Analysis of Bela Bartok's String Quartet No.4 Movement 3

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Bela Bartok¡¦s third movement of his fourth string quartet written in 18 has a highly engaging and emotive effect on the listener as Bartok¡¦s harmonic world reveals a highly sonorous and atmospheric sound-scape. It is difficult to identify any fundamental scale, mode or tonal center. However, based on Bartok¡¦s reputation in the world of ethnomusicology and his penchant for intermingling folk music and traditional western harmonic practices, it would not be any surprise to find that through set theory analysis modes play a functional in the tonal structure of the movement. This analysis focuses on the pitch class collections obtained from segmenting the movement and how it relates to traditional analytical parameters such as articulation and form.

Bartok¡¦s Sting Quartet No.4 comprises of 5 movements. The slow movement (III) is the kernel of the work, with the 4 other movements arranged in layers around it. Bartok employed an arch form when constructing the quartet A-B-C-B-A (fast-scherzo-slow-scherzo-fast). The slow movement (III) is the kernel of the work; with the 4 other movements arranged in layers around it.

The third movement contains material independent of the other movements as a means of contrast and highlighting it as the central movement and point of symmetry. Within the third movement itself Bartok has employed a ternary form that is symmetrically sectioned (the coloured bands in the score).

A- Non troppo lento [mm.1]

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„� 1 [mm. 1-1]

„� 8 [mm. 14-1]

„� 1 [mm. -4]

„� 8 [mm. 4-41]

B- Agitato [mm. 4]

„� 5 [mm. 4-46]

„� 8 [mm. 47-54]

A¡¦- Tranquillo [mm.56]

„� 8 [mm. 55bt-6bt]

„� 8 [mm. 64-71]

Each of these coloured band sections are distinct and different through Bartok¡¦s use of different pitch class sets, articulations and constant timbral and textural changes.

Form/Section Band Colour Measure Number Timbre

A 1

Bars Brown mm. 1-1 Solo Vc

PCSet -6

Accomp VnI & II, Va

PCSet 6-


Bars Yellow mm. 14-1 Solo Vc

PCSet 8-11, -6

Accomp VnI & II, Va

PCSet 6-18


Bars Orange mm. -4 Solo Vc

PCSet 7-

Accomp VnI & II, Va

PCSet 6-4


Bars Green mm. 4-41 Solo VnI

[Entire ¡§codetta¡¨ uses PCSet 8-10 as the solo Vn part does not have enough notes to form a set]

Accomp VnII, Va, Vc

PCSet 6-Z45

B 5

Bars Pink mm. 4-46 Solo VnII

PCSet 7-5

Accomp VnI, Va, Vc

PCSet 6-Z


Bars Turquoise mm. 47-54 ¡¥Solo¡¦VnII Pcset 7-1

Va Pcset 5-Z1

Canon PCSuperset 8-

Accomp VnI, Vc

PCSet 5-5

A¡¦ 8

Bars Purple mm. 55bt-6bt ¡¥Solo¡¦ Canon VnI, Vc

No Main Dominating PCSet

Accomp VnII, Va

PCSet -6, 7-5, 6-Z46, 6-

8 Red mm. 64-71 Solo VnI

PCset -6

Accomp VnII, Va, Vc

PCSet mainly 6-

An entire dissertation can be written Bartok¡¦s use of symmetry in this string quartet. This particular analysis focuses on set theory more than Bartok¡¦s use of symmetry in this movement. However symmetry is inherent in every single part of this movement eg. Form ternary; symmetry in the prominent sets found eg. -6, 7-5; use of canon (which will be discussed later). Bartok uses the chromatic sets eg. 6-1 and set 7-1 most notably that have a tonal axis of symmetry eg. mm. 47-4 in the violin II set 7-1 is used with the notes A-Bb-B-C-Db-D-Eb. C is used as a point of tonal reference (axis/mirror). However instead of utilising the chromatic possibilities in the set, Bartok plays mirror games, alternating between pitches. This is seen throughout the movement ¡VIn mm.47 in the semi-quaver triplet A rises to B, and Bb rises to C moving diatonically using the first ¡¥half¡¦ of set 7-1. In mm.48 Eb drops to Db and D drops to C. The overall set effect of movement towards the central axis, C. In contrast, in mm. 67-68 set 6-1 (0,1,,,4,5) A-G#-G--F#-F-E there is movement from the middle of the set out ie. mm. 67 beat G drops to F and F# drops to E. mm.68, F# rises to G#, and G rises to A. Using the overlap of the two central pitches G and F# there is an overall set effect of movement outwards to the ends of the set which is emphasised by the initial A-E chord on mm. 67 beat and mm. 68 beat .

A graph was made for statistical purposes showing the frequency of the pitch class sets that were segmented in the movement. The top five are as follows

PCSet Freq

6- 14

-6 7

7-5 6

4- 6

4-1 4

Set 6- had the most number of occurrences. This is attributed to the fact that it was used on numerous occasions as a chord pedal but most noticeably at the beginning of the movement mm.1-1 and at the end mm. 64-6. It is worth mentioning that although set 6- is used eg. in the beginning and the end of the movement, the chordal spacings and distribution of pitches vary and are distinctly different. However the spacings of the accompanying chord pedal are usually wide (eg. 4ths, 6ths) as a means of contrast to the diatonic-chromatic thematic material. Another trend to note from the PCSet frequency table is that eighty percent of the top five sets are symmetrical.

As in most tonal music, Bartok uses cadences at the end of sections. In the absence of keys and modulations, there are particular pitch class collections that are used cadentially or as a final chord to end a particular section.

Measure Set Note

1 6- Subset of -6

1 7-4 Subset of -6

6- �É 8- Subsets of -6

41 6-Z11 Subset of -6

54 6-4 Subset of -6

6 5- Subset of --1

6-70 8-�É7-5 Subsets of -6

Bartok assigned precise articulations (eg. sul ponticello, vibrato, pizzicato, harmonics) to particular textures and instrumentation, almost as an aural indicator. These articulations and instrumentational groupings underpinned many of the decisions in segmenting the work. Eg. Throughout the movement the accompaniment has a specific articulation as a distinguishing characteristic eg. Violin I & II & viola are the accompaniment mm.1-4 Bartok denoted non-vibrato vibrato. The oscillating ensuing texture provides a contrast to the solo violoncello mm1-4 where espressivo is specified.

Other examples where paired articulation specifications denote the solo or accompaniment texture is in mm.4-46 where a legato Violin II plays on sul IV (darker tone) stands out against the violin I, viola & violoncello¡¦s distinctive alternations of sul ponticello tremolos and ordinary bowing providing a contrasting percussive texture. Also mm.55-5 where the accompaniment (violin II & viola) use mutes (con sordino) and the thematic duo (violin I & violoncello) are marked espressivo. Again in mm.47-4 the viola line is prominent through its change in register and use of harmonics that aid in the aural identification of a new section (turquoise colour band) and the introduction of a subset of -6, 5-Z1.

The beginning of Section B (mm.4) ¡VAgitato- is structurally significant, as all preceding material (mm.4-40-codetta) appears to lead up to it. This is emphasised by the unprecedented pizzicato texture change and use of sul ponticello from mm.40. Utilising the Golden mean (0.618) based on the Fibonacci series (a series based on the sum of previous numbers) in this movement mm.4-46 are the natural climactic point or apex (¡¥in an ideal ratio¡¦) of the movement.

4/71= 0.515 4/71=0.6056 44/71=0.617 45/71=0.68 46/71= 0.647

From the ¡¥Kh Relationships ¡VMileage Chart¡¦ & the bar graph showing the total number of Kh Relationships, it can be seen that a Nexus set is present by the high number of Kh relationships that set 4- (047) has (excepting the Set ¡§¡¦s¡¨).

Despite having the next highest number of relationships that set 6- had, its function as a nexus set was dismissed as a possibility. Set 4- is a more logical choice due to a number of reasons; such as 4- is a subset that is consistently found within other sets eg. 7-5, 6-, 6-Z45. The modal aspect of the set is consistent with Bartok¡¦s reputed use of folk tunes a modal flavour that permeates through the entire movement.

A combination of -6 & 4- (subset of -6) on the Kh Mileage chart reveal that they have relationships with almost all the sets. Conversely, there are certain sets that are independent of relationships to -6 or the nexus 4-. [These are highlighted on the Kh mileage chart in yellow.] These independent sets are 5- (0,1,4,6,); 6-18 (0,1,,5,7,8); 6-Z (0,,,6,7,); 8-8 (0,1, ,4,7,8,). Their purpose is to have an unrelated pitch class set that complement and contrast with other material. eg. The use of set 6-18 as a harmonic chord pedal accompaniment mm.1-0 in Violins I & II & Viola. Section B¡¦s material for the first five bars (mm.4-46) comprise of set 6-Z, it is used in the accompaniment. Set 6-Z¡¦s super set 7-5 is used as the solo violin thematic material. Set 5- is a subset of -1. -1 and it¡¦s subsets (eg. 6-Z6, 6-Z46, 7-Z17, 7-6)is a set that is used and featured in Section A¡¦ mm.55 beat -6 mostly in the violoncello part.

-6 (0,1,,,4,5,6,8,10) is a superset that is used and whose subsets features often. In the Kh mileage chart, -6/-6 had the most Kh relationships, however that is not an objective validation as ¡§¡¦s¡¨ have a lot of relationships. -6 however does occur a lot and manifests itself through its many subsets. An interesting feature of -6 as a superset are the characteristics of its subsets chromatic (eg. 6-1, 4-1); diatonic (7-5); pentatonic (5-5 & nexus 4-) and whole-tone scale (5-) encapsulated under set -6. All these possible sets are consistently featured in the movement. These particular multi-faceted harmonic characteristics of -6 allow Bartok to create a cohesive sound world in which to combine folk modes & traditional western harmony as seen throughout the movement.

The set -6 dominates the entire first thirteen bars of A. -6 is a superset to all of the sets found through segmentation mostly by phrase or texture (i.e. Homophony which is the predominating texture in this movement).

Accompaniment- solely 6- (0457)

[whose subsets are -6 (04), 4- (047), 5-5 (047)]

Solo Vc-subsets of -6

7-(0158); 4-1 (01); 6-1 (0145); 6-Z6 (01578); 7-5 (0156810)

Set -6 is omitted throughout Section B but makes its return in the chord pedal accompaniment through muted violin II and viola in mm.56-5 (Section A¡¦).

In section A¡¦ mm. 67-71 (Red Band colour -final ¡¥codetta¡¦) set -6 is used to provide the static harmonic pedal in comparison to Section A where solo violoncello thematic material was derived from -6.

There is significant use of canons in mm. 50-54 and in Section A¡¦ (a free recapitulatory section mm.55 beat -6). Bartok does not use strict canon, instead he uses a ¡¥free¡¦ canonical form, as well as free imitation. In mm. 50 the violin II and viola are a quaver apart with the viola taking the ¡¥lead¡¦ and playing pitches higher than violin II. The violin II imitation is not exact. Bartok uses a mirror canon in mm.5-54 between violin II and the viola moving in contrary motion. The set used is 8-6 (0,1,,,5,6,7,8) which comprises of two sets of 4-1 each part playing their own respective 4-1 set. Bartok utilises the symmetry of 4-1 in the mirror canon and the exclusive pitch class set 8-6 that is unrelated to -6 and 4-.

The use of canon in Section A¡¦ (purple colour band) is between the violoncello and violin I. Beginning in mm.55 beat with violoncello (using set 7-6), violin I enters three crotchet beats later on an initially contracted imitation in almost exact contrary motion (using set 7-5). In mm. 57 beat 4 the violoncello begins another phrase (using set 8-14). Violin I answers two crotchet beats later again in almost exact contrary motion (using set 7-14). The next phrase begins with the violoncello in mm.5 beat 4 (using set 8-8) and answered two crotchet beats later by violin I a tritone higher in similar motion (using set 7-4). The next phrase begins in mm. 60 with violoncello (using -1) is a crotchet beat apart from violin I (using set 6-Z46 followed by 7-Z17 [a subset of -1]).

Set theory is useful in analysing a work such as this in order to comprehend the underlying tonal structure of the work and gain an insight into Bartok¡¦s compositional machinations. On analysis of the movement the overall harmonic world that Bartok employs in this movement is a tonal one with strong modal influences. Particular pitch collections consistently appear such as the whole-tone scale (0,,4,6,8,10); the pentatonic scale (0,,4,7,); diatonic collections such as 7-4(0,1,,4,6,8,10) and 7-5 (0,1,,5,6,8,10); and chromatic collections such as 5-1 (0,1,,,4) and 6-1 (0,1,,,4,5).

As previously mentioned the representative pitch class superset that embody Bartok¡¦s ambitions with regards to the movement (i.e. the interactions between diatonic and modal) is -6 (0,1,,,4,5,6,8,10). It is a hybrid superset that contains chromatic, diatonic and modal elements that reveal Bartok¡¦s reasons for utilising it and its subsets liberally throughout the movement. However to gain a complete insight into Bartok¡¦s compositional manoeuvrings, techniques and style, set theory is limited in its revelations. Other analytical techniques such as those of tone clock and twelve-tone analysis would be inappropriate and unsuitable in this particular work. Nevertheless, an extensive analysis of structure and symmetry would expose more clearly Bartok¡¦s compositional genius.


Any outside materials or Set Theory Ideas or information were obtained from

Jay Tomlin¡¦s Set Theory Calculator


Larry Solomon¡¦s website for Set Theory


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