Principles of Large-Scale Organization in Bartók’s Improvisations, Opus 20

by

Elizabeth Anne Kelly

Submitted in Partial Fulfillment

of the

Requirements for the Degree

Doctor of Philosophy

Supervised by

Professor Robert Hasegawa

Department of Music Theory Eastman School of Music

University of Rochester

Rochester, NY

2012

! ""!

Curriculum Vitae

The author was born in New York City, New York on August 19, 1982. She

attended Yale University from 2000 to 2004, and graduated with a Bachelors of Arts

degree, summa cum laude, in 2004. She attended the University of Michigan School

of Music from 2004 to 2006 with the support of an Ellen Marin Memorial

scholarship, and graduated with a Master of Music degree in 2006. She came to the

University of Rochester in 2006 and began graduate studies in music composition.

She received a Jacob K. Javits Fellowship from the United States Department of

Education from 2006 to 2010 and a Robert and Mary Sproull fellowship from the

University of Rochester from 2006 to 2012. She won a Frank Huntington Beebe

Fellowship to study at The Hague Royal Conservatory in the Netherlands in 2010-

2011. She pursued her research in Bartók under the direction of Professor Robert

Hasegawa.

The author’s compositions have been commissioned and performed by diverse

ensembles including the Ann Arbor Symphony, Cabrillo Festival Orchestra, New

York Youth Symphony, Netherlands Youth Orchestra, Janacek Philharmonic

Orchestra, Albany Symphony Dogs of Desire Ensemble, California EAR Unit, Asko

Schoenberg Ensemble and Aspen Contemporary Ensembles at venues throughout the

United States and Europe. Her work has been recognized with numerous awards from

the American Society of Composers, Authors and Publishers. In the Netherlands, she

won Second Prize at the 2009 Apeldoorn Young Composers Competition and First

Prize at the 2011 Young Masters XXI Competition.

! """!

Abstract

Improvisations, Opus 20 was the first work that Béla Bartók composed after

the 1920 Treaty of Trianon stripped Hungary of over two-thirds of its territory and

inhabitants. In the eight-movement set for solo piano, Bartók memorializes the forced

dismemberment of his country by including settings of peasant music collected from

the farthest reaches of the former Kingdom of Hungary. While Bartók’s sketches

indicate that he did not compose the movements in the order in which they appear in

the score, close examination reveals a carefully constructed arch form unfolding in

several dimensions. The first and second parts of the dissertation explore the regional

origins and characteristics of the peasant source materials. The third and fourth parts

of the dissertation focus on the materials that Bartók added to the peasant source

songs, particularly the modernist harmonies that he employs and the contrapuntal

structures that he creates. Pitch-class set analysis is utilized to trace the recurrence

and interaction of octatonic, whole-tone, and diatonic sets throughout the work.

! "#!

Table of Contents

Introduction 1

Part 1 Analysis of the Progression Through Peasant Source Materials 2

1.1 Regional Origins of Source Materials 2

1.2 Classification of Peasant Source Materials 4

1.3 Manifestations of “Class A” Characteristics 5 in the Peasant Source Materials 1.4 The Fourth and Sixth Improvisations: 12 The “Class C” Source Songs Part 2 Modality, Symmetry and Centricity in the Melodies of Improvisations 14 Part 3 The Harmonizations of the Peasant Melodies in Improvisations 21

3.1 Relationship Between the Source Melodies and Harmonies: 21 The Modal/Atonal Conflict 3.2 Strategies for Convergence and Divergence Between 23 the Melodic Key Centers and Bartók’s Harmonizations: A Close Reading of the First Improvisation

3.3 Interval Class 1 as Structuring and Confounding 27 Harmonic Force throughout Improvisations:

The First, Second and Eighth Improvisations 3.4 Ic1 in the Third and Fifth Improvisations 29 3.5 Structural Implications of the Tritone, ic6: 32 Imitative Counterpoint and the Third, Fifth and Eighth Improvisations

3.6 Structural Implications of the Tritone: 34 Tritone Bass Descent in the Second and Eighth Improvisations

Part 4 Prominent Pitch Class Sets in Improvisations 36

4.1 Octatonic Subsets 1: The Major/Minor Tetrachord, [0347] 37

! #!

4.2 The Role of Whole-Tone Collections and Augmented Triads 45 4.3 Octatonic Subsets 2: The Z-cell, [0167] 48

Conclusion 51 Bibliography 53

Appendix 1: Bartók’s Catalogue of Improvisations Folk Source Songs 55

Appendix 2: Map of the Kingdom of Hungary before the Treaty of Trianon 56

! #"!

List of Tables

Table Title Table 1 Regional Origins of the Eight Improvisations 3 Table 2 Table of Old Hungarian Characteristics in Each Source Song 8 Table 3 Bar Count and Duration Ratios in Improvisations 13 Table 4 Table of Pitch Centers, Modes and Symmetry 14 Table 5 Points of Convergence and Divergence Between the 26-7

Pitch Centers of the Peasant Source Melodies and Bartók’s Harmonizations

! #""!

List of Figures Figure Title Figure 1 Pentatonic Scale on G 5 Figure 2 The Third Improvisation Source Song: 6

A Typical Descending Melody Figure 3 The Seventh Improvisation Source: 6

A Parlando Transcription Figure 4 The Second Improvisation Source: 7

Invariable Dance Rhythm Figure 5 Hungarian Heptatonic Mode: 9

Non-Pentatonic but Symmetrical Figure 6 The Fourth Improvisation Source: 10

Modifications to the Pentatonic Figure 7 The Fourth Improvisation: 11

Pentatonic Grace Note (B-flats) in mm. 7-10 Figure 8 G-Pentatonic Suggestion in the Third Improvisation 16 Figure 9 Symmetry and Pentatonicism of the Dorian Mode 16

(Non-Pentatonic Notes Marked with x) Figure 10 Asymmetrical Mixolydian in Second Source 17 Figure 11 Pentatonicism and Asymmetry of G-Aeolian 17

(Non-Pentatonic Notes Marked with x) Figure 12 Asymmetrical Pentatonicism of C-Aeolian and C-Phrygian 19

in the Bimodal Seventh Improvisation C-Aeolian of mm. 1-5 (Non-Pentatonic Notes Marked with x)

Figure 13 D-flat in m. 8 of the Seventh Improvisation Shifts Tune into 19 Asymmetrical C-Phrygian and a New Pentatonic Transposition (Non-Pentatonic Notes Marked with x)

Figure 14 Aeolian Alteration in Eighth Improvisation, mm. 69-74 20 Figure 15 Dyad as Dominant in the First Improvisation, mm. 1-5 23 Figure 16 F -major emphasis of the First Improvisation, mm. 5-8 24 Figure 17 D-minor Emphasis in the First Improvisation, mm. 9-12 25 Figure 18 Destabilizing D-flat and G-flat of the First Improvisation 25 Coda, mm. 13-16 Figure 19 The Eighth Improvisation Final Chord with 28 L.H. B/C Subset Figure 20 C-sharp/F-sharp to D/G in the Third Improvisation, 29

mm. 1-4 Figure 21 The Third Improvisation closing with verticalized pedal, 30

mm. 40-end Figure 22 Unfurling to [0156] in the Fifth Improvisation, mm. 22-6 31

! #"""!

Figure 23 The Fifth Improvisation Final Chord with Bass [0156] 32 Subset Presenting as F/G/C-sharp/D

Figure 24 Tritone Between R.H./L.H. in the Third Improvisation, 33 mm. 32-37

Figure 25 Canon with tritone relationship at End of the Fifth 33 Improvisation, mm. 57-68

Figure 26 Canon at the tritone in the Eighth Improvisation, 34 mm. 53-60

Figure 27 Octatonic and Whole-Tone Scales as Stacked Thirds 37 Figure 28 [0347] tetrachords in the First Improvisation, mm. 5-8 38 Figure 29 Octatonicism in the First Improvisation, mm.9-10 39 Figure 30 Octatonic Interpenetration of C-Dorian in the 39

First Improvisation, mm. 5-8 in the Fourth Improvisation, mm. 29-32

Figure 31 [01347] in the Second Improvisation, mm. 37-53 40 Figure 32 [0347] Tetrachords in the Third Improvisation, mm. 23-30 41 Figure 33 [0347] in the Sixth Improvisation, mm. 15-18 42

the Third Improvisation opening harmony Figure 34 [0347] as Central Harmony in the Seventh Improvisation, 43 mm. 12-16 Figure 35 [0347] Harmonies in mm. 8-18 of the Eighth Improvisation 44 Figure 36 [0134567] sonority in penultimate measure of the 45 Eighth Improvisation Figure 37 Whole-Tone and Augmented Harmonies in the 46 Third Improvisation, mm. 19-22 Figure 38 Whole-Tone and Augmented Harmonies in the 47 Third Improvisation, mm. 26-30 Figure 39 Whole-Tone Implications of Accompanying Scale in the 47

Fourth Improvisation, mm. 1-4 Figure 40 Whole-Tone Dyads in Aligned Z-Cells 49 Figure 41 Octatonic Z-cell Pairs in the Eighth Improvisation Finale 50

!

!

"!

Introduction

On June 4, 1920, the Treaty of Trianon between the Allied Powers of World War

I and the Kingdom of Hungary, successor to the Austro-Hungarian Empire, radically

redrew the Hungarian map. Hungary lost over two-thirds of its territory and inhabitants.

Béla Bartók was devastated. It was now impossible for him to carry his phonograph over

the new borders to collect peasant songs.1

In September 1920, Bartók sent his publisher, Universal Edition of Vienna, one of

the short piano pieces that he would later include in Improvisations. He told his publisher

that he had already written six such pieces and that he would send the set when he had

completed twelve or fifteen of them.2 Ultimately, Improvisations would comprise eight

pieces. In Improvisations, Bartók memorialized the forced dismemberment of his country

by including settings of Hungarian peasant music from the farthest reaches of the former

Kingdom of Hungary, including music from modern Romania, Serbia, Croatia and

Slovenia.3 Most of the pieces manifest ancient Magyar (ethnic Hungarian) origins.

However, two pieces at key junctures in the set suggest influence from non-Magyar

Austro-Hungarian ethnic groups. Perhaps Bartók was mourning the end of the fruitful

ethno-musical exchanges that he had documented during his sojourns in the former

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1 Béla Bartók in Benjamin Suchoff, Béla Bartók Studies in Ethnomusicology

(Lincoln: University of Nebraska Press, 1997), xiii. 2 Ivan Waldbauer, “Analytical Notes to Bartók’s Improvisations, Op. 20 and the

Ordering of the Series” in Lazslo Vikarius and Vera Lampert, Essays in Honor of Laszlo Somfai on His 70th Birthday (Lanham, The Scarecrow Press, Inc., 2005), 425.

3 Benjamin Suchoff, Bartók: Concerto for Orchestra (New York: Schirmer Books, 1995), 74.

!

!

#!

Kingdom.4 While Bartók’s sketches indicate that he did not compose the Improvisations

in the order in which they appear in the score,5 an examination of patterns and

progressions through the piece reveals a carefully constructed arch form unfolding in

several dimensions.

In this study, I will analyze Bartók’s ordering of the peasant source materials in

Improvisations before moving into an examination of his settings of the source tunes.

Part 1. Analysis of the Progression Through Peasant Source Materials

1.1 Regional Origins of Source Materials

When Improvisations was published, Bartók furnished Universal Edition with

transcriptions of the peasant source materials. He annotated each transcription with the

name of the village and county where the song was collected.6 The regional distribution

of the peasant source songs gives the first indication that Bartók carefully chose the

ordering of his eight Improvisations.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!4 Suchoff, Béla Bartók Studies in Ethnomusicology, 138. 5 Waldbauer, “Analytical Notes,” 431. 6 See Appendix 1 for the transcriptions that Bartók provided.

!

!

$!

Table 1: Regional Origins of the Eight Improvisations7

Number Region of Origin/Orientation w/in

Kingdom of Hungary

Post-Trianon Location

1 Tolna (central) Central Hungary 2 Zala (west) Southwest Hungary on Croatian/Slovenian

border 3 Szerem (south/central) Divided between Serbia in east and Croatia

in west 4 Tolna (central) Central Hungary 5 Zala (west) Southwest Hungary on Croatian/Slovenian

border 6 Czik (east) Romania (eastern Transylvania) 7 Udvarhely (east) Romania (eastern Transylvania) 8 Szilagy (east) Romania (northwest)

The attacca markings in Improvisations suggest that the piece can be divided into

three sections – movements 1-2, 3-5 and 6-8. (In the table above and those that follow,

section 2 is italicized to demarcate it from sections 1 and 3.)

The first two sections manifest a symmetrical regional distribution. In the first

section, Bartók exclusively presents music from regions that remained in Hungary after

the Treaty of Trianon. He opens with music from central Tolna county. In the second

movement, he ventures west to the post-Trianon borderland county of Zala. Bartók opens

the second section with the first piece in the collection based on material collected

outside of post-Trianon Hungary. The Third Improvisation is a setting of a peasant song

from Szerem county, which was divided between Serbia and Croatia after 1920. Settings

of material from Tolna and Zala bring the second section to a close.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7 See Appendix 2 for a map of counties in the Kingdom of Hungary.

!

!

%!

In the third section, Bartók exclusively sets music from post-Trianon Romania,

formerly the eastern Kingdom of Hungary. Thus, there is a large-scale division between

the music from western and central Kingdom of Hungary presented in sections 1 and 2,

and the music from the east presented in section 3.

1.2 Classification of Peasant Source Materials

However, while the source material for Improvisations was thus collected from

highly disparate regions in the former Kingdom of Hungary, much of it from counties

that took on new national identities in 1920, all of the source material was sung in

Hungarian to songs derived (at least in part) from ancient Magyar traditions. Bartók

classified six of the eight source songs (1, 2, 3, 5, 7, and 8) as “Class A” old Hungarian

peasant music.8 After 1920, Bartók mainly set “Class A” songs, although these songs

represented less than a third of the total songs that he collected. He was drawn to these

ancient songs, because they were the least touched by Western European influence and

thus, despite their great age, the most “novel” to Western, classically trained ears.9 The

source songs for the Fourth and Sixth Improvisations have unusual features that led

Bartók to place them in his “Class C” of songs that manifest both Magyar and foreign

influence. The “foreign” influence was mainly transmitted by other ethnic groups living

in the former Kingdom of Hungary.10 It is noteworthy that the Fourth Improvisation, one

of the two foreign-influenced pieces in the collection, hails from central Tolna county. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

8 Vera Lampert, “Bartók’s Choice of Theme for Folksong Arrangement: Some Lessons of the Folk-Music Sources of Bartók’s Works,” Studia Musicologica Academiae Scientiarum Hungaricae 24 (1981), 406.

9 Béla Bartók, Hungarian Peasant Music in Benjamin Suchoff, Béla Bartók’s Essays. (Faber and Faber: London, 1976), 102.

10 Suchoff, Béla Bartók Studies in Ethnomusicology, 176.

!

!

&!

Before borders were erected, the free flow of a wide range of ethnic groups through the

Kingdom of Hungary had facilitated ethno-musical exchange even in the Magyar-

dominated heart of the country.

1.3 Manifestations of “Class A” Characteristics in the Peasant Source Materials

Bartók’s “Class A” old Hungarian melodies manifest similar formal, modal and

rhythmic characteristics. All “Class A” melodies feature a four-section form with each

section in the melody corresponding to a strophe of the song text. The first and fourth

sections of the melody are always different. Often, all of the sections are different. Each

section is isometric with either six, seven, eight, nine, ten, eleven of twelve syllables per

line. “Class A” melodies usually feature the ancient pentatonic scale.

Figure 1: Pentatonic Scale on G

Many “Class A” Hungarian peasant songs have a “descending structure.” These

melodies open in the upper tetrachord of their mode before descending to the lower

tetrachord of their mode in the second or third sections. The third peasant song of

Improvisations from Szerem County is a typical example of a descending melody.

!

!

'!

Figure 2: The Third Improvisation Source Song: A Typical Descending Melody11

“Class A” old Hungarian melodies display three types of rhythms. Many of the

songs are in a highly ornamented parlando rubato, particularly beloved by Bartók, who

considered these songs the “most important” and uniquely Hungarian.12

Figure 3: The Seventh Improvisation Source: A Parlando Transcription

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11 Figures 2, 3, 4 and 6 are reprinted from Universal Edition 7079. See my

Appendix 1 for transcriptions of all of the peasant source tunes supplied by Bartók to Universal.

12 Suchoff, Béla Bartók Studies in Ethnomusicology, 175.

!

!

(!

Other “Class A” songs are in invariable dance rhythm, usually in 2/4.13

Figure 4: The Second Improvisation Source: Invariable Dance Rhythm

An examination of the “Class A” old Hungarian characteristics present in each

movement’s peasant source further illuminates the architecture of the collection. The

regional distribution of the songs suggests an arch shape through the first and second

sections with a significant regional shift in the third. However, a closer examination of

the characteristics of the songs themselves demonstrates how the final section strongly

connects to the first to create a larger arch form. The final section also draws together

elements that differentiate sections 1 and 2.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

13Suchoff, Béla Bartók Studies in Ethnomusicology, 175.

!

!

)!

Table 2: Table of Old Hungarian Characteristics in Each Source Song14

# Class Pentatonic Origin?

4-section?

Descending?

# of syllables/

line

Rhythmic type

Source Tempo

Bartók Tempo

1 AI Y Y N 6 giusto

quarter=

110-20

half= 44-6

2 AI Y (in

sections 3-4)

Y N 7 dance fast fast-faster

3 AI N Y Y 6 parlando slow slow

*4

CII Y (melody was of

pentatonic origin)

6-section

Y 776/ 776

dance quarter= 93

quarter= 108 to 132-

126

5 AI Y Y Y 6 dance fast half= 84 to

92 *6

CI Y Y Y 7/7/11/11

adjustable parlando with fast,

tempo giusto

intro and close

fast quarter=108,

86, 116, 108

7 AI Y Y N 6 parlando slow quarter=66,

rubato 8 AI Y Y Y 7 dance quarter

=104 quarter = ~120

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"%!Information on Class, Rhythmic Type and Tempo and Source Tunes taken from

Vera Lampert, Folk Music in Bartók's Compositions: A Source Catalog : Arab, Hungarian, Romanian, Ruthenian, Serbian, and Slovak melodies (Budapest: Hungarian Heritage House, 2008), 149-154.!

!

!

*!

All of the songs in sections 1 and 3 are of pentatonic origin. The middle section is

strongly distinguished from the outer sections by its initial departure from this central

collection.

The Third Improvisation source song is in the non-pentatonic Hungarian

heptatonica secunda mode. The heptatonic is symmetrical around the axis of its

midpoint, between the fourth and fifth notes that divide the upper and lower tetrachords.

It is one of very few non-pentatonic songs that fall within Bartók’s “Class A” due to its

structural and rhythmic characteristics. The heptatonic mode appears more frequently in

Bartók’s “Class B” of newer Hungarian folk music.15

Figure 5: Hungarian Heptatonic Mode: Non-Pentatonic but Symmetrical

TTSTSTT

On the surface, the Fourth Improvisation source song does not appear to be of

pentatonic origin. There is a major third between the first and third scale degrees (B-

natural instead of B-flat). The raised seventh degree (F-sharp) in the first three sections

suggests G major. However, the seventh degree is flattened in the final section, hinting at

the tune’s pentatonic origin.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!15 Béla Bartók Essays, ed. Benjamin Suchoff (New York: St. Martin’s Press,

1976), 410.

!

!

"+!

Figure 6: The Fourth Improvisation Source: Modifications to the Pentatonic16

The source song for the Fourth Improvisation falls into “Class C”—pieces that

manifest non-Magyar influence. Ivan Waldbauer writes that raising the third and seventh

degrees is a common trans-Danubian modification of pentatonic folk songs, inspired by

foreign melodies in major keys.17 Bartók highlights the pentatonic origin of the fourth

source song in his setting by including the B-flat grace note alongside the B-natural in the

melody in mm. 7-10.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

16 Waldbauer, “Analytical Notes,” 428. 17 Waldbauer, “Analytical Notes,” 427.

!

!

""!

Figure 7: The Fourth Improvisation: Pentatonic Grace Note (B-flats) in mm. 7-10

The Fifth Improvisation source song returns to the pentatonic to transition back to

the completely pentatonic third section.

The sections of the piece are also distinguished by the presence of descending

melodies. Section 1 features no descending melodies. Section 2 features only descending

melodies. Section 3 draws together the first two sections with a non-descending seventh

melody sandwiched between two descending melodies.

The progression of tempi and rhythmic types through the piece further clarifies

the tri-sectional structure and reinforces the conclusive weight of the third section. Each

section moves from slower music to faster music. The first section opens with a slow

tempo giusto piece, the only slow tempo giusto piece of the set, followed by a fast dance

piece. In the second section, there is a slow parlando piece followed by two fast dance

pieces.18 The final section opens with a moderato parlando song couched in fast, episodic,

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!18 Interestingly, the parlando pieces feature dotted cadential patterns similar to the

repeated dotted rhythmic motif in the first piece.

!

!

"#!

pentatonic material (mm. 1-5 and 27-end). The seventh movement is a slow parlando

piece. The set comes to a close with a final, fast dance piece. Bartók thus creates a

coherent slow-fast temporal flow through each section. He weights the final section with

two slower pieces, both in his most cherished parlando style. The earlier sections each

feature only one slow movement.

1.4 The Fourth and Sixth Improvisations: The “Class C” Source Songs

The source melodies for the Fourth and Sixth Improvisations are the only

melodies that Bartók categorized in his “Class C” in Improvisations. Source Songs 4 and

6 are the only non-isometric songs in the collection. Song 4 is the only melody in the

piece with a 6-section rather than a 4-section structure. Songs 1, 2, 3, 5, 7 and 8 have six

or seven syllables. Song 4 has six and seven syllables. Song 6 is the only tune in the

collection with sections of a different syllable length. While the first two sections are

seven syllables, the second two sections have eleven syllables.

In his Béla Bartók: An Analysis of his Music, first published in English in 1971,

Hungarian theorist Ernö Lendvai proposed harmonic and formal analysis of Béla

Bartók’s works, particularly his later works, derived from the mathematical principle of

the golden section -- .618/1.19 Theorists in recent years have become dubious about the

importance of the golden section in Bartók’s work. However, it is interesting to note that

the Sixth Improvisation contains the golden section by bar count. The Fourth

Improvisation includes the reverse golden section (1-.618 = .382) by bar count.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"*!Ernö Lendvai, Béla Bartók: An Analysis of his Music (London: Kahn and

Averill, 1971).!

!

!

"$!

It is difficult to measure the duration of the work exactly as there is significant

room for fluctuation with the accelerandi, ritardandi and rubato markings. Bartók

himself took significant liberties with the tempi in his performances of Improvisations. In

the table below, the durations are taken from Bartók’s performances of the work, when

possible.20 According to these calculations, the Sixth Improvisation contains the golden

section by duration.

Table 3: Bar Count and Duration Ratios in Improvisations

# # of Bars Ratio of # of Bars in Movement/ # of Bars in Collection

Played Duration

of Movement (in min.)

Ratio of Played Duration of

Movement/ Duration of Complete Set

121 16 0-.043 1.25 min 0-.112 2 54 .043-.188 1 min. .112-.202 3 47 .188-.314 2.25 min .201-.403

422 40 .314-.422 .75 min 0.403-.47 5 68 .422-.604 1 min. .47-.56 6 32 .604-.69 1.33 min .56-679 7 33 .69-.78 1.75 min. .679-.83 8 82 .78-1 1.83 min. .83-1

The special status of the Sixth Improvisation is further bolstered by its position

within the progressions of modes and key centers through Improvisations discussed in

Part 2 of this study. The Fourth and Sixth Improvisations also share an accompanimental

figure unique to these two movements -- scalar figures that wedge out. These figures first

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!#+!Unfortunately, there is no extant recording by Bartók of the Third

Improvisation. Therefore this timing is taken from David Yeoman’s calculation based on tempi and performance markings in David Yeomans, Bartók for Piano (Bloomington, Indiana University Press, 1988), 97.

21 1, 2, 6, 7 and 8 from 1941 Hungaraton Recording. 22 4 and 5 from 1932 Hungaraton Recording.!

!

!

"%!

appear in mm. 1-11 of the Fourth Improvisation and return in mm. 13-14 of the Sixth

Improvisation.

Part 2. Modality, Symmetry and Centricity in the Melodies of Improvisations

Table 4: Table of Pitch Centers, Modes and Symmetry of the Melodies of Improvisations

Number Pitch

Center Mode23 Contains

Pentatonic Subset

Symmetrical Collection

Key Centers of Melody

through Movement

1 C Dorian Y Y C (3 times) 2 C Mixolydian/Dorian Y N-Y C-E-A-flat-C 3 D Heptatonic

major/minor N Y D-F-D

4 G Modified pentatonic=

G major

Y N G-modified version that moves from

F-flat to D-modified version that moves from

A to G 5 G Aeolian Y N (non-

symmetrical return to

same pitch collection as

1)

G (4 times)

6 E-flat Pentatonic Y N E-flat 7 C Aeolian/Phrygian Y N C-G-C 8 C Dorian/Aeolian

modification at end-

Dorian

Y Y B-D (modified)-

E/B-flat (modified) –C (modified)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!#$!Information on modes takes from Waldbauer, “Analytical Notes,” 427-8.!

!

!

"&!

An examination of the progressions of pitch centers and modes through the

melodies of Improvisations reinforces the tri-sectional structure that we have already

traced. There is both a large-scale arch structure (reflective of the progression of source

song types) and a small-scale arch structure through the first two sections (reflective of

the regional distribution of source materials).

The progression of pitch centers through the piece elucidates the large-scale arch

form. The piece begins with a C pitch center through section 1. In section 2, there is

movement from a D to a G pitch center reminiscent of a V/V – V progression. Bartók

distinguishes the Sixth Improvisation, the movement that contains the golden section by

both bar count and duration, with a detour to E-flat before returning to a governing C

pitch center from Seventh Improvisation through the end.

The Third Improvisation melody has a strong pull towards the G-pentatonic of the

Fourth and Fifth Improvisations melodies not only because its D pitch center is a fifth

above G, but also because of the implications of the internal pitch center movement

between different presentations of the source tune. In the Third Improvisation, Bartók

includes three transpositions of the source tune on D, F and D. The tetrachordal poles of

these transpositions are D-G-A-D and F-B-flat-C-F. The G-pentatonic is a subset of this

collection. In the Third Improvisation, Bartók thus creates a pentatonic structure around

the only non-pentatonic source song of the collection while effectively preparing the re-

transition to the pentatonic collections of the Fourth and Fifth Improvisations.

!

!

"'!

Figure 8: G-Pentatonic Suggestion in the Third Improvisation These tetrachordal poles spell the G-pentatonic collection (G-Bb-C-D-F) with one added

A (marked with x)

Improvisations begins and ends with Dorian tunes. Many of the modes that flesh

out the basic pentatonic skeleton are symmetrical. The Dorian is such a symmetrical

elaboration of the pentatonic, symmetrical around the axis of its midpoint between the

fourth and fifth notes.

Figure 9: Symmetry and Pentatonicism of the Dorian Mode (Non-Pentatonic Notes Marked with x)

TSTTTST

Bartók structures Improvisations around moving away from and then returning to

the symmetrical collections with pentatonic subsets although, in typical Bartókian

fashion, he complicates the final return to perfect symmetry in the end of the piece. In

section 1, Bartók starts in the symmetrical, pentatonic C-Dorian collection. In the

bimodal Second Improvisation melody, Bartók begins in the asymmetrical, non-

pentatonic Mixolydian collection before returning to the symmetrical Dorian.

!

!

"(!

Figure 10: Asymmetrical Mixolydian in Second Source

TTSTTST

E-flat in measure 6 moves the song into symmetrical C-Dorian TSTTTST.

Bartók opens the second section in the non-pentatonic though symmetrical

Hungarian heptatonic. (See Fig. 5.) As discussed in Part 1, the Fourth Improvisation

begins in a “modified” pentatonic. (See Fig. 6.) Bartók’s accompaniment suggests a shift

from the asymmetrical G-Ionian in the first two sections of the melody to asymmetrical

G-pentatonic in the final sections. (See Fig. 1.) In the Fifth Improvisation, Bartók sets a

piece in the pentatonic but asymmetrical G-Aeolian.

Figure 11: Pentatonicism and Asymmetry of G-Aeolian (Non-Pentatonic Notes Marked with x)

TSTTSTT

The Fifth Improvisation does not only represent a full return to the pentatonic. As

Elliott Antokoletz points out in The Music of Béla Bartók, G-Aeolian mode contains the

same pitch-classes as the C-Dorian of the First Improvisation. Thus, the Fifth

Improvisation marks an asymmetrical return to the collection of pitch-classes that opened

!

!

")!

the piece.24 (Compare Fig.s 9 and 11.) Bartók bolsters the connection between the First

and Fifth Improvisations in his settings. The First and Fifth Improvisations are the only

two pieces in the first two sections in which all of the statements of the folk source occur

at the same transposition level. These connections do suggest a complete, small-scale

arch form through the first two sections of the piece. However, the asymmetrical G mode

must be resolved to symmetrical C mode in the final section to satisfactorily resolve the

projected large-scale arch.

In the “golden” Sixth Improvisation at the beginning of the third section, Bartók

moves to the asymmetrical, pure E-flat pentatonic. (By choosing an E-flat transposition

of the mode, Bartók is able to create a completely black-key setting of the melody, which,

as we will see in Table 5, he juxtaposes with a white-key-centric accompaniment

throughout the movement.) In order to complete the arch form that he has set up, Bartók

must now take the piece back to symmetry and a C pitch center. In the Seventh

Improvisation, the return to the C tonic happens in the asymmetrical, though pentatonic-

based C-Aeolian and Phrygian modes of the bimodal Seventh Variation tune. The final

return to a symmetrical C collection awaits the final Improvisation.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!24Elliott Antokoletz, The Music of Béla Bartók (Berkeley: University of California Press,

1984), 59.

.

!

!

"*!

Figure 12: Asymmetrical Pentatonicism of C-Aeolian in the Bimodal Seventh Improvisation C-Aeolian of mm. 1-5

(Non-Pentatonic Notes Marked with x)

TSTTSTT

Figure 13: D-flat in m. 8 of the Seventh Improvisation Shifts Tune into Asymmetrical C-Phrygian and a New Pentatonic Transposition

(Non-Pentatonic Notes Marked with x)

STTTSTT

In the Eighth Improvisation, Bartók delays the return to the original C-Dorian and

complicates the return when it does occur. The final Improvisation is the only movement

that does not begin with a statement of the folk melody on the movement’s pitch center.

Instead, Bartók moves from a R.H. statement of the folk melody on B (mm. 5-13) to a

chromaticized and rhythmically altered version of the folk melody on D in the L.H. in

mm. 28-39. In measure 54, the R.H. re-states the theme on E. On the fourth eighth-note

beat, the L.H. enters with the theme on B-flat in stretto. However, there is a significant

alteration to the L.H. melody in measure 58 when scale degree six is flattened (G to G-

flat), re-orienting the tune into Aeolian. This alteration is repeated when the melody

finally returns to C-Dorian in measure 69.

!

!

#+!

Figure 14: Aeolian Alteration in Eighth Improvisation, mm. 69-74

This Aeolian inflection ties the Eighth Improvisation back to the crucial Fifth

Improvisation, which serves as a sort of asymmetrical apex within the collection. It seems

to jolt the piece back into asymmetry just at the moment when we expect a symmetrical

close. However, as will be discussed in Part 4.3, this alteration allows Bartók to draw

together symmetrical collections that he added to the folk sources throughout

Improvisations.

!

!

#"!

Part 3. The Harmonizations of the Folk Melodies in Improvisations

3.1 Relationship Between the Source Melodies and Harmonies: The Modal/Atonal Conflict

Bartók considered the source folk melodies in Improvisations and the materials

that he added to be “almost equal” in importance.25 As discussed in Part 2, the folk

melodies used in Improvisations are modal. The harmonies that Bartók employs in his

settings are highly chromatic and prominently feature subsets of the octatonic and whole-

tone collections, to be discussed in Part 4.

The conflict between the modality of the folk melodies and chromaticism of the

harmonies in Improvisations has led to considerable debate about how the work should

be analyzed. Victor Kofi Agawu discusses the debate in his article, “Analytical Issues

Raised By Bartók’s Improvisations, Opus 20,” which I will summarize below.26

Bartók himself advocated a tonal approach to his music. Following Bartók’s lead,

Hungarian theorists including Lendvai and Laszlo Somfai have suggested a tonal reading

of Improvisations, largely centered on the key center movement of the folk melodies

traced in Part 2.27

Other theorists have suggested a completely atonal approach to some works of

Béla Bartók utilizing the pitch-class set theoretical techniques developed by Allen Forte.

However, as Agawu points out, this sort of approach works better for some of Bartók’s

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!25 Suchoff, Bartók Essays, 351. 26 V. Kofi Agawu, “Analytical Issues Raised by Bartók’s Improvisations for

Piano, op 20,” Journal of Musicological Research 5 (1984): 133. 27 Agawu, “Analytical Issues,” 134.

!

!

##!

more abstract works like Fourths from Mikrokosmos, which is the subject of an atonal

Richard Parks study, than for Improvisations with its clearly modal melodic material.28

Following a line of scholarship traceable to Milton Babbitt’s pioneering article on

Bartók’s string quartets,29 other analysts, most notably Elliott Antokoletz, have put forth

readings that draw together tonal and atonal set-theoretic approaches. Like Babbitt and

Antokoletz, I believe that an analytical approach that incorporates both tonal and atonal

set-theoretical techniques is appropriate to the analysis of Improvisations. In the

discussion that follows, I will demonstrate that Bartók’s harmonizations sometimes

support the modes and key centers of the folk melodies and sometimes seem to directly

contradict the key centers and modality of the folk tunes. In the final Part, I will also trace

several important pitch set collections that are derived from structural characteristics of

the modal materials. Some of these pitch set collections recur throughout the work in

movements with melodies of different modal characteristics and become important

structural motives in the work as whole. I will use terminology derived from tonal and

atonal analytical methodologies to understand Bartók’s layered compositional practice in

Improvisations. Throughout, I will discuss how Bartók’s harmonizations and

contrapuntal approach support the tri-sectional arch form discussed in the previous Parts.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!28 Agawu, “Analytical Issues,” 133.!29 Milton Babbitt, “The String Quartets of Bartok,” The Musical Quarterly, Vol.

35, No. 3, (July 1949), pp. 377-385.

!

!

#$!

3.2 Strategies for Convergence and Divergence Between the Melodic Key Centers and Bartók’s Harmonizations:

A Close Reading of the First Improvisation

Bartók complicates the key scheme for the melodies outlined in Part 2 through his

harmonizations, beginning in the First Improvisation. In mm. 1-4 of the First

Improvisation, the simple dyad accompaniment challenges hearing the C as pitch center.

The presence of the B-flat in the R.H. dyad over the arrival at the final C in measure 4

suggests a dominant seventh chord on C, supported by the seeming resolution to an F-

major triad in measure 5.

Figure 15: Dyad as Dominant in the First Improvisation, mm. 1-5

In mm. 5-8, Bartók shifts to an F-major emphasis with strong F-major triads on

the first beat of mm. 5-7 and a final C dominant seventh chord, the fully fleshed out

version of the dyad from the end of the first phrase, in measure 8. However, his use of

non F-major triads associated with the octatonic on the weak beats of mm. 5-7 and the

!

!

#%!

first beat of measure 8 complicates a simple F-major interpretation. These octatonic

sonorities will be discussed in greater detail in Part 4 of this study.

Figure 16: F-major emphasis of the First Improvisation, mm. 5-8

In mm. 9-12, Bartók shifts to a D-minor emphasis with D-minor triads on the first

beats of measures 9-11. However, again he complicates a D-minor hearing by shifting to

harmonies that are not in D-minor on the weak beats and to a D-flat sonority for the final

measure of the strain, measure 12. As will be discussed in Part 4, these harmonies move

even further away from triadic harmonies and fill out the octatonic collection more

completely.

!

!

#&!

Figure 17: D-minor Emphasis in the First Improvisation, mm. 9-12

In mm. 13-16 of the First Improvisation, which function as a coda, Bartók brings

the piece to a rest on the final of the folk source melody, C. However, this final C has

been transformed into a highly unstable harmony as it hovers above the left hand

sonority, another D-flat with a further destabilizing G-flat tritone divide between the top

and bottom of the final melodic fragment.

Figure 18: Destabilizing D-flat and G-flat of the First Improvisation Coda, mm. 13-16

!

!

#'!

The minor second and its inversion, the major seventh, interval class 1, and the

tritone, interval class 6, become critical structural intervals as the pitch centers suggested

by the melodies and the pitch centers of the harmonizations converge and diverge

through the remainder of Improvisations, as summarized in Table 5 below.

Table 5: Points of Convergence and Divergence Between the Pitch Centers of the Peasant Source Melodies and Bartók’s Harmonizations

(Points of Convergence in Bold) # mm. Melody

Pitch Center

Harmonization Pitch Center

Contrapuntal Relationship

B/w Melody & Harmonization?

1 1-8 C F 9-12 C D 13-16 C moving to C 2 1-9 C-B# B/C-F# Pedal to Wedge-shaped Bass Motion 9-13 Episode F#-B 14-22 E D#-D Pedal to Wedge-shaped Bass Motion 22-29 Episode D-G/Ab 30-37 Ab Ab/G-D Pedal 37-41 Episode D Pedal 42-49 C C 49-54 Coda moving to C# Wedge-shaped Motion 3 1-18 D G Pedal 19-31 F E 32-39 D D Parallel Motion in Tritones 40-47 Coda C#/G Pedal 4 1-16 G G 17-31 Fb-G F-Eb/ A#-Db 32-40 Coda Gb/C 5 1-12 G G Pedal 13-20 G G Pedal 21-26 Episode G-Bb/B Wedge-shaped Contrary Motion

Expansion 27-34 G Ab Pedal 35-42 G F Pedal 43-47 Episode F-Db 48-58 G Db-F#-Db Pedal 58-68 Coda G/D-flat Canon at Tritone

!

!

#(!

# mm. Melody Pitch

Center

Harmonization Pitch Center

Contrapuntal Relationship

B/w Melody & Harmonization?

6 1-5 Introduction Wedge-shaped Contrary Motion B/w Black Keys in L.H. and White

Keys in R.H. 6-11 Eb Eb 11-19 Eb black vs. white key 20-26 Eb black vs. white key 27-32 Eb black vs. white key 7 1-11 C C 12-15 Episode D Contrary motion 16-21 G moving to Db Contrary Motion 22-28 Episode moving to C Contrary Motion 29-33 C D 8 1-12 B C-F# Pedal 13-27 Episode C 28-39 D moving 40-52 Episode F 53-65 E Bb Canon at Tritone 65-68 Episode F#-B 69-82 C moving to F#

3.3 Interval Class 1 as Structuring and Confounding Harmonic Force throughout Improvisations:

the First, Second and Eighth Improvisations

The final minor second, ic1, between the L.H. bass D-flat and R.H. final C in the

First Improvisation connects to the bold L.H. B/C pedal that begins the Second

Improvisation. Indeed, ic1 pedals initiate the first, second and third iterations of the

Second Improvisation melody. The first iteration of the melody from mm. 1-4 features a

L.H. B/C pedal. In mm. 14-18, the second iteration of the melody initiates from a D-

sharp/E conflict between the L.H. and R.H. In mm. 30-34, the L.H. features the inversion,

!

!

#)!

a major seventh pedal on A-flat/G. The final iteration, beginning in measure 42, is

doubled at the octave, bringing a measure of clarity to the final iteration. This clarity is

challenged by the final sonority, which features an ic1 conflict between the C-sharp of

the L.H. bass and B-sharp R.H. bass. This final C-sharp/B-sharp is a minor second (ic1)

higher than the initial B/C pedal of the Second Improvisation, effecting a large-scale

minor second move up through the course of the movement. This final C-sharp/B-sharp is

also the enharmonic equivalent of the final D-flat/C between the L.H. bass and R.H. final

of the First Improvisation, creating a coherent arc through the first section of

Improvisations.

The Second Improvisation’s initiating B/C pedal resonates throughout the Eighth

Improvisation. The B/C is composed out in the opening of the Eighth Improvisation,

which features a statement of the folk source tune with a B melodic center in the R.H.

juxtaposed with a C-based pedal harmony in the L.H. There is also a large-scale B-C

movement from the first to the last statements of the peasant tune. This B/C is also

contained in the final chord of the Eighth Improvisation L.H. Thus ic1 and specifically,

the B/C iteration of ic1 creates a long-term arc from the first section of the work through

the final Improvisation.

Fig. 19: B/C/ Subset in L.H. of the Final Eighth Improvisation Chord

!

!

#*!

3.4 Ic1 in the Third and Fifth Improvisations

Like the Second Improvisation, the second section of Improvisations is structured

around ic1 pedals. The Third Improvisation, the first piece of the second section, begins

with an [0156] pedal that prominently features both C-sharp/D and F-sharp/G dyads. This

pedal both sets up a long-range connection with the final movement of the second

section, the Fifth Improvisation, and creates an interesting tonal ambiguity.

The Third Improvisation [0156] pedal is structured so as to give a strong

suggestion of some sort of G pedal with linked fourths on C-sharp/F-sharp as implied

leading tones to D-G.

Figure 20: C-sharp/F-sharp to D/G in Third Improvisation, mm. 1-4

The predominance of this G pedal in the first strain of the peasant source melody

(mm. 1-10) and the move to harmonies unrelated to G or D in the second strain (mm. 11-

18) complicates hearing the final D (mm. 10-11) as the final of the mode, instead giving

the D an almost dominant feel to the strong G pedal opening. In the final presentation of

the peasant melody (mm. 32-39), this G/D ambiguity is again emphasized with the final

G pedal in mm. 36-38 giving the D a dominant pull. The second strain also notably

features an ic1 conflict between the F pitch center of the melodic material and E pitch

center of the harmonic material.

The Third Improvisation opening pedal recurs with the same pitch classes in the

final measures of the piece (mm. 40-end.) However, the different configurations of the

!

!

$+!

chord again destabilize the D final of the peasant source melody. In these final

recurrences of [0156], the two dyads are kept in the same partitioning with the C-sharp/F-

sharp in the L.H. (with C-sharp doubled for added emphasis with the exception of m. 46)

and D/G in the R.H. (with D and G doubled in different sections to change the emphasis.)

In the final iterations, the chords are rolled from the bottom up, which, as Ivan Waldbauer

points out, still give the C-sharp/F-sharp a sort of “leading tone” feel,30 although the

verticalization and doubled bass C-sharp again complicate hearing the upper D as the

final.

Figure 21: The Third Improvisation closing with verticalized pedal, mm. 40-end

In the opening measures of the Fifth Improvisation, the C-sharp/D pedal features

two of the four pitch classes from the Third Improvisation opening pedal tetrachord. In

measure 5, the first two notes of the melody combine with this dyad to form a tetrachord

with only one pitch class different from the Third Improvisation, an F instead of an F-

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$+!Waldbauer, “Analytical Notes,” 435.!

!

!

$"!

sharp. This tetrachord returns in the second iteration of the folk melody in measure 13

when a C is added to the opening C-sharp/D pedal. Eventually, an imitative wedge based

on the fourths inherent in both the Third and Fifth Improvisation pedal chord collections

unfolds into a stacked fifth iteration of [0156] in mm. 25-6.

Figure 22: Unfurling to [0156] in the Fifth Improvisation, mm. 22-6

[0156]

The F/G/C-sharp/D pedal returns as part of the formation of the final [012569]

harmony in the bass, creating an arc from the Third through the Fifth Improvisations. It is

also of note that the third iteration of the Fifth Improvisation melody features an A-flat

pitch center to the harmonic material, hearkening back to the Second Improvisation third

strain. This bolsters the connection between the final pieces of the first and second

sections.

!

!

$#!

Figure 23: The Fifth Improvisation final chord with bass [0156] subset Presenting as F/G/C-sharp/D

3.5 Structural Implications of the Tritone, ic6: Imitative Counterpoint and the Third, Fifth and Eighth Improvisations

The tritone, the melodic interval encompassed by the final melodic statement of

the coda of the First Improvisation, becomes associated with imitative contrapuntal

settings as the piece progresses. These contrapuntal episodes are sharply distinguished

from the rest of Improvisations in which the tunes are usually presented with very little

alteration. The tritone makes its first prominent melodic appearance in the first piece of

the second section. In the Third Improvisation, the final iteration of the folk tune features

a constant doubled tritone pedal.

!

!

$$!

Figure 24: Tritone Between R.H./L.H. in the Third Improvisation. mm. 32-37

This tritone doubling sets up the final strain of the second section, the Fifth

Improvisation, in which the closing figures of the folk source melody are repeated in a

canon at the minor sixth between the hands. The canon lines up such that the two hands

are always a tritone apart. This relationship persists when the canon shifts in the final

measures

Figure 25: Canon with tritone relationship at End of the Fifth Improvisation, mm. 57-68

!

!

$%!

This canon at the end of the second section strongly connects to the only other

canon in the piece in mm. 53-60 of the Eighth Improvisation The Eighth Improvisation

canon at the tritone ushers in the final tripled statement of the folk tune with altered

rhythmic emphasis. These canons at the end of the second and third sections give weight

to the end of the smaller scale arch through the first two sections and the larger arch

through the piece.

Figure 26: Canon at the tritone in the Eighth Improvisation, mm. 53-60

3.6 Structural Implications of the Tritone: Tritone Bass Descent in the Second and Eighth Improvisations

As can be seen in Table 5, tritone bass descent also plays an important role in the

harmonizations, most notably in the Second and Eighth Improvisations, further bolstering

the connection between the final pieces of the first and last sections already discussed in

!

!

$&!

section 3.3. In his analysis, Ivan Waldbauer elevates tritone bass descent to the level of

unifying structural principle throughout the work.31

The Second Improvisation includes two structural tritone descents, from the B/C

of measure 1 to the F-sharp pedal of mm. 9-19, and from the A-flat/G of mm. 30-34 to

the D pedal of mm. 37-41. The Eighth Improvisation features a smaller-scale tritone bass

descent from the C of the initiating bass pedal to the F-sharp bass pedal of mm. 12-17,

thus following the same B/C-F-sharp trajectory of the first tritone descent of the Second

Improvisation. The Eighth Improvisation also features a larger-scale tritone descent from

the opening C pedal to the final F-sharp chords.

Many analysts have discussed the prominence of the tritone in Bartók’s

oeuvre. In his axis system, Lendvai posits a tonic axis comprised of a diminished seventh

chord extending from the tonic pitch center. Lendvai suggests that any of the notes on the

“tonic axis” may function as a tonic. In his work, Hungarian theorist Janos Kárpáti

suggests that the tritone can often be heard as a “mistuned fifth.”32 This sort of

“mistuning” seems most plausible in examples like the final four measures of the First

Improvisation, where the final melodic tritone can be heard as a distortion of the fifth in

the other iterations of the folk tune. In Improvisations, the status of the tritone as a stable

or unstable interval is complicated. The “mistuning” of the final melodic statement in the

First Improvisation suggests a destabilizing role for the tonic to be resolved through the

rest of the work. The tritone bass movement of the Second and Eighth Improvisations

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$"!Waldbauer, “Analytical Notes,” 432. 32 Janos Kárpáti, Bartók’s Chamber Music (Stuyvesant: Pendragon Press, 1994),

194.!

!

!

$'!

further aligns the interval with a sort of “dominant” function. However, the prominence

of the tritone at the ends of the Third, Fifth and Eighth Improvisations do suggest some

sort of stable function for the interval.

Part 4: Prominent Pitch Class Sets in Improvisations

In 3.1, I discussed different analysts’ approaches to the tonal/atonal conflict in

Improvisations. I went on to explore how convergences and divergences between the

pitch centers of the peasant source tunes and added accompanimental materials

complicate the hearing of the C-D-G-E-flat-C key center movement of the melodies

traced in Part 2 and put forth by Lendvai as evidence of Bartók’s tonal compositional

planning for Improvisations. In Part 4, I will investigate pitch-class sets that recur

throughout the work such that they attain motivic importance in the collection.

In Improvisations, the accompanimental harmonies fluctuate between chords built

on stacked thirds and sonorities built from stacked fourths. These motivic intervals derive

from defining intervals in the modes. As discussed in Part 2, the modes are divided

tetrachordally and this tetrachordal division is reflected in many of the characteristic

melodic constructions, particularly the descending melody. The minor third is a defining

interval of the predominant pentatonic collection while major thirds define the heptatonic

collection used in the Third Improvisation.

Two collections feature prominently in the added materials – the octatonic and

whole-tone scales. As demonstrated in Fig. 27, both of these collections are built on

stacked thirds. The octatonic comprises two interlocking diminished seventh chords

while the whole-tone consists of overlaid augmented triads. In the analysis below, I will

!

!

$(!

show that octatonic subsets are prominently featured throughout Improvisations while

whole-tone subsets appear most notably in the unique, heptatonic Third Improvisation

and the Improvisations immediately preceding and following.

Figure 27: Octatonic and Whole-Tone Scales as Stacked Thirds

There are significant overlaps between diatonic, octatonic and whole-tone subsets,

which may have drawn Bartók, the atonal tonal composer, to these materials.33 János

Kárpáti posits a convincing connection between the Dorian and octatonic collections in

his analysis. Kárpáti suggests that the octatonic can be heard as a “mistuned” version of

the Dorian as the octatonic can be derived by lowering the upper tetrachord of the Dorian

a minor second and superimposing it on the Dorian lower tetrachord. Bartók initiates

presentation of the octatonic materials with the first Dorian melody, lending credence to

Karpáti’s suggestion. (Compare Figs. 9 and 27.)

4.1 Octatonic Subsets 1: The Major/Minor Tetrachord, [0347]

The first collection that I will trace superimposes a minor and major third --the

major/minor tetrachord, [0347], dubbed the “alpha chord” by Ernö Lendvai. This

harmony recurs in the First, Second, Third, Sixth, Seventh and Eighth Improvisations, but

is noticeably absent from the Fourth and Fifth Improvisations, which prominently feature !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

33 The overlap between these materials are well documented in Richard Cohn’s article cited in the Bibliography.

!

!

$)!

other octatonic subsets, most notably major arrival points at [01369] pentachords on D-

flat at measure 29 in the Fourth and measure 48 of the Fifth.

The major/minor tetrachord contributes to the harmonic ambiguity that Bartók

cultivates throughout the work. As Kárpáti discusses, the major/minor tetrachord also

evokes folk practice, which, according to Bartók’s own accounts, frequently featured the

simultaneous use of major and minor thirds.34

In mm. 5-7 of the First Improvisation, the second two dyads of each measure

combine to form [0347] tetrachords. The strong beats of measure 8 also combine to form

[0347].

Figure 28: [0347] tetrachords in the First Improvisation, mm. 5-8

The tonally ambiguous progression of major and minor triads precipitated by

these [0347] combinations through the course of the second strain of the First

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$%!Kárpáti, Bartók’s Chamber Music, 173.!

!

!

$*!

Improvisation catapult the work from the simple pentatonic world of the first strain

towards the more fully octatonic third strain. Elliott Antokoletz shows how partial and

complete octatonic collections unfold in the second and third strains of the First

Improvisation in his book, The Music of Béla Bártok.

Figure 29: Octatonicism in the the First Improvisation, mm. 9-1035

Figure 30: Octatonic Interpenetration of C-Dorian in the First Improvisation, mm. 5-836

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

35 Figure 29 taken from Antokoletz, The Music of Béla Bartók, 221. 36 Figure 30 taken from Antokoletz, The Music of Béla Bartók, 221.

!

!

%+!

In the predominantly octatonic Second Improvisation, the final episode features a

repeated [01347] sonority followed by a conclusive [01347] sonority in measure 49 to

accompany the final measure of the peasant tune in the R.H. melody.

Figure 31: [01347] in the Second Improvisation, mm. 37-53

In the heavily whole-tone Third Improvisation to be discussed in 4.2, the final

R.H. chord combines with the major third dyad articulated in measure 23 to form an

[0347] sonority. This [0347] tetrachord is repeated in mm. 24-5 with an [013457] trill

figure in mm. 29-30 before the final iteration of the peasant melody.

!

!

%"!

Figure 32: [0347] Tetrachords in the Third Improvisation, mm. 23-30

[0347] makes a brief appearance in the Sixth Improvisation in a passage based on

interlocking thirds reminiscent of the second strain of the First Improvisation in mm. 15-

18. The final three appearances feature [0347] as subset of [01469.]

!

!

%#!

Figure 33: [0347] in the Sixth Improvisation, mm. 15-18

The [0347] tetrachord is a central harmony throughout the Seventh Improvisation,

the piece in the collection most heavily dominated by thirds, which is appropriately

dedicated to Claude Debussy. [0347] presenting as C/E-flat/A-flat/B first appears in the

accompaniment for mm. 2-3. F-sharp/A/D/F-natural, another configuration of [0347],

first appears at the end of the first strain in measures 9-11. This configuration of [0347]

serves as the focal point of a chain of interlocking thirds moving in contrary motion in

mm. 12-15.

!

!

%$!

Figure 34: [0347] as Central Harmony in the Seventh Improvisation, mm. 12-16

In measure 15, the D of this configuration slides down to D-flat before returning

to D-natural in measure 16. The F-sharp/A/D/F-natural configuration of [0347] returns in

the final three measures of the movement.

In the Eighth Improvisation, after the initiating [0137] pedal point, a series of

[0347] sonorities dominates the texture from mm. 8-18 with a final [0347] in the second

chord of measure 21.

!

!

%%!

Figure 35: [0347] harmonies in mm. 8-18 of the Eighth Improvisation

[0347] sonorities return in mm. 43-44 (cf. beat 6 of measure 43) before a final

confirmation of the centrality of the [0347] in the penultimate [0134567] sonority that

combines the [0347] and [0167] z-cells. The centrality of the z-cell will be discussed

more in 4.3.

!

!

%&!

Figure 36: [0134567] sonority in penultimate measure of the Eighth Improvisation

[0134567]

4.2 The Role of Whole-Tone Collections and Augmented Triads

The first suggestion of the augmented triad comes in the pitch center movement in

the Second Improvisation. As discussed in 3.3, the opening B/C dyad is transposed to D-

sharp/E for the second iteration (mm. 14-8) and G/A-flat for the third iteration (mm. 30-

3) before the final return to the C source tune (mm. 42ff). The augmented triad reflected

in the progression through the pedals and folk source tune keys foreshadows the

augmented triads that will pervade the Third Improvisation, the first of the two central

folk tunes that feature a major third in the lower tetrachord of their modes, distinguishing

them from all of the other folk source tunes used in the collection. Thus, as Elliott

Antokoletz writes in The Music of Béla Bartók, the whole-tone/augmented emphasis in

the Third Improvisation effectively highlights the major third characteristic of the folk

tune mode.37

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!37 Antokoletz, The Music of Béla Bartók, 60.

!

!

%'!

The analysis below summarizes Antokoletz’s description of whole-tone

collections in the Third Improvisation.38 In measure 20, the two right hand dyads

combine to form a whole-tone tetrachord, [0246.] In measure 21, the two dyads combine

to form an augmented triad, [048.] In measure 21, the first two R.H. chords again

combine to form a whole-tone tetrachord.39

Figure 37: Whole-Tone and Augmented Harmonies in the Third Improvisation, mm. 19-22

In measure 26 of the Third Improvisation, there is a return to the whole-tone

tetrachord of measures 20 and 22 before a whole-tone pentachord sounds in the final beat

of the measure. The augmented triad at the bass of the R.H. in measure 26 is linked to

another augmented triad built on a shared A-sharp in measure 27. In measure 28, the first

of a series of augmented triads is sounded in the L.H. Above and below these augmented

triads in mm. 28-30, chromatic material in the R.H. and an F pedal in the bass of the

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!38 Antokoletz, The Music of Béla Bartók, 60-1. 39 Antokoletz, The Music of Béla Bartók, 60-62.

!

!

%(!

L.H., which forms a minor 2nd with the R.H. soprano E, re-transition the Third

Improvisation away from a whole-tone/augmented emphasis.

Figure 38: Whole-Tone and Augmented Harmonies

in the Third Improvisation, mm. 26-30

[0246] [02468] [048]

[048}

In the opening of the Fourth Improvisation, the scalar accompaniment in the R.H.

features a chromatic scale divided into two whole-tone trichords. This nod to the whole-

tone collection that dominated the Third Improvisation supports the major third in the

Fourth Improvisation mode before the re-transition to octatonic harmonies, beginning

with the initiating [0358] in measure 16.

Figure 39: Whole-Tone Implications of Accompanying Scale in the Fourth Improvisation, mm. 1-4

[024] [024]

!

!

%)!

4.3 Octatonic Subsets 2: The Z- cell, [0167] The second predominant octatonic subset that appears throughout Improvisations

is the z-cell, [0167]. Unlike the collections traced above, the z-cell features no thirds but

it does contain fourths, critical to the tetrachordal construction of the modes, and a

tritone. Because of its intervallic content, [0167] might also be heard as a “detuned”

version of the [0156] and [0146] initiating pedals of the Third and Fifth Improvisations

discussed in 3.4, which fall more clearly within the modal material of those movements.

Elliott Antokoletz has traced the octatonic z-cell in the accompaniments to all but

two of the Improvisations. The absence of z-cells in the Fifth Improvisation supports its

special position within the piece as asymmetrical apex. The z-cell is also absent from the

“golden” Sixth Improvisation.

The discussion below summarizes Elliott Antokoletz’s most siginificant z-cell

discussion in his book, The Music of Béla Bartók. As he writes, the Aeolian modification

to the final statement of the Eighth Improvisation tune discussed in Part 2 suggests a

background symmetrical z-cell comprised of the one tritone in C-Dorian (E-flat/A) and

the one tritone in C-Aeolian (D/A-flat).40 (Compare Fig. 9 and Fig. 12) With this implied

z-cell and the z-cells that dominate the accompaniment from measure 69 through the final

chord of Improvisations, Bartók is able to connect both the added and folk source

materials of the First and Eighth Improvisations.

The final chord of the Eighth Improvisation juxtaposes two z-cells. When aligned,

these two z-chords produce four sets of whole-tone dyads.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!40 Antokoletz, The Music of Béla Bartók, 103-9.

!

!

%*!

Figure 40: Whole-tone Dyads in Aligned Z-cells41

The top dyads, E-flat/F and B-flat/C, serve as the sole accompaniment to the

melody in the First Improvisation first strain, emphasizing the whole-tone dyads at the

top of the two C-Dorian tetrachords (mm. 1-4). The ornaments of the second strain are

initiated by a reconfiguration of these dyads with the F/C and E-flat/B-flat L.H. figures in

measure 5. The z-cell Eighth Improvisation ending thus elegantly connects to the First

Improvisation accompaniment. In the final measures of the Eighth Improvisation

accompaniment, Bartók also seems to restore the Dorian mode, completing a large-scale

modal arch form. From measure 75 on, the z-cell chords feature A-naturals but no A-

flats.

In the Eighth Improvisation, Bartók carefully combines z-cell chords to create full

octatonic collections.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

41 Figure taken from Elliott Antokoletz, “Pitch-Set Derivations from the Folk Modes in Bartók’s Music,” Studia Musicologica Academiae Scientarium Hungaricae 24 (1982), 266.

!

!

&+!

Figure 41: Octatonic Z-Cell Pairs in the Eighth Improvisation Finale42

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!42 Figure taken from Antokoletz, The Music of Béla Bartók, 214.

!

!

&"!

In the First Improvisation, Antokoletz shows how a complete octatonic statement

unfolds from the gradual development of the whole-tone dyads in measure nine. (cf. Fig.s

29 and 30.) Bartók similarly combines z-cells to form octatonic collections in the Second

Improvisation (c.f. the octatonic episodes in mm. 10-13, 25-30 and 37-42) and the

Seventh Improvisation (c.f. octatonic cadential points in mm. 2-3, 5-6 and 10-11 and the

second statement of the folk subject in mm. 16-21).43

Conclusion

In Improvisations, Bartók creates a fitting tribute to the former Kingdom of

Hungary that successfully foregrounds many of the attributes that connected ancient

Magyar songs from across the Kingdom, while also drawing special attention to certain

songs with unusual characteristics and non-Magyar influence. His ordering of pitch

centers of the melodic presentations and use of symmetrical/asymmetrical melodic modes

effectively create a large-scale arch form from the First Improvisation to the Eighth and a

small-scale arch from symmetry to asymmetry in Improvisations 1-5.

Bartók’s modernist harmonizations converge with and diverge from the pitch

centers of the melodies. His accompaniments effectively support the trajectories through

the three sections discussed above. Some of Bartók’s harmonies, derived from key

intervals in the modes and melodies, come to take on motivic importance throughout the

work, particularly two octatonic subsets – Lendvai’s alpha chord and z-cell, the [0347]

and [0167] tetrachords. The whole-tone collection plays a pivotal role in the Second and

Third Improvisations. While the pieces may not have been written in the order in which

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!43 Antokoletz, The Music of Béla Bártok, 222-8.

!

!

&#!

they appear, these large-scale principles of organization and connections demonstrate that

Bartók carefully considered the ordering of the set.

The title of Improvisations may be a reference to the folk instrumental practice of

improvising on a well known, sung folk tune. In Improvisations, Bartók acts as folk

instrumentalist, bringing his unique brand of composed contribution to the eight folk

source tunes with extreme re-harmonizations and contrapuntal constructions that

showcase his pianism.

!

!

&$!

Bibliography

Score Bartók, Béla. Improvisations, op. 20. Vienna: Universal Edition, 1922.

Books Antokoletz, Elliott. The Music of Béla Bartók. Berkeley: University of California

Press, 1984. !Lampert, Vera. Folk music in Bartók's compositions : a source catalog : Arab, Hungarian, !

Romanian, Ruthenian, Serbian, and Slovak melodies. Budapest: Hungarian Heritage House, 2008.!

Lendvai, Erno. Béla Bartók: An Analysis of his Music. London: Kahn and Averill, 1971.

Karpati, Janos. Bartók’s Chamber Music. Stuyvesant: Pendragon Press, 1994.

Suchoff, Benjamin. Bartók: Concerto for Orchestra. London: Schirmer, 1995.

Suchoff, Benjamin. Béla Bartók: Essays. London: Faber and Faber, 1976.

Suchoff, Benjamin. Béla Bartók Studies in Ethnomusicology. Lincoln: University of Nebraska Press, 1997.

Yeomans, David. Bartók for Piano. Bloomington: Indiana University Press, 1988.

Articles Agawu, Victor Kofi. “Analytical Issues Raised by Bartók’s Improvisations for piano,

op 20,” Journal of Musicological Research 1984, 131-163. Antokoletz, Elliott. “Pitch-Set Derivations of the Folk Modes in Bartók’s Music,”

Studia Musicologia Academiae Scientarium Hungaricae 1982, 262-74. Atar, Ron. “Form Created By Performance: Bartók’s Recording of his

Improvisations, op. 20,” Studia Musicologica 48/1-2, 2007, 103-11. Babbitt, Milton. “The String Quartets of Bartók,” The Musical Quarterly, Vol. 35,

No.3 (July, 1949), 377-385.

!

!

&%!

Cohn, Richard. “Bartók’s Octatonic Strategies: A Motivic Approach,” Journal of the American Musicological Society 44 (1991), 262-300.

Hyde, Martha M. “Neoclassic and Anachronistic Impulses in Twentieth-Century

Music,” Music Theory Spectrum, Vol. 18, No. 2 (Autumn, 1996), 200-235. Lampert, Vera. “Bartók’s Choice of Theme for Folksong Arrangement: Some

Lessons of the Folk-Music Sources of Bartók’s works.” Studia Musicologica Academiae Scientiarum Hungaricae 1981, 401-9.

McCandless, William Edgar. "Cantus Firmus Techniques in Selected Instrumental

Compositions, 1910-1960." Ph.D. diss. Music Theory: Indiana University, 1974. Russ, Michael. “Atonality, Modality, Symmetry and Tonal Hierarchy in Bartók’s

Improvisation, op. 20, no. 8.” Irish Musical Studies 1, 1990, 278-94.

Waldbauer, Ivan. “Analytical Notes to Bartók’s Improvisations, Op. 20 and the Ordering of the Series.” Essays in Honor of Laszlo Somfai on His 70th Birthday. Laszlo Vikarius and Vera Lampert, eds. Lanham: The Scarecrow Press, Inc., 2005, 425-443.

Wilson, Paul. “Concepts of Prolongation and Bartók’s Opus 20.” Music Theory

Spectrum Spring 1984, 79-89.

Recordings Hungaraton LPX 12333-B. Bartók at the Piano, Vol. I, 1981. Side 16, Band 2, 1941. Hungaraton LPX 12334-B. Bartók Plays and Talks, Vol. II, 1981. Side 1, Band 10,

1932.

!

!

&&!

Appendix 1: Bartók’s Catalogue of Improvisations Folk Source Songs44

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!44 Reprinted from Universal Edition 7079.

!

!

&'!

Appendix 2: Map of the Kingdom of Hungary before the Treaty of Trianon45 !

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!45 Reprinted from www.http://en.wikipedia.org/wiki/Kingdom_of_Hungary.