-Century Music 10/3: 209-28.

Forte, A. (1991) Debussy and the Octatonic, Music Analysis 10/1-2: 125-69.

Lester, J. (1989) Analytic Approaches to Twentieth-Century Music. New York: Norton.

Lewin, D. (1998) Some Ideas about Voice-Leading Between PC-Sets, in Journal of Music Theory 30/ii: 79-102.

Mancini, D. (1998) Twelve-tone Polarity in Late Works of Luigi Dallapiccola, in Journal of Music Theory 30/ii: 203-24.

Messiaen, O. (1944) Le Technique de mon language musical. Paris: Leduc, anonymous translation from

www.courses.unt.edu/jklein/files/Messiaen1_0.pdf

Schuijer, M. (2008) Analysing Atonal Music: Pitch-Class-Set Theory and its Contexts. Rochester: University of Rochester Press.

Online resources:

www.jaytomlin.com/music/settheory/help.html

www.solomonsmusic.net/setheory.htm

www.mta.ca/faculty/arts-letters/music/pc-set_project/pc-set_new/

Set calculations done online from:

www.jaytomlin.com/music/settheory

www.mta.ca/faculty/arts-letters/music/pc-set_project/calculator/pc_calculate.html

Dallapiccola Analysis Essay 2 - Alex Aitkenalexaitken.co.uk/assets/Metrical and Rhythmic Analysis...

Documents

Transcript of Dallapiccola Analysis Essay 2 - Alex Aitkenalexaitken.co.uk/assets/Metrical and Rhythmic Analysis...